Could you please answer these questions with explanation. Show your work, please

Question

Could you please answer these questions with explanation.

Show your work, please.

PROBLEM5-8 points A block of mass m is released from rest from a height h = 4R above the base of a loop-the-loop track. Express your answers in terms of m, R, and/or g. 2 points] (a) Neglecting friction and air resistance, what is the block's speed when it reaches point a? 2 points] (b) Neglecting friction and air resistance, what is the speed when the block reaches point b? 12 points] (c) Calculate the normal force acting on the block at point b. 2 points] (d) In reality, there is some friction acting on the block, and the block barely makes it around the loop without falling off at point b. Between the release point and point b, what is the net work done by resistive forces acting on the block?

Explanation / Answer

(A) Applying energy conservation,

PEi + Kei = PEf + KEf

m g (4 R ) + 0 = 0 + m v^2 /2

v = sqrt(8 g R)

(B) 4 m g R + 0 = m g (2R) + m v^2 /2

v = sqrt(2 g R)

(C) N + m g = m v^2 / r

N = m (2 g R / R) - m g

N = m g

(d) then N = m v^2 / r - m g = 0

v^2 = R g

Work done by gravity + work done by force = change in KE

m g (2 R) - W = m (R g)/2 - 0

W = 5 m g R / 2

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