2. A block has initial speed v 0 = 4 m/s up a frictionless, inclined plane. The

Question

2. A block has initial speed v0 = 4 m/s up a frictionless, inclined plane. The angle of incline is 40 above the horizontal. (a) How far up along the plane does the block go? (b) How long does it take to get there? (c) What is its speed when it gets back to the bottom?

3. A 65 kg man raises himself from the ground to a tree branch at a height of 5 m above him by holding onto a rope that runs up over a frictionless pulley and down to a hanging 70 kg sandbag. If the man starts from rest, and the sandbag does not hit the ground: (a) Find the time the man takes to reach the branch. (b) Find the speed with which the man arrives at the branch.

Explanation / Answer

a) let the length of ramp = l

height = l sin 40

using the conservation of energy

1/2 mv^2 = mgh = mg ( l sin 40)

0.5 (4^2) = 6.3 ( l)

length covered by block = 1.27 mapprx

retardation along ramp = 9.8 sin 40 = 6.3 m/s^2

b) time = 4/ 6.3= 0.635 seconds apprx

c) 4 m/s ( as there is no friction)

Q: 3 65 ( a) = T - 65 x 9.8

70 (a) = 70 x 9.8 - T

135 a= 49

a= 0.363 m/s^2

5 = 1/2 (0.363)t^2

time= 5.248 seconds apprx

v = 1.9 m/s

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