What is the coefficient of kinetic friction for the incline?

[Momentum09]

Hi, can someone please give me hints as to how to do this problem?

A 12 kg block is released from rest on an 36 degrees inclined plane and moves 2.4m during the next 4.2s. What is the coefficient of kinetic friction for the incline?

I know that the normal force = mgcos(delta), and dividing this value from the Fs would give me the coefficient, but how do I find this value?

Thank you so much!

 

[hage567]

You need to use Newton's second law. Sum up the forces in each direction (the direction perpendicular to the surface of the incline, and the direction of motion). You will get two equations that will allow you to find the coefficient of kinetic friction. You have been given enough information in the question to find the acceleration of the block down the incline. Have you drawn a diagram and labeled all of the forces present?

By the way, homework questions should be posted in the Homework Forums.

 

[m2003]

The coefficient of kinetic friction for the incline can be found by using the formula μk = Fk/Fn, where μk is the coefficient of kinetic friction, Fk is the force of kinetic friction, and Fn is the normal force. In this case, we can use the information given in the problem to calculate the normal force and the force of kinetic friction.

First, we need to find the normal force acting on the block. As you mentioned, the normal force is equal to mgcos(delta), where m is the mass of the block and g is the acceleration due to gravity (9.8 m/s^2). In this case, the mass of the block is given as 12 kg and the angle of the incline is 36 degrees. Plugging these values into the equation, we get Fn = 12 kg * 9.8 m/s^2 * cos(36 degrees) = 94.2 N.

Next, we need to find the force of kinetic friction. This can be calculated using the equation Fk = μk * Fn, where μk is the coefficient of kinetic friction and Fn is the normal force we just calculated. We can rearrange this equation to solve for μk, which gives us μk = Fk/Fn. Plugging in the values we have, we get μk = (12 kg * 2.4 m)/(94.2 N * 4.2 s) = 0.0716.

Therefore, the coefficient of kinetic friction for the incline is approximately 0.0716.