As shown in the figure, a 1.5-kg box is held at rest against a spring with a for

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 ?k = 0.40 and is 6.0 cm in length. If the speed of the box is 2.9 m/s after sliding across the rough patch, determine the initial compression d of the spring. cm

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 ?k = 0.40 and is 6.0 cm in length. If the speed of the box is 2.9 m/s after sliding across the rough patch, determine the initial compression d of the spring. cm

Explanation / Answer

Deacceleration on rough surface is:

d = 0.4*9.8 = 3.92

Now:

V^2-u^2=-2*d*s

u^2 = 2.9^2+2*3.92*0.06

u=2.98 m/s

Now:

0.5*1.5*2.98^2=0.5*720*x^2

X = 0.13602 m OR 13.602 cm

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