Inside a NASA test vehicle, a 3.50-kg ball is pulled along by a horizontal ideal

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 225 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.

Part A:Find the amplitude.

Part B: Find the frequency of the resulting oscillations of the ball.

Part C: What will be the ball's maximum speed relative to the vehicle?

Explanation / Answer

A) let A is the amplitude

F = k*A

m*a = k*A

==> A = m*a/k

= 3.5*5/225

= 0.0778 m

B) we know, angular frequency, w = sqrt(k/m)

= sqrt(225/3.5)

= 8.02 rad/s

we know, f = w/(2*pi)

= 8.02/(2*pi)

= 1.276 hz

C) Vmax = A*w

= 0.0778*1.276

= 0.100 m/s

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