Answers
We know that the total mechanical energy on a spring mass system is given by:
\(\frac{1}{2}mv^2+\frac{1}{2}kx^2\)We also know that the mechanical energy is conserved, this means that the energy oscillates between the kinetic energy of the block and the potential energy stored in the spring.
We also know that the maximum velocity happens when the potential energy is zero; this happens when the spring is not compress. With this in mind we notice that the maximum potential energy and the maximum kinetic energy is the same.
Assume that the maximum potential energy happens when x=A. In this case we know that the spring is stretch an amount A, then the potential energy is:
\(\frac{1}{2}(100)A^2\)Now, when the kinetic energy is maximum it has to have the same value then:
\(\frac{1}{2}mv^2=\frac{1}{2}100A^2\)Solving for the velocity we have that:
\(\begin{gathered} v^2=\frac{1}{m}100A^2 \\ v=\sqrt[]{\frac{1}{m}100A^2} \\ v=\frac{10A}{\sqrt[]{m}} \end{gathered}\)For the mass of 800 gr we have that the maximum velocity will be:
\(v=\frac{10A}{\sqrt[]{.8}}\)while for the mass of 200 gr the maximum velocity will be:
\(v^{\prime}=\frac{10A}{\sqrt[]{.2}}\)(we use a prime here to so we can distinguish between the two blocks).
To compare this velocities we make the quotient:
\(\begin{gathered} \frac{v}{v^{\prime}}=\frac{\frac{10A}{\sqrt[]{.8}}}{\frac{10A}{\sqrt[]{.2}}} \\ \frac{v}{v^{\prime}}=\frac{\sqrt[]{.2}}{\sqrt[]{.8}} \\ \frac{v}{v^{\prime}}=\sqrt[]{\frac{.2}{.8}} \\ \frac{v}{v^{\prime}}=\sqrt[]{\frac{1}{4}} \\ \frac{v}{v^{\prime}}=\frac{1}{2} \end{gathered}\)This means that:
\(v=\frac{1}{2}v^{\prime}\)Therefore the maximum speed of the 800 gr mass is half the maximum velocity of the 200 gr mass.
Related Questions
Where is the near point of an eye for which a spectacle lens of power +2 D is prescribed for reading purpose?
Answers
The near point of a human eye is about a distance of 25 cm.
The closest distance that an object may be viewed clearly without straining is known as the near point of the eye.
This distance (the shortest at which a distinct image may be seen) is 25 cm for a typical human eye.
The closest point within the accommodation range of the eye at which an object may be positioned while still forming a focused picture on the retina is also referred to as the near point.
In order to focus on an item at the average near point distance, a person with hyperopia must have a near point that is further away than the typical near point for someone of their age.
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explain the methods to determine specific charge of an electron ?
Answers
The methods to determine the specific charge of an electron are The J. J. Thomson Method and The Millikan Oil Drop Method.
The J. J. Thomson Method
In this method, an electric field is created between two parallel metal plates. Electrons are accelerated by this field from the negative plate to the positive plate. After that, they strike a fluorescent screen. When the electrons are shot through the electric field perpendicular to the magnetic field, they experience the Lorentz force, which is given by the formula: $F= evB$ $F= evB$
When a magnetic field is applied at right angles to an electron beam, it bends the path of the beam into a circular path. The radius of the path of an electron beam in a magnetic field is determined by the relationship:r = mv/eB. As a result, the specific charge of an electron may be calculated from the expression: $e/m = 2V / B^2r^2$
The Millikan Oil Drop Method
This is another technique for determining the specific charge of an electron. The oil drop experiment was first done by Robert A. Millikan in 1909. He did this experiment by suspending charged droplets of oil in a uniform electric field between two parallel plates.
The fall of the oil droplets in the absence of an electric field was also noted. The fall velocity of the oil droplet was determined by measuring the time taken by the oil droplet to pass through a fixed distance between the plates in the absence of an electric field. By measuring the electric field strength, the voltage applied to the plates, and the fall velocity of the oil droplet, the specific charge of the electron was determined.
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The methods to determine the specific charge of an electron are :
The J. J. Thomson Method The Millikan Oil Drop Method.How do we describe?In the J. J. Thomson Method, an electric field is created between two parallel metal plates. Electrons are accelerated by this field from the negative plate to the positive plate. After that, they strike a fluorescent screen.
