Force to push mass down inclined plane

[ChessFanatic]

Homework Statement

The angle of the ramp is 30 degrees. The mass is 40 kg. What force must be applied to keep the mass sliding down the ramp at constant velocity. The ramp is frictionless*

Homework Equations

I have missed the past few lessons in class, so I'm not sure. I do have a bunch of equations, but I have little clue on how to use them for this problem

The Attempt at a Solution

 

[lingualatina]

Assuming there is no friction, the force required to cause the mass to move at a constant rate is equal to the component of the mass's weight down the 30-degree incline. When this happens, the total net force on the mass is zero as the accelerative force (gravity) is canceled out, and it moves at a constant rate. The component of weight down the ramp is given by the expression mgcos(30). This, the force required is mgcos(30), or (40 kg)(9.8 m/s/s)(.866). It will be directed in the direction opposite the component of gravity down the ramp.

 

[Delphi51]

You might begin with a review of the forces on a block on a ramp.
You will need to find the normal force pushing the block against the ramp in order to calculate the friction force. Nice diagram here:
http://en.wikiversity.org/wiki/Motion_in_two_dimensions

 

[ChessFanatic]

I got it, thanks guys

 

[Nickie]

To calculate the force required to keep the mass sliding down the ramp at a constant velocity, we can use the equation F = mgsinθ, where F is the force, m is the mass, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of the ramp. In this case, θ = 30 degrees and m = 40 kg, so the force required would be:

F = (40 kg)(9.8 m/s^2)(sin 30 degrees) = 196 N

This means that a force of 196 N must be applied to the mass in order to keep it sliding down the ramp at a constant velocity. This is because the force of gravity acting on the mass is balanced by the force applied along the ramp, resulting in a net force of zero and a constant velocity. Since the ramp is frictionless, there is no additional force acting against the mass.