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Spring Compression, Speed and Distance

6. [SJ3 7.P.024.] A toy cannon uses a spring to project a 5.30 g soft rubber ball. The spring is originally compressed by 5.00 cm and has a force constant of 7.80 N/m. When it is fired, the ball moves 16.0 cm through the horizontal barrel of the cannon, and a constant frictional force of 0.0320 N exists between barrel and ball.

(a) With what speed does the projectile leave the barrel of the cannon?
(b) At what point does the ball have maximum speed?
cm (from the starting position)
(c) What is this maximum speed?

[SJ3 7.P.050.] A 1.50 kg object slides to the right on a surface having a coefficient of kinetic friction = 0.250 (Fig. P7.50). The object has a speed of vi = 3.50 m/s when it makes contact with a light spring that has a spring constant of k = 50.0 N/m. The object comes to rest after the spring has been compressed a distance d. The object is then forced toward the left by the spring 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 P7.50

(a) Find the distance of compression d.
(b) Find the speed v at the unstretched position when the object is moving to the left.
(c) Find the distance D.

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Solution Preview

Here is the answer to the first question in the set.

Energy placed into the ball by the compression of the spring is 1/2 kx^2 where x is the compression of the spring in meters. This energy is then 1/2 7.8 N/m x (5 x 10^(-2)m)^2 = 0.00975 J
The work done by the frictions is the force x the distance in which it acts ...

Solution Summary

This solution is provided in 766 words and attached in a .doc file. It uses concentration at equilibrium expressions to find the speed and distance. Coefficient of friction and work equations are also used to determine speed and distance.