Answer to Question #174906 in Physics for Nicole

Question

1. A ball of mass m = 0.008 kg is placed in a small toy cannon. The cannon is held horizontally and placed on a rough surface. While the ball is traveling the small distance x = 4 cm inside the cannon, it experiences a force shown in the graph above. After leaving the cannon, the ball travels a distance d before coming to rest.

(a) Determine the speed of the ball as it leaves the cannon.

(b) Determine the work done by friction during the stopping of the ball. Be sure to include the correct sign on your answer.

(c) Assume the average frictional force exerted by the rough surface is about 20.0 N. Determine the distance d that the ball will roll before stopping.

(d) If the ball was replaced by a ball which had significantly more mass, but the force exerted on the ball matched the original graph shown above, how will this affect the launch speed of the ball? The launch speed of the greater-mass ball will be…

a) Greater b) Smaller c) The same

Justify your response by referencing work and/or energy principles.

Answer 1

a)

$$0.2(0.008)v^2=0.5(70)(0.04)\\v=29.58\frac{m}{s}$$

b)

$$W=-E\\W=-0.5(70)(0.04)=-1.4\ \ J$$

c)

$$d=\frac{1.4}{20}=0.07\ m$$

d)

$$0.5mv^2=const$$

Answer: b) Smaller