A block of mass m = 1.75kg slides head-on nto a spring of spring constant k = 28

Question

A block of mass m = 1.75kg slides head-on nto a spring of spring constant k = 285N/m. When the block stops, it has compressed the spring by 6.2 cm. The coefficient of kinetic friction between block and floor is 0.24. The system contains the spring and the block.

(a) While the block is in contact with the spring and being brought to rest, what is the change in spring potential energy of the system?

(b) While the block is in contact with the spring and being brought to rest, how much work is done by the force of friction?

(c) What was the block's speed when it first made contact with the spring?

(d) If the floor had been included in the system, how much work would the force of friction have done on the system as the block was brought to rest by the spring?

(e) If the floor had been included in the system, what would have been the change in thermal energy of the system as the block was brought to rest by the spring?

Explanation / Answer

SPRING COMPRESSION = 0.5*K*X2=0.55 J

WORK BY FRCTION = F*X= 0.24*1.75*9.8*0.062 = 0.26 J

VELOCITY = 0.595 m/s

zero work will be done by friction on floor

0.26 J would increase the thermal energy of the system

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