The cart's a) linear velocity at the bottom of the hill is 5.53 m/s, b) final linear kinetic energy is 76.66 J, c) linear momentum at the bottom of the hill is 27.67 kg·m/s, d) The angular velocity of a wheel is 55.28 rad/s, e) The cart's Gravitational Potential Energy is 24.53 J.
a) Using the conservation of energy, we can find the cart's velocity at the bottom of the hill. The potential energy at the top of the hill is equal to the kinetic energy at the bottom of the hill, so: mgh = (1/2)mv²
where m is the mass of the cart, g is the acceleration due to gravity, h is the height of the hill, and v is the velocity of the cart at the bottom of the hill. Plugging in the given values, we get: (5.00 kg)(9.81 m/s²)(1.25 m) = (1/2)(5.00 kg)(v²) v = 5.53 m/s
b) The cart's final linear kinetic energy can be found using the formula: K = (1/2)mv²
where m is the mass of the cart and v is its velocity at the bottom of the hill. Plugging in the given values, we get: K = (1/2)(5.00 kg)(5.53 m/s)² = 76.66 J
c) The cart's linear momentum can be found using the formula: p = mv
where m is the mass of the cart and v is its velocity at the bottom of the hill. Plugging in the given values, we get: p = (5.00 kg)(5.53 m/s) = 27.67 kg·m/s
d) The angular velocity of a wheel at the bottom of the hill can be found using the formula: v = ωr
where v is the linear velocity of the cart at the bottom of the hill, ω is the angular velocity of a wheel, and r is the radius of the wheel. Solving for ω, we get: ω = v/r = 5.53 m/s / 0.10 m = 55.28 rad/s
e) The cart's gravitational potential energy when it is halfway down the hill can be found using the formula: U = mgh
where m is the mass of the cart, g is the acceleration due to gravity, and h is the height of the hill. Since the cart is halfway down the hill, h is 0.625 m. Plugging in the given values, we get: U = (5.00 kg)(9.81 m/s²)(0.625 m) = 24.53 J
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A sprinter starting from rest on a straight, level track is able to achieve a speed of 12 m/s in 6.0 s. What is the sprinter's average acceleration? Answer in m/s^2 (meters per second squared)
Given that a sprinter starting from rest on a straight, level track is able to achieve a speed of 12 m/s in 6.0 s. We are supposed to find the sprinter's average acceleration in m/s^2 (meters per second squared).
Average acceleration is defined as the rate at which an object changes its velocity. It is equal to the change in velocity divided by the time taken. Average acceleration = Change in velocity ÷ Time taken
Here, the change in velocity is equal to the final velocity minus the initial velocity. The initial velocity is zero because the sprinter started from rest.
Final velocity, v = 12 m/s
Time taken, t = 6.0 s
Change in velocity = Final velocity - Initial velocity
= v - u = 12 - 0 = 12 m/s
Average acceleration = Change in velocity ÷ Time taken
= 12 ÷ 6= 2 m/s^2
Therefore, the sprinter's average acceleration is 2 m/s^2 (meters per second squared).
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Stan argues that momentum cannot be conserved when a collision is not a head-on collision. Rachel insists it is conserved because each body receives an impulse of equal magnitude. Rachel is correct because?.
Rachel is correct because during the collision, each body exerts an equal and opposite force on the other, the forces act at equal time intervals, and the law of momentum and vector equation represents conservation for an isolated system.
What exactly is the law of momentum?The law of momentum conservation states that within an isolated system in which two or more bodies act on each other (collision of objects), the total momentum remains constant because momentum is neither created nor destroyed, but only changed by the application of external forces as described by Newton's laws of motion. Furthermore, the law states that the force acts on both objects at the same time and that the forces between the objects are equal.
That is stated by the law of momentum conservation. The total momentum of two or more bodies acting on each other in an isolated system remains constant unless an external force is applied.
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the teacher said to the students you can go home change the folowing sentence into indirect
Explanation:
The teacher said to the students you can go home.
Into indirect speech
The teacher told the students that they could go home.
Hope it will help :)❤
the project control process is captured in the critical success factor of:
The project control process is captured in the critical success factor of "Monitoring and Control." Monitoring and control are essential components of project management and play a vital role in ensuring project success.
Monitoring involves regularly tracking and reviewing project activities, progress, and performance against the established plans and objectives. It involves gathering data, measuring key metrics, and assessing the project's status. Monitoring allows project managers to identify any deviations or variances from the plan and take appropriate actions to address them.
