Two identical balls, A and B are launched by identical springs, each compressed

Question

Two identical balls, A and B are launched by identical springs, each compressed by a distance of 5.2cm. After launch, they roll along the frictionless tracks seen below, where the distance h shown on the track for ball B is 28 cm. Each ball has a mass of 66 g. The speed of ball A when it reaches the end of its track is 1.5 m/s. The speed of ball B when it reaches the end of its track is 2.81 m/s. (a) Describe using energy ideas why it makes sense that ball B has a higher speed at the end of its track than ball A. (b) Determine the value of the spring constant and show that it is the same in both situations.

Explanation / Answer

2)

a) Initial gravitational potential energy of A is zero.

But initial gravitational potential energy of B is not zero.

so, when they leave track ball B will have more kinetic energy than ball A.

b)

in the case of ball B

use conservation of energy

initial elastic and graviational potential energy = final kinetic energy

(1/2)*k*x^2 + m*g*h = (1/2)*m*v^2

(1/2)*k*0.052^2 + 0.066*9.8*0.28 = (1/2)*0.066*2.81^2

==> k = 58.8 N/m

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