Friction on an Inclined Plane

[mmalone11]

1. Homework Statement
The diagram shows a 5kg block of lead released from rest at the top of an incline. The block has a speed of 6 m/s when it reaches the bottom. The angle between the slope and the ground is 40° and the slope is 10 m long.
a) What is its PE at the top?
b) What is its KE at the bottom?
c) What is the work done by friction?
d) What must be the coefficient of friction?


2. Homework Equations
I am having trouble finding the friction. Once i find the friction, i know how to find the coefficient force of friciton using Ffr=mu*Fn.

3. The Attempt at a Solution
For part a first I found what the height was by doing 10(sin(40))=Height and got 6.43 m. Than i plugged that into PE=mgh... 5(9.8)(6.43) ... getting 315.07J ...
For part b I used KE=1/2(m)(v2) ... 1/2(5)(62) ... getting 90J ...

 

[rl.bhat]

What is the component of the weight normal to the surface? That will be fn.
What is the component of the weight along the surface?
In the absence of the friction, what will be the KE at the bottom?
Difference in the KE = fr*d, where d is the distance moved by the block.

 

[kerimek]

For part c I am not sure how to do it.
For part d I am not sure how to do it.

I would first commend the student for their attempt at solving the problem and correctly using the equations for potential and kinetic energy. To find the work done by friction, we can use the equation W=Fd, where F is the friction force and d is the distance traveled by the block. In this case, the distance traveled is 10m and the force of friction can be calculated using the equation Ffr=μFn, where μ is the coefficient of friction and Fn is the normal force. The normal force can be found using the equation Fn=mgcosθ, where m is the mass of the block, g is the acceleration due to gravity, and θ is the angle of the incline. With these values, the work done by friction can be calculated and compared to the values for potential and kinetic energy to ensure conservation of energy.

To find the coefficient of friction, we can rearrange the equation Ffr=μFn to μ=Ffr/Fn and plug in the values for friction and normal force calculated above. It is important to note that the coefficient of friction can vary depending on the materials and surfaces involved, so it is not a constant value. It is also affected by factors such as temperature and surface roughness. Therefore, it is important to conduct experiments and measure the coefficient of friction for a specific situation rather than relying on a single calculated value.

In conclusion, as a scientist, I would suggest conducting further experiments and calculations to determine the coefficient of friction for the specific situation described in the problem. This will provide a more accurate and reliable value for the coefficient of friction, allowing for a more precise analysis of the forces and energy involved in the block's motion on the inclined plane.