Question

A spring with spring constant 17 N/m hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 9.5 cm and released. The ball makes 32 oscillations in 16 s seconds. What is its maximum speed?

Answer 1

The ball makes 32 oscillations in 16 seconds.

So, period of the spring, T = 16 / 32 = 0.50 second

Spring constant, k = 17.0 N/m

Expression for the time period is given as –

T=2*pi* sqrt(m/k)

=> 0.50 = 2*pi* sqrt(m / 17)

=> sqrt(m / 17) = 0.50 / (2*pi) = 0.0796

=> m / k = (0.0796)^2

=> m = (0.0796)^2 * k = (0.0796)^2 * 17 = 0.1077 kg

For determining the maximum speed, we can use:

=> EP1+EK1=EP2+EK2

=> 0.5*k*x^2 + 0 =0.5*m*v^2 +0

=> 0.5*17*0.095^2 = 0.5*0.1077*v^2

=> v^2 = ( 0.5*17*0.095^2) / (0.5*0.1077)

=> v = 1.193 m/s

So, the maximum speed = 1.193 m/s (Answer)

answered by: anonymous