Question

A vertical spring (ignore its mass), whose spring stiffness constant is 950 N/m is attached to a table. the spring is compressed down 15 cm and a300 g ball is placed on it. the spring is then released and the ball field off vertically. determine (a) the initial speed of the ball. (b) the maximum height reached by the ball

Answer 1

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Answer 2

Given: A vertical spring whose spring stiffness constant is 950 N/m is attached to the table. The spring is compressed 15 cm and a 300 gram ball is placed on it. The spring is then released and the ball flies vertically.

To find: 1- The initial speed of the ball

2- The maximum height reached by the ball

Explanation: In this case, the total energy is conserved in the system, therefore the potential energy is directly converted into kinetic energy.

Compression of spring= 15 cm = 0.15 m

Spring stiffness constant= 950 N/m

Potential energy = 1/2 * k* x^2

= 1/2 * 950 * 0.0225

= 10.6875 J

Mass of ball(m)= 300 g = 0.3 kg

Since, kinetic energy= potential energy

Kinetic energy= 1/2* m* v^2

=>10.6875 = 1/2 * 0.3 * v^2

=> v^2 = 10.6875 / 0.15

= 71.25

=> v = 8.44 m/s

Maximum height reached= v^2 / 2g

= 71.25/ 20

= 3.5625 m

Therefore, the initial velocity of the ball is 8.44 m/s and maximum height reached is 3.5625 m.