Answer:
b) Best explanation is -- both balls have same momentum and hence has equal stings to be felt
Explanation:
The question is ;
A friend tosses a ball to you with a speed V. When you catch the ball , you feel a noticeable sting in your hand, due to the force required to stop the ball.
a0 If you catch the second ball with a mass 2m and speed V/2. is the sting you feel , is greater than. less than or equale to the sting you felt when you caught the first ball ? The time required to stop the two balls is same.
b) Choose the best explanation from among the following;
i) The second ball has less KE, since KE depends on V2, and hence less sting.
ii) The two balls have the same momentum , and hence produce the same sting.
iii) The second ball has more mass and hence produces the greater sting.
<em>Solution:</em>
The momentum can be found from KE = 1/2 m = 1/2
÷ m
= /2m
or KE= /2m
==> P= --- (1)
Now momentum for first ball;
mass = m1=m
Speed V1 = V
and KE = 1/2 m
Putting in eq (1)
==> P1=
==> P1 = mV
Momentum for second ball;
Mass m2= 2m
Speed V2 = V/2
KE = 1/2 m = 1/2 (2m)
=
For momentum putting value of KE and mass m =3m in eq 1;
==> P2 =
==> P2 = mV
So we see that both the balls have same momentum i-e change in momentum is zero - or we can say both ball hit the hand with same force -- hence with same sting to be felt.
b) Best explanation is -- both balls have same momentum and hence has equal stings to be felt