A 5-lbm toy car is at the end of a spring compressed 2 inches. The linear spring

Question

A 5-lbm toy car is at the end of a spring compressed 2 inches. The linear spring has a force constant of k = 3 lbf/in. (Recall that for a linear spring, F=kx). Neglect friction in all parts.

(A). How much energy is stored in the compressed spring? (ANS: Wsp = 6 lbf in)

(B). If the spring is released, what is the maximum velocity of the car on a level surface in ft/s? (ANS: V = 2.54 ft/s)

(C). If the car approaches at 15 degree incline, how much further will the car travel before it stops? (ANS: s=0.386ft)

(D). IF instead a motor is used to maintain a constant velocity on the incline, what horsepower is required? (ANS: PE=0.00598hp)

(E). If instead the car approaches at 15 degree decline, what is the maximum velocity 5 feet further along the track? (ANS: V=9.43ft/s)

These are the questions and answers, I'm interest in how to get those answers. Please be very specific and how you arrived at the answers, including the name of any table you used. Thanks.

Explanation / Answer

A) W = 0.5*k*x^2 = 0.5*3*2^2 = 6 lbf in
B) PE = KE
0.5*k*x^2 = 0.5*m*v^2

v = x* sqrt(k/m)= 2.54 ft/s

C) EPE = GPE
0.5*k*x^2 = mgh
6 = 5*h
h = 6/5 in=1.2 in

sin15 = h/s

s = h/sin15 = 4.64 in

1 in = 0.0833 ft
s = 4.64*0.0833 = 0.386 ft

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