Answers
Given data:
* The coefficient of static friction is,
\(\mu_s=0.46\)* The mass of the fridge is m = 100 kg.
Solution:
The normal force acting on the fridge is,
\(\begin{gathered} F_N=mg \\ F_N=100\times9.8 \\ F_N=980\text{ N} \end{gathered}\)The frictional force acting on the fridge is,
\(\begin{gathered} F_r=\mu_s\times F_N \\ F_r=0.46\times980 \\ F_r=450.8\text{ N} \end{gathered}\)The force required to start moving the fridge is equal to the frictional force.
Thus, the force required in the given case is 450.8 N.
Related Questions
What force acts on a projectile in the horizontal direction?
Answers
The force that acts on a projectile in the horizontal direction is Gravitational force.
A projectile is an object upon which the only force is gravity. Gravity acts to influence the vertical motion of the projectile, thus causing a vertical acceleration. The horizontal motion of the projectile is the result of the tendency of any object in motion to remain in motion at constant velocity.
Due to the absence of horizontal forces, a projectile remains in motion with a constant horizontal velocity. Horizontal forces are not required to keep a projectile moving horizontally. Hence, The only force acting upon a projectile is gravity.
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The nonreflective coating on a camera lens with an index of refraction of 1.23 is designed to minimize the reflection of 631-nm light. If the lens glass has an index of refraction of 1.52, what is the minimum thickness of the coating that will accomplish this task
Answers
Answer:
the minimum thickness of the coating is 128.25 nm
Explanation:
The computation of the minimum thickness of the coating is shown below:
In the case of non-reflective coatings, for determining the minimum film thickness needed we need to apply the following formula
Thickness = t = Wavelength ÷ 4n
where
n represent index of refraction of the coating material.
t = 631 ÷ (4 × 1.23)
= 128.25 nm
Hence, the minimum thickness of the coating is 128.25 nm
please help i’ll mark u branliest
Answers
Answer:
62
Explanation:
it doesn't need explanation
You are a musician and want to know the frequency of a guitar string. You measure the length of the string to be 0.6 meters and the tension in the string to be 60 Newtons. If the mass of the string is 0.01 kg, what is the frequency of the string? (Units: frequency -hertz (Hz), length -meters (m), tension -newtons (N), mass -kilograms (kg))
Answers
Answer:
Explanation:
I frequency = 278 Hz
Bella is taking an adventurous trip through the jungle. First, she trekked for 1 hour into the thick jungle at an average speed of 6 km/h. next, she took a boat to cross a lake which rode her at an average speed of 20 km/h for 0.5 hours. for the lost part of her trip, she hiked for 2 hours at an average speed of 4 km/h. find the total distance on her trip.
Answers
The total distance of Bella's trip through the jungle is 24 kilometers.
To find the total distance of Bella's trip, we need to calculate the distance traveled during each leg of her journey and then sum them up.
Let's calculate the distance traveled in each segment:
Trekking in the thick jungle:
Bella trekked for 1 hour at an average speed of 6 km/h.
Distance = Speed × Time
Distance = 6 km/h × 1 hour
Distance = 6 km
Crossing the lake by boat:
Bella rode a boat at an average speed of 20 km/h for 0.5 hours.
Distance = Speed × Time
Distance = 20 km/h × 0.5 hour
Distance = 10 km
Hiking for the remaining part:
Bella hiked for 2 hours at an average speed of 4 km/h.
Distance = Speed × Time
Distance = 4 km/h × 2 hours
Distance = 8 km
Now, let's calculate the total distance:
Total distance = Distance of trekking + Distance of crossing the lake + Distance of hiking
Total distance = 6 km + 10 km + 8 km
Total distance = 24 km
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Can someone explain how to do the algebra for this question? I know everything else, I just don’t know how to rearrange the question to solve for v.
Answers
Answer:
Refer to the step-by-step Explanation.
