A child presses a toy car with mass mc = 750g against a spring (with spring cons

Question

A child presses a toy car with mass mc = 750g against a spring (with spring constant k = 69 J/m2 ) compressing it a distance x = 17cm. Note, for this entire problem use: g = 10.0 m/s2

a) If the track and the car are on a level surface, what will be the speed of the car after the spring has been fully uncompressed? Assume no friction or air resistance.

b) After the car has moved a distance of d = 2.5m it encounters a ramp. What will be the maximum height above the horizontal track for the toy car.

c) After the car reaches its maximum height it goes back down the ramp. Once it is on the track, the wheels are locked up and they skid along the track. If there is a coefficient of kinetic friction between the tires and the track of µk = 0.65, how much work will be done by friction while the car is sliding to a stop?

d) How far does the car skid before coming to a stop?

Explanation / Answer

(A) Applying energy conservation,

k x^2 /2 = mv^2 /2

69(0.17^2) = 0.750 v^2

v = 1.63 m/s

(B) Applying energy conservation,

m g h = mv^2 /2

h = 1.63^2 / (2 x 10) =0.133 m

(C) Work done by friction = change in KE

= - 0.997 J

(d) f = 0.65 x 0.750 x 10 = 4.875 N

W = - f. d

d = 0.205 m

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