Question

As shown in the figure, a 1.5 kg box is held at rest against a spring with a force constant k = 720 N/m that is compressed a distance d. When the box is released, it slides across a surface that is frictionless, except for a rough patch that has a coefficient of kinetic friction μk = 0.40 and is 6.0 cm in length. If the speed of the box is 2.3 m/s after sliding across the rough patch, determine the initial compression d (in cm) of the spring.

Answer 1

Spring potential energy + work done by friction= change in kinetic energy

1/2kx^2-0.4*1.5*9.81*6*10^-2= 0.5*1.5*2.3*2.3=3.9675

X^2= 2*3.614/720, x=0.10m

, x=10cm