Question

, on a hill. Dr. L., Jimmie and Kepler (Total mass = MT ) are all on a massless sled together. They are on a hill that is at an angle of θ above horizontal… Ok. Now we know Dr. L. is lazy. This is the third problem he’s reused… Assume they start from rest and that there is no friction between the sled and hill. a.) How fast will the sled be going when it reaches the bottom of the hill. --- Now assume there’s friction between the sled and hill. The coefficient of kinetic friction is µK. b.) Draw a free body diagram of the sled. c.) What is the force of friction acting on the sled? d.) Now use energy and determine the final velocity of the sled with friction. Is it less than it was before? Good! It better be.

Answer 1

Okay, the problem statement is incomplete...but i understand that sled is moving down on a slope.

The hill has some vertical height (h) ......The slope has a length L

Then to find h , you can use trigonometry

h = L*sin

Then using conservation of energy

mgh = 1/2mv²

gh = v² / 2

v = sqrt (2gh)

where v is the speed of sled at the bottom of the hill.

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Now, we must consider friction

Here is the free body diagram

where F_k is the force of kinetic friction and it acts in the opposite direction of motion.

Force of friction

F_k = u_kN

F_k = u_kmgcos

Now, work done by friction = u_kmgcos* L

where L is length of slope

so,

finally

equating the initial and final energy, we get

mgh + u_kmgcos* L = 1/2mv²

gh + u_kgcos* L = 1/2v²

2 (gh + u_kgcos* L) = v²

v = sqrt (2gh + 2u_kgcos L)