A mass M = 0.435 kg moves with an initial speed v = 3.43 m/s on a level friction

Question

A mass M = 0.435 kg moves with an initial speed v = 3.43 m/s on a level frictionless air track. The mass is initially a distance D = 0.245 m away from a spring with k = 811 N/m, which is mounted rigidly at one end of the air track. The mass compresses the spring a maximum distance d, before reversing direction. After bouncing off the spring, the mass travels with the same speed v, but in the opposite direction.

a) Determine the maximum distance that the spring is compressed.

b) Find the total elapsed time until the mass returns to its starting point.

Explanation / Answer

Given

Mass ,M = 0.435 kg

Initial speed, v = 3.43 m/s

Spring constant, k = 811 N/m

a)The kE of the mass is equal to the PE of the spring

  1/2Mv^2 = 1/2kx^2

0.435 kg *(3.43 m/s)^2 = 811N/m(x)^2

x = 0.08 m

b)Total distance travelled by the mass, S = (0.245 m+ 0.08m)*2   [since the mass comes back travelling

                                                                                                 the same distance]

S = 0.65 m

velocity of the mass, v = 3.43 m/s

Time taken for the mass to return to its starting point

T = S/v = 0.65 m/3.43 m/s

T =0.18 s

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