# What is the applied force required to push an object up a ramp?

• KenMasters
In summary, a cabinet weighing 100 kg is pushed up a ramp at an angle of 10 degrees. The friction coefficient is 0.30. The minimum applied force required to push the cabinet up the ramp is 461 N. However, there is uncertainty about the acceleration and time it takes to push the cabinet up the ramp due to unclear information about the use of "minimum applied force."

## Homework Statement

A cabinet is pushed up a ramp at angle of 10 degrees. The cabinet weighs 100 kg. The friction coefficient is 0.30. What is the minimum applied force required to push the cabinet up the ramp? Calculate the time it takes to push the object up the ramp. The ramp is 15 meters long and elevated to 2.6 meters.

## Homework Equations

All I know how to do is calculate Fdown which is Fdown = Fg(sin10) which is 170 N. Would I add 170 to 0.30 to find the applied force?

## The Attempt at a Solution

See above.

Your help is much appreciated. :)

Welcome to PF!

Hi Ken! Welcome to PF!

The kinetic friction force is the normal force times µ.

(and remember that the applied force is horizontal, so that will affect the normal force )

Remember that the coefficient of friction is a pure number ratio between the normal reaction to the weight of the object on a ramp and the frictional force needed to stop it moving =]

in other words:

$$\mu \ge \frac{F_{f}}{F_{n}}$$

I figured the applied force needs to be 461 N.

Now I just have absolutely no clue how to calculate the acceleration of the cabinet up the ramp and how to calculate the time. What equation can I use for that?

Thanks again guys. I really appreciate it.

KenMasters said:
A cabinet is pushed up a ramp at angle of 10 degrees. The cabinet weighs 100 kg. The friction coefficient is 0.30. What is the minimum applied force required to push the cabinet up the ramp? Calculate the time it takes to push the object up the ramp. The ramp is 15 meters long and elevated to 2.6 meters.
KenMasters said:
Now I just have absolutely no clue how to calculate the acceleration of the cabinet up the ramp and how to calculate the time. What equation can I use for that?

Hi Ken!

I don't understand that part of the question

if "minimum applied force" is used, the acceleration is zero, and the speed can be infinitesimally small, and so the question has no answer.

If two coefficients of friction were given, µs and µk, I would assume that the question meant that the force was the "minimum applied force" to get the cabinet started, ie to overcome µs, and then of course once it has started moving, it only has to overcome µk, and so does accelerate.

But only one µ is given.

Thanks tiny-tim. :)

Is there a way to find the time it takes to push the cabinet up the 15m if a minimum applied force is used of 461 N?

tiny-tim said:
Hi Ken!

I don't understand that part of the question

if "minimum applied force" is used, the acceleration is zero, and the speed can be infinitesimally small, and so the question has no answer.

If two coefficients of friction were given, µs and µk, I would assume that the question meant that the force was the "minimum applied force" to get the cabinet started, ie to overcome µs, and then of course once it has started moving, it only has to overcome µk, and so does accelerate.

But only one µ is given.

I think the coefficient of friction in this case is just for whilst the cabinet is in motion on the ramp, as the question does not state initial rest.

Through drawing a free-body force diagram I have come up with very different answers from the OP.(although likely wrong)

The normal reaction to the curve can easily be given in non-vector form as $$F_{n} = mgcos \theta$$ and by subbing in values: $$F_{n} = 100 \times 9.81 \times cos(10) = 966.1N$$

Then, by finding the frictional force through $$\mu \ge \frac{F_{f}}{F_{n}}$$ and rearranging we get $$F_{f_{max}} = 0.3 \times 966.1 = 289.83N$$

Through resolving the components of the force(289.83N) we now know is pushing up the ramp,$$F_{m}$$ (as there is movement, friction must be at max) we can get the horizontal component of this, $$F_{x}$$ to be $$F_{x} = F_{m}} - F_{n}sin10 - F_{f_{max}}sin80$$

Hi Cilabitaon,

So I calculated Fx to be -167. Now how do I use that number to calculate the time it takes? Sry I'm a physics noob. :) Thanks.

Well, upon further review I have just spouted a load of crap in that last post, sorry =[

Well would Fnet not equal Fpush - Fdown - fk? If I knew what the Fnet was I could determine the acceleration.

If the applied force is 500N(i've changed it from 461N) and Fdown is 171N and fk is 290N then would Fnet not equal 39 N?

Thanks everyone. :)

## 1. What is the relationship between applied force and the angle of the ramp?

The greater the angle of the ramp, the more force is required to push the object up the ramp. This is because the steeper the angle, the more the force of gravity is acting against the object.

## 2. How does the weight of the object affect the required applied force?

The weight of the object directly affects the required applied force. The heavier the object, the more force is needed to push it up the ramp against the force of gravity.

## 3. Does the type of surface of the ramp affect the required applied force?

Yes, the type of surface of the ramp can affect the required applied force. A smoother surface will require less force compared to a rougher surface, as there is less friction between the object and the ramp.

## 4. What is the role of friction in determining the required applied force?

Friction plays a crucial role in determining the required applied force. Friction is the force that opposes motion and it increases as the angle of the ramp increases. This means that more force is needed to overcome the force of friction and push the object up the ramp.

## 5. How does the height of the ramp affect the required applied force?

The height of the ramp does not directly affect the required applied force, but it does indirectly affect it through the angle of the ramp. A higher ramp will result in a steeper angle and therefore, more force will be required to push the object up the ramp.