Two pucks are on an ice rink. The mass of the second puck is 4 * the mass of the

Question

Two pucks are on an ice rink. The mass of the second puck is 4 * the mass of the first.

Both pucks start from rest and are pushed by the same force for the same amount of time.

a. What is the ratio of the momentum of the second puck to the momentum of the first after the pushing is done (p2/p1)?

b. What is the ratio of the velocity of the second puck to the speed of the first after the pushing is done (v2/v1)?

Now, instead, let's say that both pucks start from rest and are pushed by the same force over the same distance.

c. What is the ratio of the kinetic energy of the second puck to the kinetic energy of the first after the pushing is done (K2/K1)?

d. What is the ratio of the velocity of the second puck to the speed of the first after the pushing is done (v2/v1)?

Explanation / Answer

v=1/2*at F=ma F/m*1/2*t=v momentum is m*v. mv=F/m*1/2*t*m=F*1/2*t momentum is independent of mass (we could also find this by Ft=momentum) so 1. b. velocity = 1/4. c. 1/2*m*v^2=KE vf^2=2ad for 1st: 1/2*m*2ad for 2nd: 1/2*4m*2ad remember a is F/m. So: 1/2*m*2*F/m*d and 1/2*4m*2*F/(4m)*d So KE is the same. (also can be done by F*d=Energy, force is the same, distance is the same). If KE's are the same: 1/2*4m*(v1)^2=1/2*m*(v2)^2 4*v1^2=v2^2 2v1=v2 2:1 (my v1 and v2 are likely backwards from yours)

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