Question

Darth Maul is driving a 860 kg car (note, your diagram might show a different value ... but use this mass!) that strikes a huge spring at a speed of 21 m/s (See Figure below). The car compresses the spring a distance of 10.0 m.

Darth Maul in a car!

(a) What is the spring stiffness constant of the spring?

N/m

(b) How long is the Darth Maul's car in contact with the spring before it bounces off in the opposite direction?

s

Answer 1

Given is:-

Mass of the car

speed of the car

compression in the spring

At the instant of maximum compression the speed of the car reduces to zero. Taking the kinetic energy of the car to be zero at the horizontal part, the conservation of energy shows

or

by putting all the values

Thus the stiffness of the spring or the spring constant is 3792.6N/m

Part-b

we know that

the time period of the osillation of spring is

where m is the mass of the particle and k is the spring constant

And time for maximum compression is =

Thus time taken for maximum compression is t   

by putting all the values we get

Therefore the Darth Maul's car takes 0.74 seconds before it bounces off in the opposite direction