Question

A ball weights 0.5kg hit a table at 12.27m/s,the table is rigid and weights 4kg with a length of 2 meters between the support points a and b and 1 meter from the floor. If the ball has a coefficient of restitution of 0.75. How i can obtain the impulse transferred to the table and impulse at support points?

Answer 1

drawing?

Answer 2

that's just lazy. is the ball being dropped vertically down onto the table?

do you have an idea as to why that might be a relevant question?

Answer 3

Not its not being dropped vertically, and no i don't why it could be relevant can you please explain me?

Answer 4

if ball is dropped straight down on table, there is little to do here. because C = .75, we know the ball will bounce back up with velocity 12.27 * .75 and that the table will experience an impulse equal and opposite to he impulse on the ball. I = F dt = m dv = 0.5 * 12.27 * 1.75 = 10.74.

but table does not move, no transfer of momentum to table.

however, if the ball hits the table at some unknown angle then its more complicated.

assuming a smooth table is wrong assumption, i believe, as no momentum is transferred from ball to table in horizontal direction whilst you have been given table's mass, presumably to calculate how much momentum it acquires from the collision with the ball.

i have worked out the **net impulse** on ball, and the table, given the various inputs (plus coefficient restitution and conservation momentum laws) and i get this, where x' and y' are the initial horizontal and downward vertical components of the balls velocity:
\[I = \sqrt{(\frac{x'}{8})^{2} + (\frac{ 7y'}{8})^{2}}\]

it is clear to me from this that you need to know the angle to do this, certainly as i see it being done.

the fact that (x')^2 + (y')^2 = 12.27^2 does not help move this forward.

Answer 5

Thanks for all your patience and effort to help me trough this. Cold you help me out by explaining the steps for solve the problem if a angle is given? Lets say a 35 degree or any other angle will work, since i really need to understand how to approach such problems.

Answer 6

no worries.

make it 30 or 60 as the trig ratios are better?

Answer 7

Yeah sure you can use 30.

Answer 8

here is the working plus a calc at the end assuming 30deg.

i hope it is clear - and that you do not find any mistakes(!!!).

let me know if this is at all helpful.

Answer 9

Looks great for me. My only doubt is the value for c = 3/4, how did you obtained it?

Answer 10

**If the ball has a coefficient of restitution of 0.75.**

ie i took it from the question.

pls let me know if you find any errors. thanks.