When the electrons are shot through the electric field perpendicular to the magnetic field, they experience the Lorentz force.
The Millikan Oil Drop Method is an experiment by which is created by suspending charged droplets of oil in a uniform electric field between two parallel plates.
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Scott drives a jeep 12 km east, then 4 km north, then finally 3 km west. He traveled a total distance of:
Answers
Answer:
Using the pythagoras theorem
S²=9²+4²
S²=81+16
S²=97
S=9.85km.
In finding the direction
tan□=opposite/Adjacent
=4/9
□=23.96
¤=90-23.96
=66.03 degrees
9.85, N 66.03 E
Someone has been shot! We found a blood drop that was measured to be 0.8 mm wide and 2.1 mm long. The drop landed 5.1 feet away. How high up was the person shot?
Answers
To determine the height from which a person was shot based on the distance traveled by a blood drop, we can use projectile motion calculations considering the vertical component and apply the equations for the time of flight and vertical distance traveled.
To determine how high up the person was shot, we can use the properties of a projectile motion and the dimensions of the blood drop.
First, convert the distance from feet to meters, as it is a more commonly used unit in physics calculations. 5.1 feet is approximately 1.55 meters.
The blood drop is assumed to follow a parabolic trajectory, where its horizontal and vertical motion are independent. We can focus on the vertical component to determine the height.
The horizontal distance traveled by the blood drop is not relevant to calculating the height.
The vertical distance traveled by the blood drop can be calculated using the equation:
d = ut + (1/2)gt^2
Where:
d is the vertical distance traveled (height),
u is the initial vertical velocity (0 since the drop starts at rest),
t is the time of flight,
g is the acceleration due to gravity (approximately 9.8 m/s^2).
Rearranging the equation, we have:
t = sqrt((2d)/g)
The time of flight can be found using the measured distance, as the horizontal and vertical motion take place simultaneously:
t = distance / horizontal velocity
The horizontal velocity is the horizontal distance divided by the time of flight, which is 1.55 meters divided by the time of flight.
Substitute the time of flight from step 5 into the equation from step 6 and solve for the horizontal velocity.
Now, we know the horizontal velocity, and we can calculate the time it takes for the blood drop to travel from the person to the landing point, which is the horizontal distance divided by the horizontal velocity.
Finally, we can use the time of flight obtained in step 8 and substitute it back into the equation from step 5 to calculate the height.
Please note that this calculation assumes ideal projectile motion without considering factors like air resistance or other variables that may affect the trajectory. Additionally, the size of a single blood drop may not accurately reflect the height from which a person was shot. It is important to consult medical professionals and forensic experts for accurate analysis and interpretation of crime scene evidence.
Therefore, We can use projectile motion calculations with the vertical component and apply the equations for time of flight and vertical distance travelled to determine the height from which a person was shot based on the distance travelled by a blood drop.
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Suppose an automobile has a kinetic energy
of 2300 J.
When it moves with nine times the speed,
what will be its kinetic energy?
Answer in units of J.
Answers
Answer:
\(KE_{new}=186300 J\)
Explanation:
Given:
\(KE=2300J\) \(n=9\)
\(v_{new}=n*v_{old}\)
\(\frac{KE_{new}}{KE_{old}}=\frac{v^2_{new}}{v^2_{old}}=\frac{(n*v_{old})^2}{v^2_{old}}=n^2\)
\(KE_{new}=n^2KE_{old}\)
\(KE_{new}=(9)^2(2300)\)
\(KE_{new}=186300 J\)
Scientific notation
\(KE_{new}= 1.863*10^5 J\)
Hope it helps
1. Calculate the electric field due to a single +1nC point charge at a distance of lm, 2m, and 3m
Answers
Answer:
Approximately \(9.0\; \rm N \cdot C^{-1}\) at \(1\; \rm m\) from this charge, pointing away from the point charge.Approximately \(2.2\; \rm N \cdot C^{-1}\) at \(\rm 2\; \rm m\) from this charge, pointing away from the point charge.Approximately \(1.0\; \rm N \cdot C^{-1}\) at \(3\; \rm m\) from this charge, pointing away from the point charge.Assumption: there is no object between this point charge and the observer.
Explanation:
The electric field of a point charge is inversely proportional to the square of the distance from that point charge.