Control refers to the process of taking corrective actions based on the information gathered during monitoring. It involves analyzing the data, evaluating the project's performance, and making adjustments as necessary. Control activities may include revising schedules, reallocating resources, managing risks, and making decisions to keep the project on track.
The critical success factor of "Monitoring and Control" ensures that projects are actively managed, potential issues are identified early, and necessary adjustments are made to ensure project objectives are met within the defined constraints.
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Which of the following is NOT a characteristic of vibrations?
(a) Time period
(b) Amplitude
(c) Density
(d) Frequency
Answer:
answer is (c) density is not a characteristics of vibration.
hope it is right answer for it!!
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.What are some observations we can make to determine if something has energy?
Answer:
if somthing is warm or if somthing moves it usally has energy
Identify the medium for the following waves:
ripples
The sound waves from a radio speakers
Seismic waves
Answer:
The sound waves from a radio speakers
Explanation:
What will be the length of the gold wire?
What will be the length of the copper wire?
What will be the length of the aluminum wire?
Gold has a density of 1.93×1041.93×104 kg/m3kg/m3. What will be
th
1. The length of the gold wire would be 0.064 meters.
2. The length of the copper wire would be approximately 0.460 meters.
3. The length of the aluminum wire would be 0.574 meters.
What will be the lengths of the wires required?To calculate the length of each wire, we can use the formula for resistance:
R = (ρ * L) / Awhere
R is the resistance, ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.
For each wire:
Gold wire:
Resistance (R) = 5.00 Ω
Diameter (d) = 2.00 mm = 0.002 m
Radius (r) = d/2 = 0.001 m
Area (A) = π * r² = π * (0.001 m)²
Area = 3.14 x 10⁻⁶ m²
Resistivity (ρ) for gold = 2.44 x 10⁻⁸ Ω·m
Using the resistance formula, we can solve for the length (L):
L = (R * A) / ρ
L = (5.00 Ω * 3.14 x 10⁻⁶ m²) / (2.44 x 10⁻⁸ Ω·m)
L ≈ 0.064 m
Copper wire:
The resistance and diameter of the copper wire are the same as the gold wire.
Resistivity (ρ) for copper = 1.72 x 10⁻⁸ Ω·m (at room temperature)
Using the same resistance formula:
L = (R * A) / ρ
L = (5.00 Ω * 3.14 x 10⁻⁶ m²) / (1.72 x 10⁻⁸ Ω·m)
L ≈ 0.460 m
Aluminum wire:
The resistance and diameter of the aluminum wire are the same as the gold and copper wires.
Resistivity (ρ) for aluminum = 2.75 x 10⁻⁸ Ω·m (at room temperature)
Using the same resistance formula:
L = (R * A) / ρ
L = (5.00 Ω * 3.14 x 10⁻⁶ m²) / (2.75 x 10⁻⁸ Ω·m)
L ≈ 0.574 m
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Complete question:
You want to produce three 2.00-mm-diameter cylindrical wires, each with a resistance of 5.00 at room temperature. One wire is gold and one is aluminum (pa =2.75 108 - m). What will be the length of the gold wire? What will be the length of the copper wire? What will be the length of the aluminum wire? Gold has a density of 1.93×1041.93×104 kg/m3kg/m3.
A small rock is thrown vertically upward with a speed of 18.0 m/s from the edge of the roof of a 28.0 m tall building. The rock doesn't hit the building on its way back down and lands in the street below. Air resistance can be neglected. What is the speed of the rock just before it hits the street? Express your answer with the appropriate units. Part B How much time elapses from when the rock is thrown until it hits the stree Express your answer with the appropriate units.
3.5 s is the time elapses from when the rock is thrown until it hits the street when thrown vertically upward.
Every area of our lives is impacted by the concept of time. It determines the duration of an event and the tempo of our daily activities. Time begins to move forward as soon as we open our eyes in the morning, reminding us of the obligations we have to fulfil and the dates we have to meet. We use time to organise our lives, prepare our calendars, communicate with others, and plan events. Time is an elusive and philosophical term that defies simple explanations despite the many ways it forms and affects our life. It passes in the blink of an eye while also appearing to go on forever. It is both finite and endless.
