Question

If you now catch a second ball, with a mass 2m and speed v/2, is the sting you feel greater than, less than, or equal to the sting you felt when you caught the first ball? The time required to stop the two balls is the same.

Answer 1

Complete Question:

A friend tosses a ball of mass m 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.

(Part A)

If you now catch a second ball, with a mass 2m and speed v/2, is the sting you feel greater than, less than, or equal to the sting you felt when you caught the first ball? The time required to stop the two balls is the same

1-greater than the sting you felt when you caught the first ball

2-less than the sting you felt when you caught the first ball  

3-equal to the sting you felt when you caught the first ball

(Part B)

Choose the best explanation from among the following

1-The two balls have the same momentum, and hence they produce the same sting

2-The second ball has less kinetic energy, since kinetic energy depends on v2, and hence it produces less sting.

3-The second ball has more mass, and hence it produces the greater sting.

Answer:

Part A: 3) Equal to the sting you felt when you caught the first ball

Part B: 1) The two balls have the same momentum, and hence they produce the same sting

Explanation:

Momentum is the product of mass and velocity. If the initial ball has a momentum that equals the final ball, the sting you feel when you catch both balls will be the same.

Initial momentum = mv

Final momentum = 2m * v/2

Final momentum = mv

Since initial momentum = Final momentum, the two balls will produce the same sting.

Answer 2

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.

Solution:

The momentum can be found from KE = 1/2 m$V^{2}$ = 1/2  $(mV)^{2}$ ÷ m

= $P^{2}$/2m

or KE= $P^{2}$/2m

==> P= $\sqrt{KE (2m)}$  --- (1)

Now momentum for first ball;

mass = m1=m

Speed V1 = V

and KE = 1/2 m$V^{2}$

Putting in eq (1)

==> P1= $\sqrt{\frac{1}{2} m V^{2} (2m)}$

==> P1 = mV

Momentum for second ball;

Mass m2= 2m

Speed V2 = V/2

KE = 1/2 m$V2^{2}$ = 1/2 (2m) $(V/2)^{2}$ = $\frac{mV^{2} }{4}$

For momentum putting value of KE and mass m =3m in eq 1;

==> P2 = $\sqrt{\frac{mV^{2} }{4} } (2(2m))$

==> 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