Physics help?

Question

A rubber ball with a mass of 200 g is released from rest from a height of 2.0 m. It falls to the floor, bounces, and rebounds. The graph at right depicts the magnitude of the upward normal force that the floor exerts on the ball at various instants in time. The graph only shows the narrow window of time surrounding the interval when the ball was in contact with the floor. d) What is the impulse on the ball by the floor during the 10 ms the ball is in contact with the floor? e.) What is the impulse on the ball by the earth’s gravitational pull during the same 10 ms? f.) By how much does the ball’s momentum change as a result of this 10-ms period? g.) How high does the ball rebound?

Link to graph needed:
http://i179.photobucket.com/albums/w298/simplestarlight/49794.jpg

Answer 1

What happened to parts a.) through c.) ? Nevertheless ---

The ball rebounds to a height of (approximately) 1.62 metres.

Here is how this was found:

d.) The impulse is the area under the curve, that is 0.005 x 480 Ns

= 2.4 Ns.

e.) The "impulse" of the earth's gravitational pull on the ball of mass 200 g (= 0.200 kg) during that same 10ms (= 0.10 s) is simply the CONSTANT mg times (0.010s) = 0.200 (9.8) (0.010) Ns.

= 0.0196 Ns.

f.) The ball's momentum will therefore change by (2.4 - 0.0196) Ns

= 2.3804 Ns.

g.) The ball was released from a height of 2.0 m. Using v^2 = 2gh, it hit the ground with speed v given by:

v = sqrt [2(9.8) 2.0] = 6.260990337... m/s

Its downward momentum is 0.200 v kg m/s = 1.252198067... Ns.

Thus it returns upward with momentum (2.3804 - 1.252198067...) Ns

= 1.128201933... Ns, therefore with an UPWARD speed of

1.128201933.../0.200 m/s = 5.641009665... m/s.

(Phew! At least it's a bit LESS than the original downwards speed. That's good!)

Using v^2 = 2 g h again, the height h reached will be:

h = v^2 / (2g) = 1.6235199... m.

Frankly, the given data (plus my use of 9.8 m/s^2 for ' g ') doesn't justify more than two sig. figs., but I'll give you three anyway:

The ball rebounds to a height of (approximately) 1.62 metres.

Live long and prosper.