17. Two Identical springs. In the accompanying figure a 5.0 N ball is fastened t

Question

17. Two Identical springs. In the accompanying figure a 5.0 N ball is fastened to two identical springs that pull in opposite directions and can slide on a frictionless horizontal surface. The ball is initially stationary and is then moved 3. cm. to the right and released from rest. a. Find the magnitude and direction of the net force on the ball just after it is released. b. What is the potential energy of the system just as the ball is released. c. Find the maximum speed of the ball.         k=12N/cm

Explanation / Answer

Here ,

for the ball ,

A) displacement , x = 3 cm = 0.03 m

spring constant ,k = 12 N/cm

Now , for the net force on the ball ,F = 2 * k * x

F = 2 * 12 * 3 N

F = 72 N

and the force will be oposite to it's displacement

the net force is 72 N in the left direction

b)

for the potential energy in system

potential energy = 2 * 0.5 * k * x^2

potential energy = 12 * 100 * 0.03^2

potential energy = 1.08 J

c)

let the maximum speed if v

Using conseravtion of energy

0.5 * (5/9.8) * v^2 = 1.08

solving for v

v = 2.06 m/s

the maximum speed of the ball is 2.06 m /s

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