Step-by-step Explanation:
Simplify the equation with given substitutions,
Given Equation:
\(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2\)
Given Substitutions:
\(\omega=v/R\\\\ \omega_{_{0}}=v_{_{0}}/R\\\\\ I=(2/5)mR^2\)\(\hrulefill\)
Start by substituting in the appropriate values: \(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2 \\\\\\\\\Longrightarrow mgh+(1/2)mv^2+(1/2)\bold{[(2/5)mR^2]} \bold{[v/R]}^2=(1/2)mv_{_{0}}^2+(1/2)\bold{[(2/5)mR^2]}\bold{[v_{_{0}}/R]}^2\)
Adjusting the equation so it easier to work with.\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)
\(\hrulefill\)
Simplifying the left-hand side of the equation:
\(mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)
Simplifying the third term.
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2}\cdot \dfrac{2}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)
\(\\ \boxed{\left\begin{array}{ccc}\text{\Underline{Power of a Fraction Rule:}}\\\\\Big(\dfrac{a}{b}\Big)^2=\dfrac{a^2}{b^2} \end{array}\right }\)
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2 \cdot\dfrac{v^2}{R^2} \Big]\)
"R²'s" cancel, we are left with:
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5}mv^2\)
We have like terms, combine them.
\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{7}{10} mv^2\)
Each term has an "m" in common, factor it out.
\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)\)
Now we have the following equation:
\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)
\(\hrulefill\)
Simplifying the right-hand side of the equation:
\(\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac12\cdot\dfrac25\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\cdot\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15mv_{_{0}}^2\Big\\\\\\\\\)
\(\Longrightarrow \dfrac{7}{10}mv_{_{0}}^2\)
Now we have the equation:
\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)
\(\hrulefill\)
Now solving the equation for the variable "v":
\(m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)
Dividing each side by "m," this will cancel the "m" variable on each side.
\(\Longrightarrow gh+\dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2\)
Subtract the term "gh" from either side of the equation.
\(\Longrightarrow \dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2-gh\)
Multiply each side of the equation by "10/7."
\(\Longrightarrow v^2=\dfrac{10}{7}\cdot\dfrac{7}{10}v_{_{0}}^2-\dfrac{10}{7}gh\\\\\\\\\Longrightarrow v^2=v_{_{0}}^2-\dfrac{10}{7}gh\)
Now squaring both sides.
\(\Longrightarrow \boxed{\boxed{v=\sqrt{v_{_{0}}^2-\dfrac{10}{7}gh}}}\)
Thus, the simplified equation above matches the simplified equation that was given.
You apply 10 N to a machine and the machine applies 10 N to another object. What is the mechanical advantage ? Rocket Science
Answers
Answer:
The mechanical advantage is 1.
Explanation:
Given;
input force, F₁ = 10 N
output force, F₀ = 10 N
mechanical advantage is called force ratio and it is given as;
M.A = output force / input force
M.A = 10 N / 10 N
M.A = 1
This is an ideal machine scenario.
Therefore, the mechanical advantage is 1.
Shrinking Loop. A circular loop of flexible iron wire has an initial circumference of 167 cm , but its circumference is decreasing at a constant rate of 13.0 cm/s due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnitude 1.00 T , which is oriented perpendicular to the plane of the loop. Assume that you are facing the loop and that the magnetic field points into the loop.
(a) Find the emf induced in the loop at the instant when 9.0 s have passed.
(b) Find the direction of the induced current in the loop as viewed looking along the direction of the magnetic field.
Answers
Answer:
a) fem = - 0.0103 V, b) the applied field is in a vertical upward direction, the induced current is clockwise.