\(mgh = \frac{1}{2}mv^2 + mgh_{\text{roof}}\)
v =\(\sqrt{2gh}\)
= \(\sqrt{2(9.81\ \text{m/s}^2)(28\ \text{m})} \approx \boxed{18.8\ \text{m/s}}\)
h =\(\frac{1}{2}gt^2\)
t =\(\sqrt{\frac{2h}{g}}\)
=\(\sqrt{\frac{2(28\ \text{m})}{9.81\ \text{m/s}^2}} \approx \boxed{3.5\ \text{s}}\)
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A penny is made of the element zinc plated with the element copper; a nickel is made of a mixture of the elements nickel and copper. Some isotopes of various elements are listed below by their atomic number and mass number. Use the periodic table on p. 131 to identify which atoms you would expect to find in the penny, which you would expect to find in the nickel, which you would expect to find in both, and which you would expect to find in neither coin.
Answer: We need the referenced table to discern which isotopes are likely to be found. But there is still an interesting piece of information.
Explanation:
An interesting story behind the US penny. It has been around since 1787 and consisted of primarily a copper, or copper-plated coin. In 1982 the design was changed, due to the high price of copper. A zinc core was copper plated to have the same appearance, but less expensive composition. If one of these pennies is slightly filed to expose the zinc, it can be placed in a strong acid that will react with and dissolve the zinc core. Fun, but a waste of money.
Answer:
in the penny Cooper(Cu),un the nickel nickel(Ni),in both Cooper(Cu)
Explanation:
A car drives 16 miles south and then 12 miles west. What is the magnitude of the car’s displacement?
Answer:20 miles
Explanation:
PLS HELP U WILL GET 21 POINTS PLS
Which statements describe a physical property of matter? Check all that apply.
A cumulus cloud is puffy and white.
Vinegar has a very sour smell.
A mixture of baking soda and vinegar produces gas.
Iron rusts when it is exposed to water.
Water boils at 100 degrees Celsius.
Answer:
A cumulus cloud is puffy and white. Vinegar has a very sour smell. Water boils at 100 degrees CelsiusExplanation:
Physical properties are used to perceive and express matter and they can be preserved or regulated without varying the configuration of matter ( which involves shape, texture, color, odor, melting point, boiling point, density, solubility, polarity, e.t.c.).
It takes 35 J to push a large box 5 m across a floor.
Assuming the push is in the same direction as the
move, what is the magnitude of the force on the
box?
a. 5N b. 7N c. 35 N d. 175 N e. none of
the above
Answer:
7 N
Explanation:
Work = Force * distance
35J = Force * 5 meters Divide by 5
35/5 = Force
7 Newtons = Force
What does the following measurement mean? Wrist flexion: 15 – 85
degrees.
No limitation
A limitation in extension
A limitation in flexion
Limitation in both flexion and extension
The following measurement means "no limitation". This measurement indicates the range of motion for wrist flexion, which is the movement of the wrist towards the palm of the hand.
What is wrist flexion?
Wrist flexion is the movement of the wrist towards the palm of the hand. It is the opposite movement of wrist extension, which is the movement of the wrist away from the palm of the hand. Wrist flexion is an important motion for many daily activities such as typing, writing, and holding objects.
What does 15-85 degrees of wrist flexion mean?
When measuring wrist flexion, the range of motion is measured in degrees. In this case, the measurement is 15-85 degrees. This means that the normal range of motion for wrist flexion is between 15 and 85 degrees. If the measurement falls within this range, then there is no limitation in wrist flexion. However, if the measurement falls outside of this range, then there may be a limitation in wrist flexion.A limitation in extension refers to a decreased range of motion when moving the wrist away from the palm of the hand. A limitation in flexion refers to a decreased range of motion when moving the wrist towards the palm of the hand. A limitation in both flexion and extension refers to a decreased range of motion in both movements.
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how much heat transfer is necessary to raise the temperature
The amount of heat transfer required to raise the temperature of a substance depends on its specific heat capacity (often denoted as "C") and its mass.
The formula to calculate the heat transfer (Q) is given by Q = m * C * ΔT, where "m" represents the mass of the substance and ΔT is the change in temperature.
The specific heat capacity is a measure of how much heat energy is required to raise the temperature of a given mass of a substance by one degree Celsius or Kelvin. Different substances have different specific heat capacities, which means they require varying amounts of heat transfer to achieve the same temperature change.
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The electric field from a sheet of charge is perpendicular to the sheet and has a constant magnitude of Q/(Aeo), where A is the area of the sheet and Q is the charge on the sheet. If the sheet has an area, A=32.93 cm2, and a charge of 20.93 microC, what force, in nanoNewtons, would an electron experience due to this electric field?
