Solving AP Physics Problem - Find Total Impulse on 5kg Ball

[aber]

Hey I am in 12 grade but this is advanced placement so its college level... Anyways i could use some help on this problem i have

A 5kg ball initally rest at the edfe of a 2-meter long, 1.2 meter high frictionless tavle, as show above. A hard plastic cude of mass .5kg slides across the table at a speed of 26 m/s and strikes the ball, causing the ball to leave the table in the direction in which the cude was moving. The figure below shows a graph of the force exerted on the ball by the cude as a function of time

graph is:

as time goes from 0-4 seconds, the force rises o-2.0(x10^3 Newtons).
from 4.0-6.0 seconds the F stays at 2.0 (x10^3 Newtons)
6-10 seconds force falls to 0. so it looks like a table /**\ type thing...

Anyways, it wants the total impulse given to the ball?

 

[aber]

i know impulse=change in potentional, or the intengral of dt? i haven't taken calculas yet so i have no idea about derivatives and integrations

 

[Skomatth]

Impulse is F \Delta t

You can easily determine this from the graph, just the same way you get displacement from a velocity vs time graph, or work from a Force vs displacement graph.

 

[aber]

Whats that symbol infront of time... we haven't learned displacement yet...

 

[aber]

nevermind change in time... ok thanks

 

[Skomatth]

F \Delta t is read F delta t and the delta means change in (time for this case). I'm amazed you have learned anything about displacement (maybe you refer to it simply as distance which is a scalar quantity unlike displacement, a vector). But to concentrate on this problem how would you find impulse looking at the graph?

 

[aber]

so i did J=2000(6-4), J=4,000.. so basically area under the FxT graph is the impulse... sasme as area in VxT=distance... next part is to find the horizontal velocity of the ball, which so if i know mv of block, i can use J=change in momentum... so 4000=(26x.5)-(5xV). so Velocity= hm... nevermind that doesn't seem right... i guess we don't know change in momentum

 

[aber]

o wait, wouldn't it be 4000=(.5x26)-(.5v), V=7974... that defiantly isn't right

 

[NateTG]

Do you know any calculus? (oops, nevermind, just saw the inital post.)

The impulse is going to be equal to the area under the force curve in the force-time graph. You can check to make sure that force times time gives units equal to momentum, and be sure to check the scales.