9. An air car called the target car is connected to a spring that is Connected t

Question

9. An air car called the target car is connected to a spring that is Connected to a post at the end of the air track. The car Is pulled 3.00 cm past the equilibrium point for the spring and released. The resulting simple harmonic motion has a period of 1.00 sec. A second air car of mass 250gm is also placed on the air-track. This second car is given a push and then collides with the stationary target car and sticks to it. The two joined cars now undergo simple harmonic motion with a period of root 1.50 sec and amplitude of 3.00 cm. What is a) the mass of the target car, b) the velocity of the incoming car?

Explanation / Answer

Solution:

Mass of the target car = m1

Mass of the 2nd air car = 250g= 0.25 kg

Time period T1= 1 s

Time period = T2= sqrt(1.5)

T1/T2 = sqrt (m1/(m1+m2) from the SHM equation for time period,T=2 pi sqrt(m/k)

=> 1/sqrt(1.5)= sqrt(m1+m1+0.25)

square both sides

1/1.5 = m1/(m1+0.25)

=> 1.5 m1 = m1+0.25

=> 1.5 m1 - m1 = 0.25

=> 0.5 m1 = 0.25

=> m1= 0.5 kg = 500grams

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