Explanation:
a) For this exercise we use Faraday's law
fem = \(- \frac{d \phi}{dty}\)
the magnetic flux is
Ф = B. A = B A cos θ
The bold letters indicate vectors, in this case the direction of the magnetic field and the normal to the circumference is parallel therefore the angle is zero and the cos 0 = 1
fem = - B dA / dt
the area of a circle is
A = π r²
l
et's perform the derivative
dA / dt =π 2r \(\frac{dr}{dt}\)
we substitute
fem = - B 2π r \(\frac{dr}{dt}\)
the circumference of a circle is
L = 2π r
we substitute
fem = - B L ( L )
fem =
Let's find the circumference for the 9 s, let's use a direct rule of proportions
If the circumference changes 13cm at t = 1. how much does it change at t=9s
ΔL = 13cm (9s / 1s) = 117cm
the circumference that is
L = Lo - ΔL
L = 167 - 117
L = 50 cm
let's reduce all magnitudes to the SI system
L = 0.50 m
= 0.130 m / s
calculate us
fem = - 1.00 0.50 0.130
fem = - 0.0103 V
b) the electromotive force induced in the opposite direction to the change of the radius and is decreasing with time, the current follows the direction of the decreased voltage therefore the current is induced in the opposite direction to the change of the magnetic flux.
If the applied field is in a vertical upward direction, the induced current is clockwise.
How does something(the big bang) come from nothing by nothing i mean the first universe although we don't know where the first universe is but we do know that nothing can't come from something.
Answers
The Big Bang theory is the most widely accepted explanation for the origins of the universe, but it does not necessarily imply that the universe emerged from nothing.
It is possible that new discoveries or insights may shed light on this fundamental question in the future. The universe may have arisen from a pre-existing state or through some other natural process that we do not yet understand.
Instead, the theory describes how the universe underwent a rapid expansion from a very dense and hot state. The conditions and laws of physics that applied during the earliest moments of the universe may not necessarily be the same as those we observe today, and there are many unknowns and uncertainties in our understanding of these early stages.
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28. Batman is sitting in the Batmobile at a stoplight.
As the light turns green, Robin passes Batman in his lime-green Pinto at a constant speed of 60 km/h. If Batman gives chase. accelerating at a constant rate of 10 km/h/s. determine
a) now long 1t takes batman to attain the
same speed as Robin.
b) how far Batman travels in this time.
c) how long it takes for Batman to catch up
to Robin.
Answers
If Batman gives chase and accelerating at a constant rate of 10 km/h/s then:
a) 6 seconds
b) 360 meters
c) 12 seconds
Accelerating is a process whereby an object, or a system of objects, increases its speed or rate of change. It is a fundamental concept in physics and is used to describe the motion of objects, such as an acceleration due to a force, or the rate of change in velocity. Accelerations can also be caused by a change in direction, or due to changes in gravity, such as when accelerating towards the surface of a planet.
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A siren emits a sound at 1700 Hz. Assume a speed of sound of 332 m/s. What frequency would a stationary observer hear if the car with the siren is travelling at:A. 25 m/s towards the observerB. 25 m/s away from the observerC. 140 km/h towards the observer
Answers
F source = 1700 HZ
v= source
S sound =332 m/s
Doppler equation:
F listener = F source ( speed of sound / speed of sound - v source)
A) v source 25 m/s
F = 1700 hz ( 332 m/s / 332m/s - 25m/s) = 1,838 HZ
B) v = - 25 m/s
F = 1700 hz ( 332 m/s / 332m/s + 25m/s) = 1581 HZ
C) 140 km/h = 39 m/s
F = 1700 hz ( 332 m/s / 332m/s - 39m/s) = 1,926 HZ
4 x10^4
---------------
3.63 x 10^-4
O 1.10 x 10^8
O 2.36 x 10^-8
O 2.36 x 10^-3
Answers
For a company to develop an effective customer-centric culture, there is always room for:
A. Larger product research and development investment
B. Improvement
C. More customers
D. More accurate market research
Answers
Continuous improvement helps a company to develop an effective customer-centric culture.
Such a company regards its customer experience and satisfaction as a core component of its business vision, mission, and strategies.
In a customer-centric culture, the company's actions and communications will be driven by the need to achieve the highest customer satisfaction.
