1. A 1.40 -kg object slides to the right on a surface having a coefficient of ki

Question

1. A 1.40-kg object slides to the right on a surface having a coefficient of kinetic friction 0.250 (Figure a). The object has a speed of vi = 2.70 m/s when it makes contact with a light spring (Figure b) that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distance d (Figure c). The object is then forced toward the left by the spring (Figure d) and continues to move in that direction beyond the spring's unstretched position. Finally, the object comes to rest a distance D to the left of the unstretched spring (Figure e).

(a) Find the distance of compression d.
m

(b) Find the speed v at the unstretched position when the object is moving to the left (Figure d).
m/s

(c) Find the distance D where the object comes to rest.
m

2. A toy cannon uses a spring to project a 5.20-g soft rubber ball. The spring is originally compressed by 4.92 cm and has a force constant of 7.93 N/m. When the cannon is fired, the ball moves 14.2 cm through the horizontal barrel of the cannon, and the barrel exerts a constant friction force of 0.032 6 N on the ball.

(a) With what speed does the projectile leave the barrel of the cannon?
m/s

(b) At what point does the ball have maximum speed?
cm (from its original position)

(c) What is this maximum speed?
m/s

A 1.40-kg object slides to the right on a surface having a coefficient of kinetic friction 0.250 (Figure a). The object has a speed of vi = 2.70 m/s when it makes contact with a light spring (Figure b) that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distance d (Figure c). The object is then forced toward the left by the spring (Figure d) and continues to move in that direction beyond the spring's unstretched position. Finally, the object comes to rest a distance D to the left of the unstretched spring (Figure e). Find the distance of compression d. Find the speed v at the unstretched position when the object is moving to the left (Figure d). Find the distance D where the object comes to rest. A toy cannon uses a spring to project a 5.20-g soft rubber ball. The spring is originally compressed by 4.92 cm and has a force constant of 7.93 N/m. When the cannon is fired, the ball moves 14.2 cm through the horizontal barrel of the cannon, and the barrel exerts a constant friction force of 0.032 6 N on the ball. With what speed does the projectile leave the barrel of the cannon? At what point does the ball have maximum speed? What is this maximum speed?

Explanation / Answer

a) 0.5*m*v^2 = u*mgd + 0.5*k*d^2

0.5*1.4*2.7^2 = 0.25*1.4*9.8*d + 0.5*50*d^2

5.103 = 3.43d + 25d^2

d = 0.388m = 38.8cm

b) 0.5*kd^2 = u*mgd + 0.5*mv^2

0.5*50*0.388^2 = 0.25*1.4*9.8*0.388 + 0.5*1.4*v^2

v = 1.864m/s

c) 0.5*1.4*1.864^2 = 0.25*1.4*9.8*D

D = 0.709m = 70.9cm

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