# Washer Hanging from Box Moving Down a Ramp

• Gwozdzilla
In summary, the problem involves a crate sliding down a ramp with a steel washer suspended inside by a string. The crate has a mass of 180kg and the person inside has a mass of 55kg. The washer is at rest when the string makes an angle of 68° with the top of the crate. To find the coefficient of kinetic friction between the ramp and the crate, the equations ƩF=ma and fk=μn are used. The tension in the string and the forces on the washer are also considered. The ƩFwasher equations come from the free body diagram for the washer. Another way to approach the problem is to consider the angle the washer would make if the crate were stationary on the
Gwozdzilla

## Homework Statement

A steel washer is suspended inside an empty shipping crate from a light string attached to th top of the crate. The crate slides down a long ramp that is inclined at an angle of 37° above the horizontal. The crate has mass 180kg. You are sitting inside (with a flashlight); your mass is 55kg. As the crate is sliding down the ramp, you find the washer is at rest with respect to the crate hen the string makes an angle of 68° with the top of the crate. What is the oefficient of kinetic friction between the ramp and the crate?

ƩF=ma
fk=μn

## The Attempt at a Solution

Let mc = mass of crate
and my = mass of you
and m = mass of washer
ƩFcrate system = (mc + my)a = (mc + my)gsin(37) - μ(mc + my)cos(37)

Canceling out the combined mass and solving for μ gives:

μ = [gsin(37) - a]/[gcos(37)]

Apparently...
Let T = tension in string
ƩFy-washer = ma1 = Tsin(22) -mgsin(37)
and
ƩFx-washer = ma2 = Tcos(22) -mgcos(37)

And a2 = 0 allowing for these two equations to be rearranged and then divided by each other giving...
tan(22) = [gsin(37) - a]/[gcos(37)]

My actual question:

Where are the ƩFwasher equations coming from? I have the attached picture to help, but I still don't understand.

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Where are the ƩFwasher equations coming from? I have the attached picture to help, but I still don't understand.
Free body diagram for the washer.
So you didn't derive the equations yourself then?

You can also look at it from the POV of you - if the crate were stationary on the slope, what angle would the washer make to the ceiling?

## 1. How does the angle of the ramp affect the motion of the washer hanging from the box?

The angle of the ramp determines the acceleration of the box and the washer. As the angle increases, the acceleration decreases, resulting in a slower descent down the ramp. This is due to the force of gravity being split into two components: one parallel to the ramp and one perpendicular. The parallel component is responsible for the acceleration down the ramp.

## 2. What factors influence the speed of the washer while moving down the ramp?

The speed of the washer is influenced by the angle of the ramp, the mass of the box and the washer, and the presence of any friction between the box and the ramp. Additionally, the initial height of the box and the ramp also play a role in the speed of the washer.

## 3. How does the mass of the washer and box affect the motion down the ramp?

The mass of the washer and box affects the acceleration of the objects. According to Newton's Second Law of Motion, the greater the mass, the greater the force needed to accelerate the objects. This means that a heavier box and washer will require more force to move down the ramp at the same rate as a lighter box and washer.

## 4. Does the motion of the washer depend on the presence of friction on the ramp?

Yes, the presence of friction on the ramp can affect the motion of the washer. Friction is a force that opposes motion, so if there is significant friction between the box and the ramp, it will slow down the acceleration of the box and the washer. This can result in a slower descent down the ramp.

## 5. Can the motion of the washer be used to determine the coefficient of friction between the box and the ramp?

Yes, by measuring the acceleration of the box and the washer and taking into account the mass and angle of the ramp, the coefficient of friction can be calculated using Newton's Second Law of Motion. However, other factors such as air resistance and the smoothness of the ramp can also affect the motion, so multiple trials may be needed for an accurate measurement.

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