Thus, there is always room for improvement as the company continuously seeks for opportunities to improve customer satisfaction.
a block of mass 5.0 kg starts at point A with a speed of 15.0 m/s on a flat frictionless surface. At point B, it encounters an incline with coefficient of kinetic friction uk 0.15. The block makes it up the incline to a second flat frictionless surface. What is the work done by friction? What is the velocity of the block at point C? The incline is 2.2m long at an angle 0=15
Answers
44.4 is the work done by friction 14.4 s the velocity of the block at point C . Correct Option a)
What is friction and example?Friction is the force that prevents solid surfaces, fluid layers, and material components from moving against each other. There are various kinds of friction.
Dry friction is the force that resists the relative lateral motion of two in touch solid surfaces. Dry friction is further classified as static friction ("stiction") between non-moving surfaces and kinetic friction ("stiction") between moving surfaces. Dry friction, with the exception of atomic or molecular friction, is caused by the interplay of surface characteristics known as asperities . Fluid friction explains the friction that occurs between sliding segments of a thick fluid.
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Full Question: In the figure below, a block of mass 5.0 kg starts at point A with a speed of 15.0 m/s on a flat frictionless surface. At point B, it encounters an incline with a coefficient of kinetic friction uk = 0.15. The block makes it up the incline to B a second flat frictionless surface. The incline is 22 m long at an angle = 15° What is the total work done in joules when the block goes from A to C and what is the speed of the block at point C in m/s? (fist value is work, second is speed) A) 44.4; 14.4 B) 44.4, -14.4 C) 14.4, 44.4 D) 44.4, 14.4 E) 44.4, 44.4
In an attempt to deliver a parcel on time, the dispatch rider had to ride 10km 15 degrees SE, he then rode 11 km 30 degrees NE and then takes a shortcut at 22km W .find the rider's displacement
Answers
The total displacement of the dispatch rider is calculated as 43km.
Data;
10km 15 degrees SE11km 30 degrees NE22km WTotal DisplacementTo calculate the total displacement of the dispatch rider, we can simply add up the total distance covered by the rider.
This becomes;
\(10+11+22 = 43km\)
The total displacement of the dispatch rider is calculated as 43km.
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A steel ball is dropped from a height of 12.09 m above the ground. What is its speed 2.101 m above the ground
Answers
So, the final velocity of the ball when it is 2.101 above the ground is 13.99 m/s or can be rounded to 14 m/s.
IntroductionHi ! In this question, I will help you. This question will addopt the principle of final velocity in free fall. Free fall is vertical downward movement that occurs when any object dropped without initial velocity. In othee word, the object that falls is only affected by the presence of gravity and its initial high. In general, the final velocity in free fall can be expressed by this equation :
\( \boxed{\sf{\bold{v = \sqrt{2 \times g \times h}}}} \)
With the following condition :
v = final velocity (m/s)h = height or any other displacement at vertical line (m)g = acceleration of the gravity (m/s²)Problem SolvingWe know that :
\( \sf{h_1} \) = initial height = 12.09 m\( \sf{h_2} \) = final height = 2.101 mg = acceleration of the gravity = 9.8 m/s²Note :
At this point (2.101 m above the ground), the object can still complete its movement up to exactly 0 m above the ground.
What was asked :
v = final velocity = ... m/sStep by Step
\( \sf{v = \sqrt{2 \times g \times \Delta h}} \)
\( \sf{v = \sqrt{2 \times g \times (h_1 - h_2)}} \)
\( \sf{v = \sqrt{2 \times 9.8 \times (12.09 - 2.101)}} \)
\( \sf{v = \sqrt{19.6 \times 9,989}} \)
\( \sf{v \approx \sqrt{195.78}} \)
\( \boxed{\sf{v = 13.99 \: m/s \approx 14 \: m/s}} \)
ConclusionSo, the final velocity of the ball when it is 2.101 above the ground is 13.99 m/s or can be rounded to 14 m/s.
See More :My work on a similar problem regarding the final velocity of free fall https://brainly.com/question/26377041What are the products of a fission reaction?
A. A smaller nucleus and a positron.
B. Energy and a larger nucleus.
C. Energy and two or more smaller nuclei
D. A larger nucleus and an electron.
Answers
Answer: B. Energy and a larger nucleus.
