How do I determine the force on a object moving on a curve?

[js430]

Homework Statement

Variables are all given as arbitrary constants

Homework Equations

W=∫F⋅dl
y=½bx^2
μ=cx^2

The Attempt at a Solution

The obvious force action on the object is the downward gravity force. I don't see how to calculate the force that 'moves' the object down the curve or the friction force since it is a curve.

 

[berkeman]

Welcome to the PF.

Please draw the free body diagram (FBD) for the particle as it moves down the slope under the forces of gravity, friction, and the normal force. That will get you started...

 

[kuruman]

Pretend that the mass is on an inclined plane with continuously changing slope. Call the instantaneous angle θ which you can easily find an expression for. Draw the FBD as @berkeman suggested. Remember that, unlike the inclined plane, acceleration has components both parallel and perpendicular to the incline.

 

[Ray Vickson]

Homework Statement

Variables are all given as arbitrary constants

Homework Equations

W=∫F⋅dl
y=½bx^2
μ=cx^2

The Attempt at a Solution

The obvious force action on the object is the downward gravity force. I don't see how to calculate the force that 'moves' the object down the curve or the friction force since it is a curve.

Compute the (vector) acceleration $\vec{a}(t) = \frac{d^2}{dt^2} \vec{x}(t).$ The force is $\vec{F} =\frac{1}{m} \vec{a},$ where $m$ is the object's mass. Of course, to do that you need to know $\vec{x}(t)$ explicitly. If you are looking at a problem which asks you to find $\vec{x}(t)$ by using some other inputs, then that is another matter.