Inside a NASA test vehicle, a 3.50-kg ball is pulled along by a horizontal ideal
ID: 1731815 • Letter: I
Question
Inside a NASA test vehicle, a 3.50-kg ball is pulled along by a horizontal ideal spring fixed to a friction-free table. The force constant of the spring is 222 N/m . The vehicle has a steady acceleration of 5.00 m/s2, and the ball is not oscillating. Suddenly, when the vehicle's speed has reached 45.0 m/s, its engines turn off, thus eliminating its acceleration but not its velocity.
a) find the amplitude
b) Find the frequency of the resulting oscillations of the ball.
c)What will be the ball's maximum speed relative to the vehicle?
Explanation / Answer
a)
ma = k*x;
where a = acceleration,
k = force constant of the spring,
x = shift from the initial length of the spring.
So,
b = x = ma/k
= 3.50 * 5 / 222
= 0.078 m
b)
Frequency of the oscillations f = sqrt(k/m)/ (2 pi)
= sqrt(222/3.50) /2pi
= 1.27 Hz.
c)
v = w*sqrt(b^2-x^2)
w = sqrt(k/m)
= sqrt(222/3.50)
= 7.96
v = 7.96*sqrt(0.078^2-0)
= 0.62 m/s