Explanation:Nuclear fission products are the atomic fragments left after a large atomic nucleus undergoes nuclear fission. Typically, a large nucleus like that of uranium fissions by splitting into two smaller nuclei, along with a few neutrons, the release of heat energy (kinetic energy of the nuclei), and gamma rays.
What is the reason that the moon looks dimmer before eclipse? Why does it take some time to be brighter again after eclipse?
Answers
Answer:
Why does it take sometimes to be brighter again after eclipse? The moon looks dimmer before lunar eclipse because the moon enters into shadow of penumbra region of earth. As a result, the brightness of moon decreases and looks dimmer.
Explanation:
Answer: The moon looks dimmer before lunar eclipse because the moon enters into shadow of penumbra region of earth. As a result, the brightness of moon decreases and looks dimmer.
Explanation:
What happens to the temperature of a substance while it is changing state?
Answers
Answer:
its temperature stays constant
Explanation:
the weight of an object is measured in air to be 7N the object is then immersed in water and its apparent weight is measured to be 4N determined the buoyant force and state whether or not the object float
Answers
The buoyant force can be determined by subtracting the apparent weight of the object in water from its weight in air. In this case, the buoyant force would be 7N - 4N = 3N.
Based on the information provided, since the buoyant force (3N) is less than the weight of the object (7N), the object will not float.
Floating occurs when the buoyant force is greater than or equal to the weight of the object.
In this scenario, the object will experience a net downward force, indicating that it will sink rather than float in water.
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A roller coaster is at a peak of 20m and has a mass of 900kg. What is the potential energy of the roller coaster?
O 100000 J
10000 J
O 9.8 J
O 176400 J
Answers
The potential energy of the roller coaster is 176,400 J (joules).
The potential energy of an object is given by the formula PE = mgh, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or vertical position of the object.
In this case, the roller coaster is at a peak of 20m and has a mass of 900kg. The acceleration due to gravity, g, is approximately 9.8 \(m/s^2\).
Using the formula, we can calculate the potential energy:
PE = mgh
= (900 kg)(9.8 \(m/s^2\))(20 m)
= 176,400 J
Therefore, the potential energy of the roller coaster is 176,400 J (joules).
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A kangaroo can jump over an object 2.20 m high with a vertical speed of 6.57 m/s. how long is it in the air
Answers
The kangaroo is in the air for approximately 0.667 seconds.
What is the velocity?Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.
A kangaroo with a vertical speed of 6.57 m/s may jump over an object 2.20 m high.
To find the time a kangaroo is in the air, we need to calculate the time it takes to reach the peak of its jump and then double that time (to account for both the ascent and descent).
We can use the formula for vertical motion under constant acceleration (g = 9.8 m/s²):
t = √(2h / g)
where h is the height of the jump (2.20 m) and g is the acceleration due to gravity (9.8 m/s²).
Plugging in the values, we get:
t = √(2 × 2.20 m / 9.8 m/s²)
t = √(0.447)
t ≈ 0.667 s
So the kangaroo is in the air for approximately 0.667 seconds.
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Theodore is running at 2m/s as he runs off a bluff and drops 10 meters into a water filled rock
quarry. Calculate the time it takes for Theodore to splash down. Calculate the distance he lands
away from the edge of the bluff? (show one's work)
Answers
5 second is the time it takes for Theodore to splash down running at 2m/s velocity as he runs off a bluff and drops 10 meters into a water filled rock
quarry.
velocity= 2m/s
distance=10 meters
velocity=distance/time
time=distance/velocity
time=10 meters/2m/s
time=5 second
A vector number known as velocity describes "the pace at which an item changes its location." Imagine a person moving quickly, taking one stride ahead, one step back, and then beginning from the same place each time. A vector quantity is velocity. As a result, velocity is aware of direction. One must consider direction while calculating an object's velocity. Saying that an item has a velocity of 55 miles per hour is insufficient. The direction must be included in order to adequately characterize the object's velocity. Simply said, the velocity vector's direction corresponds to the motion of an item
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what is meant by the MA of a machine is 2?