Let \(k\) denote Coulomb's constant (\(k \approx 8.98755 \times 10^{-9}\; \rm N \cdot m^{2} \cdot C^{-1}\).) Let the magnitude of that point charge be \(q\). At a distance of \(r\) from this charge, the electric field due to this charge would be:
\(\displaystyle E = \frac{k \cdot q}{r^{2}}\).
Convert the magnitude of the point charge in this question to standard units:
\(q = 1\; \rm nC = 10^{-9}\; \rm C\).
Apply that equation to find the magnitude of the electric field due to this point charge:
\(r = 1\; \rm m\):
\(\begin{aligned} E &= \frac{k \cdot q}{r^{2}} \\ &= \frac{8.98755 \times 10^{-9}\; \rm N \cdot m^{2} \cdot C^{-2} \times 10^{-9}\; \rm C}{(1\; \rm m)^{2}} \\ &\approx 9.0\; \rm N \cdot C^{-1}\end{aligned}\).
\(r = 2\; \rm m\):
\(\begin{aligned} E &= \frac{k \cdot q}{r^{2}} \\ &= \frac{8.98755 \times 10^{-9}\; \rm N \cdot m^{2} \cdot C^{-2} \times 10^{-9}\; \rm C}{(2\; \rm m)^{2}} \\ &\approx 2.2\; \rm N \cdot C^{-1}\end{aligned}\).
\(r = 3\; \rm m\):
\(\begin{aligned} E &= \frac{k \cdot q}{r^{2}} \\ &= \frac{8.98755 \times 10^{-9}\; \rm N \cdot m^{2} \cdot C^{-2} \times 10^{-9}\; \rm C}{(3\; \rm m)^{2}} \\ &\approx 1.0\; \rm N \cdot C^{-1}\end{aligned}\).
The direction of the electric field at a point is the same as the direction of a force from this field onto a positive point charge at this point.
Because the \((+1\; \rm nC)\) point charge here is positive, the electric field of this charge would repel other positive point charges. Hence, the electric field around this \((+1\; \rm nC)\!\) point charge at any point in the field would point away from this charge.
A car is driven for 60 miles. The first 10 miles are through a large city at a speed of 40 mph; once out of the city a speed of V mph is maintained. (a) Calculate the average speed for the 60-mile trip. (b) If you want to average 60 mph for the trip, how fast need you go during the last 50 miles?
Answers
He should go with the speed of 66.67mph during last 50 miles.
What is speed?
Speed is the rate of change of distance with respect to time. It is the scalar quantity that is measured in meters per second (m/s). Speed measures how quickly an object is moving in a particular direction. Speed is an important concept to understand in science, engineering, and mathematics. It is used to calculate the time taken for an object to travel a certain distance, or to calculate the distance an object will travel in a certain amount of time. Speed can also be used to measure the motion of an object in a gravitational field, such as on Earth.
Given: -
Total distance covered d = 60 miles
Speed for first 10 miles V1 = 40mph
Speed for next 50 miles = V
a. Average Speed = Total distance / Total Time
For 10 miles time t1 = 10/40 = 0.25 hrs
For 50 miles time t2 = 50/V hrs
Average Speed Vo= 60 / t1 + t2 = 60 / {0.25 + (50/V)}
Average Speed Vo= 60 V / (0.25V + 50)
b. For Vo= 60 mph
60 = 60 V / (0.25V + 50)
0.25V + 50 = V
V = 50/0.75
V = 66.67 mph
So, he should go with the speed of 66.67mph during last 50 miles.
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A 2 kg object and a 1 kg object are dropped from the same height.
Given that the inertia
masses of these objects are not the same, what hypothesis explains
why the two objects
fall with the same acceleration?
Select one:
O a. The force of gravity is the same for the 1 kg object as for the 2 kg object
O b. The force of friction is the same for the 1 kg object as for the 2 kg object.
O c. The force of gravity on the 1 kg object is twice as great as on the 2 kg object.
Od. The force of friction on the 2 kg object is twice as great as on the 1 kg object.
Answers
The first choice (A) will be accurate.
Objects weighing 1 kg and 2 kg are dropped from the same height.
Because the force of gravity is the same for both the 1 kg and the 2 kg objects, the two objects fall with the same acceleration.
