In the figure, a ball of mass m = 58 g is shot with speed v i = 24 m/s (in the n

Question

In the figure, a ball of mass m = 58 g is shot with speed vi = 24 m/s (in the negative direction of an x axis) into the barrel of a spring gun of mass M = 253 g initially at rest on a frictionless surface. The ball sticks in the barrel at the point of maximum compression of the spring. Assume that the increase in thermal energy due to friction between the ball and the barrel is negligible. (a) What is the speed of the spring gun after the ball stops in the barrel? (b) What fraction of the initial kinetic energy of the ball is stored in the spring?

Thank you

In the figure, a ball of mass m = 58 g is shot with speed vi = 24 m/s (in the negative direction of an x axis) into the barrel of a spring gun of mass M = 253 g initially at rest on a frictionless surface. The ball sticks in the barrel at the point of maximum compression of the spring. Assume that the increase in thermal energy due to friction between the ball and the barrel is negligible. (a) What is the speed of the spring gun after the ball stops in the barrel? (b) What fraction of the initial kinetic energy of the ball is stored in the spring? Thank you

Explanation / Answer

a)

let the final speed of gun is v

here , using conservation of momentum ,

v*(58 + 253) = 58 *24

v = 4.48 m/s

the final of spring gun is 4.48 m/s

c)

Here ,

KE final = 0.5 * (0.058 + 0.253)* 4.8^2

KEfinal = 3.11 J

KEini = 0.5 * 0.058 * 24^2

KE ini = 16.7 J

fraction of the initial kinetic energy of the ball is stored in the spring , k = (KEini - KEfina)/KEini

k = 16.7 -3.11 /16.7

k = 0.814

the fraction of the initial kinetic energy of the ball is stored in the spring is 0.814

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