Answers
Explanation:
it means that the ratio of the load or force exerted by the machine to the effort put in is 2:1
What is the speed of light (in m/s) in air? (Enter your answer to at least four significant figures. Assume the speed of light in a vacuum is 2.997 ✕ 108 m/s.) m/s What is the speed of light (in m/s) in polystyrene? m/s
Answers
Answer:
The speed of light in air is 2.996x10⁸ m/s, and polystyrene is 1.873x10⁸ m/s.
Explanation:
To find the speed of light in air and in polystyrene we need to use the following equation:
\( c_{m} = \frac{c}{n} \)
Where:
\(c_{m}\): is the speed of light in the medium
n: is the refractive index of the medium
In air:
\(c_{a} = \frac{c}{n_{a}} = \frac{2.997 \cdot 10^{8} m/s}{1.0003} = 2.996 \cdot 10^{8} m/s\)
In polystyrene:
\(c_{p} = \frac{c}{n_{p}} = \frac{2.997 \cdot 10^{8} m/s}{1.6} = 1.873 \cdot 10^{8} m/s\)
Therefore, the speed of light in air is 2.996x10⁸ m/s, and polystyrene is 1.873x10⁸ m/s.
I hope it helps you!
Jonas has a 10.0 kg box, which he places on a scale inside an elevator. When the
elevator begins to move, the scale shows that the box weighs 83.4 N. What is the
magnitude and direction of the elevator's acceleration?
Answers
Answer:
a = - 1.47 [m/s²], descending or going down
Explanation:
To solve this problem we must use Newton's second law which tells us that the sum of forces on a body is equal to the product of mass by acceleration.
∑F = m*a
where:
∑F = Forces applied [N]
m = mass = 10 [kg]
a = acceleration [m/s²]
Let's assume the direction of the upward forces as positive, just as if the movement of the box is upward the acceleration will be positive.
By performing a summation of forces on the vertical axis we obtain all the required forces and other magnitudes to be determined.
\(-m*g + N = m*a\\\)
where:
g = gravity acceleration = 9.81 [m/s²]
N = normal force measured by the scale = 83.4 [N]
Now replacing:
\(-(10*9.81)+83.4=10*a\\-14.7=10*a\\a=-1.47[m/s^{2} ]\)
The acceleration has a negative sign, this means that the elevator is descending at that very moment.
it 3 Review
tors and 2-D Kinematics
Find the direction of the sum
of these two vectors:
16.3 m
BV
7.70 m
A
27.8°
20.0°
Answers
When two vectors of magnitudes 16.3 m and 7.7 m are combined at an angle of 137.8 degrees, the resultant is equivalent to 23.87 metres.
What is the parallelograms law of vector addition?
The adjacent sides drawn from a point can be used to indicate the magnitude and direction of two vectors acting concurrently at a point.
7.7 m in size, with vector 1 pointing at the x-axis at a 27.8 degree angle.
vector 2 of magnitude 16.3 m, 20 degrees off the negative y plane.
Using the law of parallelogram vector addition
i.e.
resultant vector = √((v₁) ² + (v₂) ² + 2 × v₁ × v₂ × cos (angle between two vectors))
substituting given value in parallelogram vector addition we get,
resultant vector = √ (570)
resultant vector = 23.87 meters
As a consequence, the product of the two vectors, which have magnitudes of 16.3 metres and 7.7 metres and an angle of 137.8 degrees, is equal to 23.87 metres.
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Question:
Find the direction of the sum
of these two vectors:
16.3 m
7.70 m
20.0°
magnitude (m)
A 27.8°
A ball is thrown down vertically with an initial speed of v0 from a height of h. (a) What is its speed just before it strikes the ground? (b) How long does the ball take to reach the ground? What would be the answers to (c) part a and (d) part b if the ball were thrown upward from the same height and with the same initial speed? Before solving any equations, decide whether the answers to (c) and (d) should be greater than, less than, or the same as in (a) and (b).
