# Calculating the frictional forces on a sliding box on a ramp

• Karagoz
In summary, the equation for the friction force when the box is moving upwards is: F_x = ma - G_x - R and the equation for the friction force when the box is moving downwards is: F_x = ma + G_x + R.
Karagoz

## Homework Statement

We kick a box upwards a ramp. The box slides upwards, then slides backwards again. We ignore the air drag and other factors. We only look at the gravity, normal forces and friction forces.

Forces on the box when it's moving upwards:

Weight of the box is 0.123 KGs.

Angle α is 24°.

Gravitational acceleration is -9.81 m/s^2

Acceleration of the box when it's moving upwards is: -6.9 m/s^2.

Acceleration of the box when it's moving downwards is -1.16 m/s^2

The question is to find the R (frictional force) when the box is moving upwards and downwards.

G_x = mg*sin(α)

## The Attempt at a Solution

I have attemted to solve the problem, and I got almost equal values for R (ca. 0.35N). But in the "answer key" of the problem this is how the problem is solved:

Friction force when box is moving upwards:
F_x = ma
-G_x - R = ma
R = -ma -G_x
R = -ma -mg*sinα
R = -m(a + g*sinα)
R = -0.123kg(-6.9m/s^2 + 9.81m/s^2 * sin24)
R = -0.41N

Friction force when force is moving downwards:
F_x = ma
-G_x + R = ma
R = ma -G_x
R = ma +mg*sinα
R = -m(a + g*sinα)
R = 0.123kg(-1.16m/s^2 + 9.81m/s^2 * sin24)
R = 0.35N

Is the blueprint wrong or?

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Karagoz said:
R = -0.123kg(-6.9m/s^2 + 9.81m/s^2 * sin24)
R = -0.41N
Plug these numbers into a calculator and see if you get the same result.

There seems to be a confusion of negative signs regarding magnitudes and directions of vectors especially when you substitute numerical values. The problem gives you the two accelerations as negative numbers. We know that the acceleration is downhill regardless of the direction of the velocity therefore the positive axis is uphill and the negative direction is downhill.

Now when the block is moving uphill, all vectors point downhill, so the proper equation to write is (and I put numbers although I find this distasteful, but I have to make the point clear) $$0.123(kg)*[-9.81(m/s^2) \sin24^o ]+(-R_{up})=0.123(kg)*[-6.9(m/s^2)]$$ For the downhill motion, the force of friction changes sign and $$0.123(kg)*[-9.81(m/s^2) \sin24^o ]+R_{down}=0.123(kg)*[-1.16(m/s^2)]$$
Note that ##R_{up}## and ##R_{down}## denote, respectively, the magnitude of the frictional force when the block is sliding up and down the incline. As such, when the equations are solved, they should come out positive.

## 1. How do I calculate the frictional force on a sliding box on a ramp?

To calculate the frictional force on a sliding box on a ramp, you will need to first determine the coefficient of friction between the box and the ramp. This can be found by dividing the force of friction by the normal force. Once you have the coefficient of friction, multiply it by the weight of the box to get the frictional force.

## 2. What factors affect the frictional force on a sliding box on a ramp?

The frictional force on a sliding box on a ramp is affected by the weight of the box, the angle of the ramp, the surface material of the box and the ramp, and the coefficient of friction between the two surfaces.

## 3. How does the angle of the ramp affect the frictional force?

The steeper the angle of the ramp, the greater the frictional force will be. This is because as the angle increases, the weight of the box exerts a greater downward force on the ramp, increasing the normal force and thus the force of friction.

## 4. What is the difference between static and kinetic friction?

Static friction is the force that prevents an object from moving when a force is applied to it. Kinetic friction is the force that acts on an object as it is moving. In the case of a sliding box on a ramp, static friction would be the initial force that prevents the box from sliding down the ramp, while kinetic friction would be the force acting on the box as it is sliding.

## 5. How can I reduce the frictional force on a sliding box on a ramp?

To reduce the frictional force on a sliding box on a ramp, you can decrease the weight of the box, use a surface material with a lower coefficient of friction, or decrease the angle of the ramp. Additionally, using lubricants such as oil or wax can also help reduce the frictional force.

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