What is gravity?Gravity pulls you toward the ground because all objects with mass, such as our Earth, actually bend and curve the fabric of the universe, known as spacetime. Gravity is the curvature of the earth. Gravity, also known as gravitation, is a force that exists between all physical objects in the universe. The force of gravity tends to attract any two objects or particles with nonzero mass toward each other. Gravity affects objects of all sizes, from subatomic particles to galaxy clusters. Gravity is the force that pulls objects toward the center of a planet or other entity. Gravity keeps all of the planets in orbit around the sun.To learn more about gravity, refer
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Question 1 of 10
Which quantity is expressed in units of watts (W)?
O A. Potential difference
O B. Current
O C. Power
O D. Equivalent resistance
SUBMIT
Answer is C
Answers
Answer:
C. Power
Explanation:
Watts and horsepower are units of power. Resistance is usually in ohms or kilo ohms.
Check all the answers that apply. Energy is the ability to
A. Change temperature
B. Change speed
C. Do work
D. Change direction
Answers
Answer:
D. Do work
Explanation:
Answer:
c: do work and b: change speed
Explanation:
An Alaskan rescue plane drops a package of emergency rations to a stranded party of explorers. The plane is travelling horizontally at 30.0 m/s at a height of 200.0 m above the ground. What horizontal distance does the package fall before landing?
Question Blank 1 of 1
type your answer...
meters
Answers
Answer:
the answer is 191.7
Explanation:
i dont know the math for it
two wharves A and B are directly opposite each other on a 40m wide river which flows in the direction shown. a boat leaves A and heads at constant speed at right angles to the flow of the river. it lands at point C, with the trip taking 20 seconds.
find;
a) the displacement from C to A
b) the speed of the boat as seen by people standing at A.
c) the speed of the water in the river
d) the speed of the boat as seen by a fish drifting with the river.
e) Draw a vector diagram and u
se it to find the direction the boat should head ( at the same constant speed as before) if it is to travel directly from A to B.
Answers
Answer:
a)40 meters
b)2 m/s
c)2 m/s
d)0 m/s
e)45 degrees northeast
Explanation:
a) The displacement from C to A is the distance directly across the river, which is 40 meters.
b) The speed of the boat as seen by people standing at A is the magnitude of the boat's velocity vector, which is equal to the displacement divided by the time taken:
Speed = displacement / time = 40 m / 20 s = 2 m/s.
c) Let v be the speed of the water in the river. The boat is moving at right angles to the flow of the river, so the water exerts a perpendicular force on the boat. The time taken for the boat to travel from A to C is 20 seconds, during which time the boat will have been carried downstream by the river by a distance equal to v times the time taken.
Distance carried downstream = v × time = v × 20 m.
Since the boat landed at C, which is directly across the river from A, the distance it traveled horizontally is 40 meters. Therefore:
40 m = (boat speed) × (time taken) = (boat speed) × 20 s.
Hence, the speed of the boat is:
Boat speed = 40 m / 20 s = 2 m/s.
So, we have two equations:
Distance carried downstream = v × 20 m
Boat speed = 2 m/s
From the first equation, we get:
v × 20 m = 40 m
Therefore, the speed of the water in the river is:
v = 40 m / 20 m = 2 m/s.
d) The speed of the boat as seen by a fish drifting with the river is the difference between the speed of the boat and the speed of the water in the river:
Boat speed - Water speed = 2 m/s - 2 m/s = 0 m/s.
So, the speed of the boat as seen by a fish drifting with the river is zero.
e) The boat should head in a direction that makes its velocity vector point directly from A to B. Since A and B are directly opposite each other, this means the velocity vector should be perpendicular to the line connecting A and B.
We know the boat's velocity vector has a magnitude of 2 m/s and is at right angles to the velocity vector of the water in the river, which has a magnitude of 2 m/s. So, we can draw a vector diagram with the velocity vector of the boat pointing straight up and the velocity vector of the water pointing straight to the right. The vector connecting the tail of the water velocity vector to the head of the boat velocity vector will then point directly from A to B.
The angle between the boat's velocity vector and the line connecting A and B can be found using trigonometry. Let θ be this angle. Then:
tan(θ) = (boat speed) / (water speed) = 2 m/s / 2 m/s = 1.
Taking the inverse tangent of both sides gives:
θ = tan^(-1)(1) = 45°.
So, the boat should head in a direction 45 degrees to the right of straight up, or northeast.
How far has a 15 kg object moved, when a force of 22 N is applied for 5 seconds if it started at 3 m/s?
