CH6. A cart full of whistles and bells rolls down a slope (ignore friction) and

Question

CH6. A cart full of whistles and bells rolls down a slope (ignore friction) and impacts a spring at the base of the hill. The initial height and velocity of the car are given. a) By how much, x, does the cart compress the spring before coming to m 3.0 kg a complete stop? vo 5.0 m/s k 630 N/m b) The spring rebounds and the cart is sent back up the hill. What is the maximum height, hma, of the cart above the ground when it comes to a momentary stop? 000 c) In the absence of friction this exchange will just go on forever. But h m 1.2 m. in the real world where does the cart end up?

Explanation / Answer

a)

using conservation of energy

spring potential energy due to compression = initial potential energy of cart

(0.5) k x2 = mgh

(0.5) (630) x2 = 3 x 9.8 x 1.2

x = 0.335 m

b)

using conservation of energy again

final potential energy of cart = spring potential energy due to compression

(0.5) k x2 = mgh

hmax = 1.2 m

c)

in real work , the cart will loose some energy and hence comes to a stop finally after moving several times

H7)

using conservation of energy

(0.5) (m1 + m2) Vo2 + m2 gh = (0.5) (m1 + m2) Vf2

(0.5) (8 + 5) (2.5)2 + (5) (9.8) (1.4) = (0.5) (8 + 5) Vf2

Vf = 4.1 m/s

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