How to calculate force given Newtons, degrees, and friction

AI Thread Summary
To calculate the force required to slide a 400N trunk down a 20-degree incline at constant velocity, one must consider the forces acting on the trunk, including gravity, normal force, and friction. The gravitational force can be resolved into components parallel and perpendicular to the incline. The normal force acts perpendicular to the surface, while friction opposes the motion. The coefficient of kinetic friction (0.56) is crucial for determining the frictional force. Properly resolving these forces will lead to the calculation of the necessary driving force.
Josef
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Homework Statement


A 400N trunk is on a 20 degree inclined plane and has a coefficient of kinetic friction of 0.56. What force must be exerted on the trunk to make it slide down the plane at a constant velocity?

Homework Equations

The Attempt at a Solution


I have drawn a free body diagram of the situation but am not able to derive an equation to calculate the force needed. Given an angle, I assume I will be using a trigonometric function.
 
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Josef said:
I have drawn a free body diagram
So what forces are there on the trunk and in what directions do they act?
 
The force of gravity acts upon it (downward direction), The normal force (parallel to the surface), and The force of friction in the opposite direction of the movement of the trunk.
 
Josef said:
The normal force (parallel to the surface)
Not parallel. It is called the normal force for a reason.
There is also the driving force to be found.

Next, you need to resolve all the forces into components. You can either choose the component directions to be vertical and horizontal or normal to the plane and parallel to the plane. Your choice.
 
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Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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