Answers
TRUE OR FALSE When four-wheel drive is selected in a vehicle equipped with a four-wheel drive transfer case, the mode fork, which is similar to a shift fork found in a manual transmission, moves a synchronizer sleeve to the input shaft chain sprocket.
True
False
Answers
This statement is True because A synchronizer sleeve is moved to the input shaft chain sprocket by the mode fork, which resembles a shift fork in a manual transmission, once four-wheel drive .
Is manual transmission a stick shift?When a vehicle has a manual transmission, the driver controls the clutch and selects the appropriate gear. Most drivers believe a manual transmission, or stick gear as it is commonly known, gives them a greater sense of involvement with the car's operation and makes driving more enjoyable.
Why would you use a manual transmission?A manual gearbox is essentially a gear train that allows the driver to select from a variety of gear ratios to operate the vehicle. Higher gear ratios provide less torque but more speed, while lower gear ratios provide more torque but less speed.
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In an attempt to reduce the extraordinarily long travel times for voyaging to distant stars, some people have suggested traveling at close to the speed of light. Suppose you wish to visit the red giant star Betelgeuse, which is 430 lyly away, and that you want your 20,000 kgkg rocket to move so fast that you age only 36 years during the round trip.
A. How fast (v) must the rocket travel relative to earth?
B. How much energy is needed to accelerate the rocket to this speed?
C. How many times larger is this energy than the total energy used by the United States in the year 2000, which was roughly 1.0 x 10^20 J?
Answers
Answer:
a) \(v=0.999124c\)
b) \(E=7.566*10^{22}\)
c) \(E_a=760 times\ larger\)
Explanation:
From the question we are told that
Distance to Betelgeuse \(d_b=430ly\)
Mass of Rocket \(M_r=20000\)
Total Time in years traveled \(T_d=36years\)
Total energy used by the United States in the year 2000 \(E_{2000}=1.0*10^20\)
Generally the equation of speed of rocket v mathematically given by
\(v=\frac{2d}{\triangle t}\)
\(v=860ly/ \triangle t\)
where
\(\triangle t=\frac{\triangle t'}{(\sqrt{1-860/ \triangle t)^2}}\)
\(\triangle t=\frac{36}{(\sqrt{1-860/ \triangle t)^2}}\)
\(\triangle t=\sqrt{(860)^2+(36)^2}\)
\(\triangle t=860.7532\)
Therefore
\(v=\frac{860ly}{ 860.7532}\)
\(v=0.999124c\)
b)
Generally the equation of the energy E required to attain prior speed mathematically given by
\(E=\frac{1}{\sqrt{1-(v/c)^2} }-1(20000kg)(3*10^8m/s)^2\)
\(E=7.566*10^{22}\)
c)Generally the equation of the energy \(E_a\) required to accelerate the rocket mathematically given by
\(E_a=\frac{E}{E_{2000}}\)
\(E_a=\frac{7.566*10^{22}}{1.0*10^{20}}\)
\(E_a=760 times\ larger\)
A sound wave travels with a velocity of 1.5 m/s and has a frequency of 500 Hz. What is its wavelength?
Answers
Wave velocity (v) is how fast a wave propagates in a given medium. Its unit is meter per second. Check the speed calculator for more information about speed and velocity.
Wavelength (λ) is the distance over which the shape of a wave repeats. It depends on the medium in which a wave travels. It is measured in meters.
Frequency (f) of a wave refers to how many times (per a given time duration) the particles of a medium vibrate when the wave passes through it. The unit of frequency is Hertz or 1/second.
A boy throws an arrow at an original speed of 2m / s to create an angle 0 referring to the balloon at a distance of 3m from the departure point. Calculate the angle 0 and the height of the arrow. Let g = 10m / s2.
Answers
Calculate the horizontal component of the velocity. The horizontal component of the velocity is given by:
v_x = v * cos(theta)
where v is the original speed of the arrow and theta is the angle of projection.In this case, v = 2 m/s and theta is unknown. Solving for theta, we get:
theta = arccos(v_x / v)
theta = arccos(2 / 2) = 45 degrees
Calculate the vertical component of the velocity. The vertical component of the velocity is given by:
v_y = v * sin(theta)
In this case, v = 2 m/s and theta = 45 degrees. Solving for v_y, we get:
v_y = 2 * sin(45 degrees) = 1.414 m/s
Calculate the time of flight. The time of flight is given by:
t = 2 * v_y / g
In this case, v_y = 1.414 m/s and g = 10 m/s^2. Solving for t, we get:
t = 2 * 1.414 / 10 = 0.283 seconds
Calculate the height of the arrow. The height of the arrow is given by:
y = v_y * t - 0.5 * g * t^2
In this case, v_y = 1.414 m/s, t = 0.283 seconds, and g = 10 m/s^2. Solving for y, we get:
y = 1.414 * 0.283 - 0.5 * 10 * 0.283^2 = 0.303 meters
Therefore, the angle of projection is 45 degrees and the height of the arrow is 0.303 meters.
