3. (10 pts total) An 0.2 kg steel ball is dropped from rest from a height of 2.4

Question

3. (10 pts total) An 0.2 kg steel ball is dropped from rest from a height of 2.4 m onto a a. What is the speed of the ball just before it strikes the floor? You may neglect air resistance. b. The ball then strikes the floor and bounces back upward at the same speed you found above (but in the opposite directionl) If the ball is in contact with the floor for 0.005 s, what average net force (magnitude and direction) is exerted on the ball during its collision with the floor? c. Find the average normal force (magnitude and direction) exerted by the floor on the ball. 4. (10 pts) A 32 kg child is at rest on a playground swing when the 18 kg family dog unexpectedly jumps horizontally at 5 m/s into her arms, causing the child and dog together to swing back and up. Determine the maximum height to which the child and dog swing after this "collision." When you make use of a conservation principle in your solution, make sure to explicitly state that principle (either in words or as an equation) ^^

Explanation / Answer

Apply conservation of energy

mgh = 1/2 mv^2

v= sqrt 2gh

= sqrt 2 ( 9.8) )(2.4)

=6.858 m/s

(b) from the impulse momentum theorem

Ft = m ( vf- vi)

= 0.2 ( -6.858- 6.858 )

=-2.7434

F = -2.7434/0.005

= -548.685 N

magnitude of average net force 548.685 N direction down ward

(c)

average normal force is

548.685 N ( upward)

(4)

Apply conservation of momentum

m1 u1 + m2 u2 = ( m1 + m2) v

32 (0) + 18 (5) = ( 32 + 18) v

v = 1.8 m/s

height reached by bot girl and dog is

h = v^2/ 2g = ( 1.8)^2/ 2 ( 9.8) = 0.1653 m

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