2 Question involving momentum and collisions

[DWigs87]

Please Help! 2 Question involving momentum and collisions

Just some questions in calc-based physics. Thanks in advance.

1) A 25 kg child is in a 10 kg sled that travels 1 m/s east on ice. The child throws a 3 kg snowball at 40 m/s at an angle of 50 degrees north of east. Find the velocity of the sled after the snowball leaves the child’s hand.

2) Cube B is at rest on the edge of a frictionless horizontal table that is 5 m above the ground. It has a mass of 5 kg. Cube A, with a mass of 20 kg travels towards it at 20 m/s. The two cubes collide and the force that cube A exerts on B during the collision is given by F(t)=3x10^6t-2x10^8t^2 i (N). The collision lasts 10 milliseconds.

a) Find the velocity of cube B immediately after the collision
b) Find the velocity of cube A immediately after the collision
c) Find the coefficient of restitution for the collision
d) Find the speed with which each cube hits the ground

 

[Päällikkö]

Do show what you've tried.
https://www.physicsforums.com/showthread.php?t=94379
https://www.physicsforums.com/showthread.php?t=5374

 

[DWigs87]

Oh, i c. Sorry, I didn't see that.

1) I know that the problem deals with the conservation of momentum equation (Pi=Pf) broken down into x and y components. For the X component, I get the following equation

38(1)=35(Vfx)+3(40cos50)

But I'm not too sure about the y component. I know what to do after they are both obtained though

r=sqrt(Pfx^2+Pfy^2)
Theta=tan^-1(Pfy/Pfx)

2)
a + b) The way you obtain velocity from a force function is by integrating it to find the impulse since it's defined as MdeltaV/deltaT, correct? I have the general idea of these two, but I'm not sure where to put the numbers when it comes down to solving for the velocities.
c) I never really learned this; maybe it was covered when I didn't attend lecture (one of the prime reasons why I'm having so much trouble with this section; I've had several problems in my family recently), but I truly have no idea about the concept of the coefficient of restitution. I tried looking it up online, but that made me even more confused. I'd appreciate if someone could explain this to me.
d) I'd like to think this last part comes from simple kinematics, modeled by a free fall equation(s), but then comes the problem of finding V0 for both the blocks, which I couldn't figure out when I tried to form just an equation to solve for the problem, even if I didn't have any numbers (this didn't turn out too successfully)

Hopefully the above suffices.

Thanks a lot for your help.

 

[DWigs87]

Bump

Sorry, I'm probably being very impatient...

 

[Kelju Ivan]

1) You can solve easily solve the momentum of the snowball. Then you need to solve its y component with the help of sine. Because momentum is conserved, the net y-component for the whole system must be zero, so the sled gets an equal but opposite increase in momentum (towards south). Of course this also applies to the x-direction and thus the sled is slowed a bit in the east-west-axis.

2) a&b) Because you know both blocks' mass and velocity, you can solve their momentums. When you integrate the force function from t=0 to t=10ms you get the impulse that B gives to A (so A's momentum increases by an amount while B's momentum decreases by that same amount). Now just add these to their initial momentums and solve the speeds.

c) I've never heard that term, so I can't help you there.

d) Because there is no friction the blocks move at constant speed after the collision and will keep that same horizontal speed after they fall of the table. Now you just need to find out how long it takes them to fall down that 5 meters when their initial vertical speed is 0. Using the equation v=gt will then provide you with their final vertical speeds. Now you just combine the x- and y-components.

 

[DWigs87]

I think I got it now; thanks a lot for the help!