A woman of mass 55 kg stands on the rim of a frictionless merry-go-round of radius 2.0m and rotational inertia 1250 kg-m2 that is not moving. She throws a rock of mass 350g horizontally in a direction that is tangent to the outer edge of the merry-go-round. The speed of the rock, relative to the ground, is 2.0m/s. Afterward, what are (a) the angular speed of the merry-go-round and (b) the linear speed of the woman
Answers
Answer:
a) \(\omega=9.10*10^{-4}rad/sec\)
b) \(V=1.8217*10^{-3}\)
Explanation:
From the question we are told that:
Mass of woman \(M_w=55kg\)
Radius of merry go round \(r=2.0m\)
Rotational inertia \(i= 1250 kg-m2\)
Mass of rock \(M_r=350g \approx 0.350kg\)
Speed of rock \(V_r=2.0m/s\)
Tangent angle to the outer edge \(\theta=1\)
a)
Generally the equation for conservation of momentum is mathematically given by
\(M_r(ucos\theta)r=(I+M_wr^2)\omega\)
\(0.350(2.0cos1)(2.0)=(1250+(55)(2.0)^2)\omega\)
\(1.3998=1470\omega\\\omega=\frac{1.339}{1470}\)
\(\omega=9.10*10^{-4}rad/sec\)
b)
Generally the equation for linear speed V is mathematically given by
\(V=r\omega\\V=2.0*9.10*10^{-4}\)
\(V=1.8217*10^{-3}\)
Question 5 of 10
Which of the following is most likely to happen when energy is transferred to
an object?
O A. The force on the object will decrease.
O B. The object will begin to move.
O C. The object will stay exactly the same.
O D. The mass of the object will increase.
Answers
Answer:
B: The object will start moving
Explanation:
If energy is transferred the object will definitely change so it can't be a. If you add energy the object will have more force so it cant be c. The mass of an object can't increase just by giving an object energy so it cant be d
Help!!!!
A car has an oil drip. As the car moves, it drips oil at a regular rate, leaving a trail of spots on the road. Which diagram shows the spots
of car that is continuously slowing down?
Answers
The period of a pendulum is the time it takes the pendulum to swing back and forth once. If the only dimensional quantities that the period depends on are the acceleration of gravity, g, and the length of the pendulum, l, what combination of g and l must the period be proportional to
Answers
Explanation:
Let T is the period of a pendulum. The SI unit of time is seconds (s).
It depends on the acceleration of gravity, g, and the length of the pendulum, l.
The SI unit of acceleration of gravity, g and the length of the pendulum, l are m/s² and m respectively.
If we divide m and m/s², we left with s². If the square root of s² is taken, we get s only i.e. the SI unit of period of a pendulum.
So,
\(T\propto \sqrt{\dfrac{l}{g}}\)
Hence, this is the required solution.
What is the intensity level of a sound that is loud enough to rupture a human eardrum at 160 dB?
Answers
Answer:
A sudden very loud noise can cause an eardrum to tear or rupture. The noise intensity to rupture an eardrum would have to be very loud, usually 165 decibels or more.
Explanation:
1. Determine the potential energy of a 2kg rock at the top of a hill that is 20m high.
2. Determine the kinetic energy of a 2000 kg roller coaster car that is moving with a speed of 25 m/s.
3. A 80kg freezer is located in an office on the 59 floor of an office building 200 meters above the ground. What is the potential energy of the freezer?
Answers
Answer:
1) 392 joules
2) 625,000 joules
3) 156,800 joules
Explanation:
Gravitational potential energy = mgh. m = mass in kg, g = acceleration due to gravity and h = height in meters.
