Applied Force to a Sliding Frictionless Ramp

In summary, the conversation discusses a problem involving a frictionless ramp and block on a frictionless surface. The problem asks for the horizontal force needed to prevent the block from moving. The solution involves analyzing the forces on the block and the ramp+block system, and equating their accelerations. The correct solution is (m+M)*g*tan(θ).
  • #1
Rook2012
2
0

Homework Statement



Hello all, kinda angry at myself for posting this but my brain has hit a brick wall.
This is an easy problem too... anyway.

A frictioness ramp of mass M and incline θ sits on a frictionless surface. A block of mass m sits on the ramp. What horizontal force F must be applied to the ramp to ensure the block does not move?

Homework Equations



F = ma
Newton's Third Law

The Attempt at a Solution



I know the answer is (m+M)*g*tan(θ). But I'm having trouble making myself believe it.

I started with a force diagram of the block, the only 2 forces acting on it are gravity directly downward and the normal force (N) at an angle of θ above the horizontal.

So the net force on the block is F[itex]_{block}[/itex] = N sin(θ) i + (mg-(N cos(θ)) j = ma

Then I looked at the ramp+block system and determined
F[itex]_{system}[/itex] = (M+m)a[itex]_{system}[/itex]

Here for some reason the gears stop turning. I went on to say that the y components on the block sum to zero, so the Normal force is [itex]\frac{mg}{cosθ}[/itex].

From here I substitued in for N in the x direction and then equated "a" in both equations but I know that's wrong. Got me the right answer, but its the wrong way of doing it. Any help would be appreciated.
 
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  • #2
Come to think of it, equating the acceleration of the system and the block is alright isn't it? They are both moving at the same acceleration which is all in the x direction.

If I let ma = Nsin(theta) because the forces in the vertical direction cancel, and then solve for "a" as I did... maybe that it the right way to go about it. Let me know if I'm delusional, peace.
 
  • #3
Rook2012 said:
Come to think of it, equating the acceleration of the system and the block is alright isn't it? They are both moving at the same acceleration which is all in the x direction.
yes, correct
If I let ma = Nsin(theta) because the forces in the vertical direction cancel, and then solve for "a" as I did... maybe that it the right way to go about it. Let me know if I'm delusional, peace.
yes, just be sure to determine N by looking at sum of forces in the vertical y direction = 0.
 

FAQ: Applied Force to a Sliding Frictionless Ramp

1. What is applied force to a sliding frictionless ramp?

Applied force to a sliding frictionless ramp refers to the force that is applied to an object as it slides down a ramp with no friction. This force is typically measured in Newtons and can be calculated using the equation F=ma, where F represents force, m represents mass, and a represents acceleration.

2. How does the angle of the ramp affect the applied force?

The angle of the ramp can affect the applied force in two ways. First, a steeper angle will result in a greater force being applied to the object, as it will have a greater vertical component. Second, a shallower angle will result in a smaller force being applied, as it will have a smaller vertical component. In both cases, the horizontal component of the force will remain the same.

3. What is the relationship between applied force and friction on a ramp?

On a frictionless ramp, the applied force is the only force acting on the object. However, on a ramp with friction, the applied force must overcome the force of friction in order to move the object. The greater the applied force, the greater the force of friction must be to prevent the object from sliding down the ramp.

4. How does the mass of the object affect the applied force?

The mass of the object does not directly affect the applied force on a frictionless ramp. However, the mass of the object does affect the force of friction on a ramp with friction. A heavier object will have a greater force of friction acting against it, requiring a greater applied force to overcome it.

5. What are some real-life applications of applied force on a sliding frictionless ramp?

Applied force on a sliding frictionless ramp can be seen in a variety of real-life applications, such as roller coasters, playground slides, and wheelchair ramps. It is also an important concept in physics and engineering, as it helps to understand the motion and forces acting on objects in different scenarios.

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