A moving 1.30 ka block collides with a horizontal spring whose spring constant i

Question

A moving 1.30 ka block collides with a horizontal spring whose spring constant is 244 N/m. The block compresses the spring a maximum distance of 9.50 cm from its rest position. The coefficient of kinetic friction between the block and the horizontal surface is 0.480, What is the work done by the spring in bringing the block to rèst? Submit Answer Tries 0/8 ow muc mechanical energy is being dissipated by the force of friction while the block is being brought to rest by the spring? Submit Answer Tries 0/8 What is the speed of the block when it hits the spring? Submit Answer Tries 0/8

Explanation / Answer

work done on the spring is

Ws = -del U = Ui - Uf = 0 - ½ k d2,

Ws = - ½ (244N/m)(0.095 m)2

=-1.1 J

(B)

If the block moves through a displacement d, then the energy dissipated by the force of friction while the block is being brought to rest by the spring is

del E = - fk d = - uk mg d = -0.48*1.3(9.8) (0.095)= -0.58 J

(C)

del E = del KE + del U

del KE = del E- del U

0- 1/2 mv^2 = -0.58 - (1.1) = 1.68

v= sqrt 2 ( 1.68)/1.3=1.6 m/s

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