Kinetic energy = 1/2(m)(v)^2, m = mass in kg, v = velocity in meters per second
1) P.E = 2 x 9.8 x 20 = 392 joules
2) K.E = 1/2 x 2000 x (25)^2 = 625,000 joules
3) P.E = 80 x 9.8 x 200 = 156,800 joules
Answer:
\(1)\:392\:\text{J}\:(400\:\text{J with one significant figure)},\\2)\:625,000\:\text{J}\:(600,000\:\text{J with one significant figure)},\\3)\:156,800\:\text{J}\:(200,000\:\text{J with one significant figure)},\)
Explanation:
1. The potential energy of an object is given by \(PE=mgh\). Substituting given values, we have:
\(PE=2\cdot 9.8\cdot 20=\boxed{392\:\text{J}}\)
2. The kinetic energy of an object is given by \(KE=\frac{1}{2}mv^2\). Substituting given values, we have:
\(KE=\frac{1}{2}\cdot 2000\cdot 25^2 =\boxed{625,000\: \text{J}}\)
3. 1. The potential energy of an object is given by \(PE=mgh\). Substituting given values, we have:
\(PE=80\cdot 9.8\cdot 200=\boxed{156,800\:\text{J}}\)
The amount of energy needed to a power a 0.20kw bulb for one minute would be just sufficient to lift a 2.5 kg object through a vertical distance of
Answers
The amount of energy needed to power a 0.20 kW bulb for one minute would be just sufficient to lift a 2.5 kg object through a vertical distance of approximately 29.03 meters.
To calculate the energy required to lift a 2.5 kg object through a vertical distance, we need to consider the gravitational potential energy formula:
Potential energy (PE) = mass (m) × gravity (g) × height (h)
Where:
m = 2.5 kg (mass of the object)
g = 9.8 m/s² (acceleration due to gravity on Earth)
h = ? (height)
First, let's find the height (h) by rearranging the formula:
h = PE / (m × g)
Now, let's calculate the potential energy (PE) needed to lift the object. We are given that the power of the bulb is 0.20 kW, and we want to find the energy required for one minute. To convert kilowatts (kW) to joules (J), we multiply by the conversion factor of 3,600 (60 seconds × 60 minutes):
Energy (E) = power (P) × time (t)
E = 0.20 kW × 1 min × 3,600 J/kW
Now, we can substitute the values into the equation to find the height:
h = (0.20 kW × 1 min × 3,600 J/kW) / (2.5 kg × 9.8 m/s²)
Calculating the expression on the right side:
h ≈ 0.20 × 1 × 3,600 / (2.5 × 9.8) ≈ 29.03 meters (rounded to two decimal places)
Therefore, the amount of energy needed to power a 0.20 kW bulb for one minute would be just sufficient to lift a 2.5 kg object through a vertical distance of approximately 29.03 meters.
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One of the fastest roller coasters (2000 kg) in the world is the Magnum XL - 200 at
Cedar Point Park in Sandusky, Ohio. This ride includes an initial vertical drop of 59.3 m.
Assume that the roller coaster has a speed of nearly zero as it crests the top of the hill.
a. If the track was frictionless, find the speed of the roller coaster at the bottom of
the hill.
Answers
The speed of the roller coaster at the bottom of the hill is 33.9 m/s.
The conservation of mechanical energy is used to determine the speed of the roller coaster at the bottom of the hill, as there is no friction. According to the law of conservation of energy, mechanical energy is constant at all points in a frictionless environment.Let's look at the equation below:PEg + KE = PEg + KEwhere PEg is gravitational potential energy and KE is kinetic energyThe kinetic energy is maximum and the gravitational potential energy is zero when the roller coaster is at the bottom of the hill. The gravitational potential energy is highest when the roller coaster is at the top of the hill, with its potential energy equal to its kinetic energy when it reaches the bottom of the hill.Initially, the roller coaster is at rest at the top of the hill. The gravitational potential energy of the roller coaster is transformed into kinetic energy as it descends the hill. We can calculate the speed of the roller coaster using the law of conservation of energy.Solution:Given,Height of the hill, h = 59.3 mGravitational acceleration, g = 9.8 m/s²Mass of roller coaster, m = 2000 kgWe need to find the speed of the roller coaster at the bottom of the hill, v.To begin, calculate the potential energy at the top of the hill.Potential energy at the top of the hill = mgh Where m is the mass of the roller coaster, g is the acceleration due to gravity, and h is the height of the hill.