Answers
Answer:
a) v² = v₀² + 2 g h, b) t = v₀/g (1+ √ (1 + 2gh/ v₀²))
Explanation:
a) This is an exercise that we can solve using conservation of energy.
Starting point. High point
Em₀ = K + U = ½ m v₀² + m gh
Final point. Soil
\(Em_{f}\) = K = ½ m v²
energy is conserved because there is no friction
Emo = Em_{f}
½ m v₀² + m g h = ½ m v²
v² = v₀² + 2 g h
b) the time it takes to reach the ground can be calculated with kinematics
let's create a reference frame with positive upward direction
v = vo - g t
when it reaches the ground it has a velocity v, the initial velocity is downwards v₀ = -v₀
v = -v₀ - gt
t = - (v + v₀) / g
we substitute the velocity values calculated in the previous part
t = - (√(v₀² + 2 g h) + vo) / g
we will simplify the equation a bit
t = - v₀/g (1+ √ (1 + 2gh/ v₀²))
c) is now thrown vertically upward with the same initial velocity vo.
To find the final velocity we use the conservation of energy where the velocity is squared, so it does not matter if it is positive or negative, therefore in this section the value should be the same as in part a
v = √ (v₀² + 2gh)
d) for this part if there is change since the speed is not squared
v₀ = v₀
v = v₀ - gt
t = (v₀ - v) / g
t = (v₀ - √(v₀² + 2 g h)) / g
t = v₀/g (1 - √(1 + 2gh / v₀²))
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1) a meal for 6 cost £12 per person. as it is one of the diners birthday , the other 5 decided to pay for his meal. how much do each of the five friends need to pay?
Answers
Each of the five friends needs to pay £12 to cover the cost of their own meals and contribute towards the birthday person's meal. Using mean allows us to distribute the cost equally among the friends, ensuring a fair division of expenses for the meal.
To determine how much each of the five friends needs to pay, we can use the concept of averages (mean) and divide the total cost by the number of people paying.
In this scenario, the total cost of the meal for 6 people is £12 per person. Since the other 5 friends have decided to pay for the birthday person's meal, they will collectively cover the cost of their own meals plus the birthday person's meal.
To calculate the total cost covered by the five friends, we can subtract the cost of one person's meal (since the birthday person's meal is being paid by the group) from the total cost. The cost of one person's meal is £12.
Total cost covered by the five friends = Total cost - Cost of one person's meal
= (£12 x 6) - £12
= £72 - £12
= £60
Now, to find out how much each of the five friends needs to pay, we divide the total cost covered by the five friends (£60) by the number of friends (5).
Amount each friend needs to pay = Total cost covered by the five friends / Number of friends
= £60 / 5
= £12
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What is the magnetic force on a 2.0-m length of (straight) wire carrying a current of 30 A in a region where a uniform magnetic field has a magnitude of 55 mT and is directed at an angle of 20° away from the wire?
Answers
To determine the magnetic force on a straight wire carrying a current in a uniform magnetic field, we can use the formula for the magnetic force:
F = I * L * B * sin(θ)
where:
F is the magnetic force,
I is the current in the wire,
L is the length of the wire,
B is the magnitude of the magnetic field, and
θ is the angle between the wire and the magnetic field.
In this case, the values are:
I = 30 A (current in the wire)
L = 2.0 m (length of the wire)
B = 55 mT = 0.055 T (magnitude of the magnetic field)
θ = 20° (angle between the wire and the magnetic field)
Substituting the values into the formula:
F = 30 A * 2.0 m * 0.055 T * sin(20°)
Calculating sin(20°):
F = 30 A * 2.0 m * 0.055 T * 0.3420
F ≈ 1.5714 N
Therefore, the magnetic force on the 2.0-meter length of wire carrying a current of 30 A in a region with a uniform magnetic field of magnitude 55 mT and at an angle of 20° away from the wire is approximately 1.5714 N.
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