The exercise tells us that the electric field is given by the following equation:
\(\vec{E}=\frac{Q}{A\epsilon_0}\)And it also gives us, A and Q. Thus, our electric field inside the capacitor is:
\(E=\frac{20.93*10^{-6}}{(32.93*10^{-4})*(8.85*10^{-12})}=718181521.8\frac{V}{m}\)As we know, the electric force can be written as:
\(F=q.E\)The charge of an electron is a constant, which is q=1.6*10^(-19) C.
Finally, our force can be written as:
\(F=1.6*10^{-19}*718181521.8=1.149*10^{-19}=0.00001149microN\)Our final answer is 0.00001149 micro Newtons
What is an atomic theory?
A.because science
B.the theory of space
C.how we think an atom is structured
D.the one person who discovered an atom
Answer: the theory that all matter is made up of tiny indivisible particles (atoms). According to the modern version, the atoms of each element are effectively identical, but differ from those of other elements, and unite to form compounds in fixed proportions.
Answer:
C.)
Explanation:
The theory that all matter is made up of tiny indivisible particles (atoms). According to the modern version, the atoms of each element are effectively identical, but differ from those of other elements, and unite to form compounds in fixed proportions.
plz help me guys thank you
A force of 150 N is exerted 22◦north of east. Therefore, the northward component is 139 N north.
Given :
A force of 150 N is exerted 22◦ north of east.
To Find :
The northward component of force .
Solution :
The angle between the force and east direction is 22° .
So , component of Force F in north direction is given by :
\(Fsin\ \theta\\\\150\times sin\ 22^o\\\\56.19\ N\)
Therefore , the component of force in northward direction is 56.19 N .
Hence , this is the required solution .
what would happen to the size of the shadow if the distance between the light and the hand is increased.
what is the link between the observation that the universe is expanding and the big bang theory? choose one: a. all objects in the universe are moving away from earth, which means the big bang began with our solar system. b. the big bang theory refers to nuclear fission, where particles explode into more particles constantly and sporadically. these particles are emitted outward, expanding the universe. we call these explosions the big bang. c. the discovery of expansion provided the proof that the universe began as a large explosion known as the big bang. d. the discovery that all objects in the universe are spreading apart led to the idea that everything must have been together at some point and then began to expand. this idea is known as the big bang theory.
b. the big bang theory refers to nuclear fission, where particles explode into more particles constantly and sporadically. these particles are emitted outward, expanding the universe. we call these explosions the big bang is the link between the observation that the universe is expanding and the big bang theory
What is the idea that explains the universe's expansion?
The prevalent view, known as the isotropy hypothesis, contends that the cosmos is expanding not just in all directions, but also at the same rate.
The Doppler red-shift of light from distant stars and galaxies indicates that the universe is expanding (moving away from a central point). This enables Big Bang Theory, since following a "bang," all matter goes away from the place of origin.
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20.0 l of a monatomic ideal gas at a pressure of 100 kpa expand adiabatically until the volume doubles. what is the pressure in the gas at that point?
The pressure in the gas at that point is equal to the initial pressure, 100 kPa.
To expand adiabatically, there must be no heat transfer involved. Adiabatic expansion means that no heat is transferred between the gas and its surroundings; this means that if we double the volume of our gas, nothing should change in terms of temperature as long as there is no heat transfer to or from our system during expansion.
Since we're starting out with a monatomic ideal gas, we know that its entropy is going to stay constant throughout this process, so the ideal gas law gives us a relationship between pressure, volume, and temperature: PV = nRT
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what is the foemula for this problem
A coil of resistance 10Ω and inductance 140mH is connected in parallel with a 260Ω resistor across a 230V, 50Hz supply. Calculate the following (i) Current in the coil and phase angle of this current. (ii) Supply current(iii) Circuit impedance (iv) Power factor (v) Power consumed (b) Explain what is meant by the term " Power Factor Correction".
The current in the coil is approximately 21.02A with a phase angle of 23.21°. The supply current is approximately 0.86A. The circuit impedance is approximately 10.94Ω. The power factor is approximately 0.92. The power consumed is approximately 181.59W. Power factor correction is the process of improving the power factor in an electrical circuit by adding reactive elements to make the circuit more efficient and reduce energy losses.
(i) To calculate the current in the coil and the phase angle, we need to consider the impedance of the coil, which consists of both resistance and inductance. The impedance (Z) can be calculated using the formula:
Z = √(R^2 + (ωL)^2)
Where R is the resistance, L is the inductance, and ω is the angular frequency given by 2πf, where f is the frequency.
In this case, R = 10Ω, L = 140mH (which can be converted to 0.14H), and f = 50Hz.