The potential energy at the top of the hill is given by:PEg = mgh= 2000 kg × 9.8 m/s² × 59.3 m= 1.15 × 10⁶ JNow, let's figure out the velocity at the bottom of the hill.Using the conservation of energy, we can write,PEg = KE + KEwhere PEg is gravitational potential energy and KE is kinetic energyThe gravitational potential energy is equal to the kinetic energy.KE = PEg= 1.15 × 10⁶ JKE = 1/2 × mv²Where m is the mass of the roller coaster and v is the velocity of the roller coaster.Substituting the given values in the above equation, we get;1.15 × 10⁶ = 1/2 × 2000 × v²v² = (2 × 1.15 × 10⁶) / 2000v² = 1150v = √1150v = 33.9 m/s.
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There are n moles of an ideal gas contained in a sealed chamber at pressure P. The volume of the
container is then reduced to one half of its initial value. In this particular process, the temperature
of the gas and n do not change. Which one of the following statements concerning the final
pressure in the container is true?
a) The final pressure will be 2P.
b) The final pressure will be 0.5P.
c) The final pressure will be 4P.
d) The final pressure will be 0.25P.
e) The pressure cannot be determined without knowing the values of n, P, T, and the initial
volume.
Answers
The final pressure in the container will be 2P. The correct answer is a)
According to Boyle's Law, at a constant temperature, the product of pressure and volume of a gas is constant. Therefore, if the volume is reduced to half, the pressure must double to maintain the constant product of pressure and volume.
Mathematically, we can represent this as P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume. Since the volume is reduced to half (V2 = V1/2), the final pressure (P2) must be twice the initial pressure (P1).
Therefore, the final pressure is 2P. The answer is (a).
Note that the value of n (number of moles) and T (temperature) are not relevant to the solution, as the problem statement specifies that they remain constant during the process.
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8. How quickly does a 100kg object accelerate when pushed with a 400N force?
Answers
Answer:4m/s2
Explanation:
It is because if we take the equation of force
F=ma so
a=F/m
Put the values
a=400/100
a=4
Unit of the accelaration is m/s2. So
a=4m/s2
The answer is 4 m/s²
The mass is 100 kg
The force is 400N
The acceleration can be calculated as follows
a= force/mass
= 400/100
= 4 m/s²
Hence the object will move quickly at 4 m/s²
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Does anyone understand this?
A cannon is recovered from a shipwreck. Why does the buoyant force on the cannon stay the same as long as it is fully under water? Explain your reasoning. (3 points)
Answers
The buoyant force on the cannon stays the same as long as it is fully under water because the buoyant force is determined by the volume of fluid that the cannon displaces and not by the weight or mass of the cannon itself.
Archimedes' Principle states that the buoyant force on an object in a fluid is equal to the weight of the fluid that the object displaces. This means that as long as the cannon remains fully submerged in the water and does not change its volume, the amount of water it displaces and thus the buoyant force on the cannon will also remain the same.
In other words, the buoyant force is dependent on the fluid's density and the volume of the object, not its weight. So, as long as the volume of the cannon and the density of the fluid surrounding it remain constant, the buoyant force will also stay constant.
The buoyant force on the cannon will stay the same as long as it is fully under water.
The buoyant force on an object is equal to the weight of the fluid displaced by the object. The buoyant force is always directed upwards, and it opposes the force of gravity. As long as the cannon is fully under water, the amount of water displaced by the cannon will stay the same. This means that the buoyant force on the cannon will also stay the same.
The buoyant force on an object depends on the density of the fluid, the volume of the object, and the acceleration due to gravity. The density of water is constant, so the buoyant force on the cannon will only change if the volume of the cannon changes or if the acceleration due to gravity changes.
Neither of these factors change. The volume of the cannon does not change as it is being recovered from the shipwreck. The acceleration due to gravity also does not change, as it is the same on Earth's surface as it is underwater.
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An object, initially at rest, is subject to an acceleration of 45 m/s^2. How long will it take that object to travel 1000m? Round to one decimal place.
Answers
Answer:
6.7 seconds
Explanation:
d=(1/2)at^2
equation
1000=(1/2)45t^2.
substitute
2000=45t^2.
multiply by 2 for both sides
44.44=t^2.
divide both sides by 45
6.7=t
take the square root of both sides
You did 550 J of work lifting a 220 N backpack. How high did you lift the backpack?
Answers
Answer:
0.255 meters
Explanation:
cause formula to calculate work done against gravity is mgh where m refers mass g refers acceleration due to gravity and h refers height