Plugging in these values, we have:
Z = √(10^2 + (2π × 50 × 0.14)^2)
≈ √(100 + (6.28 × 50 × 0.14)^2)
≈ √(100 + 4.44^2)
≈ √(100 + 19.7)
≈ √119.7
≈ 10.94Ω
The current in the coil (Ic) can be calculated using Ohm's Law:
Ic = V / Z
Where V is the supply voltage, which is 230V in this case. Plugging in the values, we have:
Ic = 230V / 10.94Ω
≈ 21.02A
The phase angle (θ) can be calculated using the formula:
θ = arctan((ωL) / R)
Plugging in the values, we have:
θ = arctan((2π × 50 × 0.14) / 10)
≈ arctan(4.44 / 10)
≈ arctan(0.444)
≈ 23.21°
(ii) The supply current (Is) can be calculated by dividing the supply voltage by the total circuit impedance:
Is = V / (R + Z)
Plugging in the values, we have:
Is = 230V / (260Ω + 10.94Ω)
≈ 0.86A
(iii) The circuit impedance is already calculated in part (i) as 10.94Ω.
(iv) The power factor (PF) can be calculated by taking the cosine of the phase angle (θ):
PF = cos(θ)
Plugging in the value of θ calculated in part (i), we have:
PF = cos(23.21°)
≈ 0.92
(v) The power consumed by the circuit can be calculated using the formula:
P = V × Is × PF
Plugging in the values, we have:
P = 230V × 0.86A × 0.92
≈ 181.59W
(b) Power Factor Correction (PFC) is the process of improving the power factor of an electrical circuit by adding reactive elements such as capacitors or inductors. The power factor is a measure of how effectively the electrical power is being used in a circuit. A low power factor indicates that the circuit is drawing more reactive power (VARs) than necessary, leading to a less efficient use of electrical energy.
By adding reactive elements, the power factor can be brought closer to unity (1). This helps to reduce the reactive power and improve the overall efficiency of the circuit. Power factor correction is commonly employed in industrial and commercial settings to optimize power usage, reduce energy losses, and improve the capacity of power distribution systems.
Power factor correction is achieved by analyzing the power factor of the circuit and determining the appropriate reactive element
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A runner runs around a track consisting of two parallel lines 96 m long connected at the ends by two semicircles with a radius of 49 m. She completes one lap in 100 seconds. What is her average speed?
A) 2. 5 m/s
B) 0 m/s
C) 5. 0 m/s
D) 1. 3 m/s
E) 10 m/s
1.3 m/s is the average speed of runner. Option D is the correct answer.
The total distance covered by the runner in one lap is equal to the distance around the two semicircles plus the distance along the two parallel lines. The distance around one semicircle is πr = π(49 m) and since there are two semicircles, the total distance around the semicircles is 2π(49 m). The distance along each parallel line is 96 m, and since there are two parallel lines, the total distance along the parallel lines is 2(96 m). Therefore, the total distance covered by the runner in one lap is:
Total distance = 2π(49 m) + 2(96 m) = 2π(49 m + 48 m) = 2π(97 m)
The time taken by the runner to complete one lap is given as 100 seconds. Therefore, her average speed is:
Average speed = Total distance / Time taken = [2π(97 m)] / (100 s) = 1.93 m/s
Rounding to two significant figures, the average speed of the runner is 1.9 m/s, which corresponds to option (D) 1.3 m/s.
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when the vertical face of a trench shears along a tension crack line it is known as
The term for the shearing along a tension crack line in the vertical face of a trench is known as a "trench cave-in" or "trench collapse."
When the vertical face of a trench shears along a tension crack lineThis is a significant safety concern in the construction industry. Proper trench shoring and safety procedures are crucial to prevent such incidents, which can potentially lead to serious injuries or fatalities.
This happens when the soil is cohesive, and the force of gravity acting on the mass of soil is greater than the soil's internal resistance to sliding. The tension crack line is a critical weak point where this sliding can occur.
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Explain which movement Jamal should make (which car and which point), and why that movement will result in the largest increase in potential energy. Describe the magnetic force that will act on the vehicle he moves.
Because potential energy increases with separation distance, Jamal should move the toy car with the greatest separation distance.
What do you mean by potential energy ?The term potential energy is defined as stored energy that depends upon the relative position of various parts of a system. Potential energy is energy that cannot be transfer to kinetic energy. It has the capacity to do work but is not presently doing so.
Because magnetic force is inversely proportional to the separating distance between the cars, the magnetic force acting on the vehicles will decrease as he moves the cars away from each other.
Thus, potential energy increases with separation distance, Jamal should move the toy car with the greatest separation distance.
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Which situations might cause two observers (A and B) to measure different frequencies for the same vibrating object? Select the two correct answers. (2 points)
Observer A and Observer B are both stationary and at the same distance from the object.
Observer A and Observer B are both stationary and at the same distance from the object.
Observer A is stationary and Observer B is moving.
Observer A is stationary and Observer B is moving.
Observer A and Observer B are moving at different speeds relative to each other.
Observer A and Observer B are moving at different speeds relative to each other.
Observer A and Observer B are stationary but at different distances from the vibrating object.
We want to explain why two different observes may measure different frequencies for the same vibrating object.
We will see that the two correct options are:
Observer A is stationary and Observer B is moving.Observer A and Observer B are moving at different speeds relative to each other.Let's assume that the vibrating object is a guitar string. Thus, the string makes a noise, and from that noise, we can estimate the frequency at which the string vibrates.
Now there appears a really cool effect, called the Doppler Effect. It says that the apparent change of frequency is due to the motion of the observer or the source of the frequency (or both).
For example, if you move towards the vibrating string, the perceived frequency will be larger, and you will hear a "higher" sound.
While if you move away from the string, the opposite happens, and you will hear a "lower" sound.
Then the only thing that impacts in how we perceive the frequency is our velocity relative to the source.
So, why do observers A and B measure different frequencies?
The two correct answers are:
Observer A is stationary and Observer B is moving.Observer A and Observer B are moving at different speeds relative to each other.If you want to learn more, you can read:
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Your Answers for Redshift and Blueshift Quick Check are down here ↓
Which situations might cause two observers (A and B) to measure different frequencies for the same vibrating object? Select the two correct answers. (2 points)
Observer A is stationary and Observer B is moving. * A = yes
Observer A and Observer B are moving at different speeds relative to each other. * B = yes
Observer A and Observer B are stationary but at different distances from the vibrating object. No
Observer A and Observer B are both stationary and at the same distance from the object. No
Why do scientists observe blueshift in certain stars?(1 point)
Light wave frequencies increase as an object moves toward the observer. * A = yes
Stars with lower temperatures emit more light waves at the blue end of the spectrum. No
Light wave frequencies decrease as an object moves toward the observer. No
Stars with higher temperatures emit more light waves at the blue end of the spectrum. No
When will a scientist observe redshift in the spectrum of a distant space object?(1 point)
when the object is stationary. No
when the object is moving toward the scientis. No
when the object is moving away from the scientist * C = yes
when the object is in the same frame of reference as the scientist. No
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Just like traditional film cameras, the small opening that allows light to pass through the lens of a digital camera is called the
Answer:
dsadadas
Explanation:
dadadda
A 25.0 kg box of textbooks rests on a loading ramp that makes an angle α with the horizontal. The coefficient of kinetic friction is 0.250, and the coefficient of static friction is 0.350.
A) As α is increased, find the minimum angle at which the box starts to slip.
B)As this angle, find the acceleration once the box has begun to move
c) at this angle, how fast will the box be moving after it has slid a distance 4.7m along the loading ramp
(a) As σ is increased, The minimum angle will be "19.2°".
(b) The acceleration will be "0.91 m/s²"once the box has began to move.
(c) The speed will be "3 m/s" as the box slid a distance 4.7 m along the loading map.
According to the question,
Mass = 25.0 kg
Kinetic friction = 0.25
Coefficient of static friction = 0.35
(a) We know,
⇒ static friction = mg sine
⇒ mg cosine * u = mg sine
then,
tan A = u = 0.35
a = 19.2
Therefore, as α is increased, the minimum angle at which the box starts to slip is 19.2°.
(b) We know that:
Kinetic friction = mgCos19.2 * 0.25
= 2.31m
and,
Net force downwards = mgSin19.2 - mgCos19.2* 0.25
By substituting the values, we get
= m(3.22-2.31)
= 0.91m/s²
Therefore, As this angle, the acceleration once the box has begun to move at 0.91 m/s².
(c) since the box is sliding at a distance of 4.7 meter:
Thus,
The speed will be:
→ \(v^{2} - u^{2} + 2as\)
\(0 + 2* 0.91* 5\)
= 9.21
\(v = 3m/s\)
Therefore, at this angle, at 3m/s will the box be moving after it has slid a distance 4.7m along the loading ramp
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