Hi aishu,
It will be good if together with the questions, you also show what you tried yourself. Then you will learn better. Anyway, since you asked, let me answer.
1. If speed is doubled, then momentum doubles.
Reason: Momentum = mass * velocity
Speed is magnitude of velocity. So if speed doubles, this means velocity doubles in magnitude and that means momentum doubles in magnitude.
If speed doubles, then kinetic energy becomes 4 times.
Reason: Kinetic energy = 1/2 M v^2
where M = mass, v = speed. As you can see, if v doubles, then v^2 becomes 2^2 i.e. 4 times. Therefore, kinetic energy becomes 4 times.
2. Mass of baseball M1 = 0.145 kg
Mass of bullet M2 = 3.00 g = 3.00 * 10^-3 kg
Speed of bullet v2 = 1.5 * 10^3 m/s
A. Speed of baseball v1 = ?
Momentum of baseball = momentum of bullet
Therefore M1 v1 = M2 v2
Or v1 = M2 v2/M1 = 3.00 * 10^-3 * 1.5 * 10^3/0.145 = 4.5/0.145 = 31.03 m/s
B. Kinetic enegry of baseball K1 = (1/2)M1 v1^2
Kinetic energy of bullet K2 = (1/2)M2 v2^2
M1 v1 = M2 v2
Squaring both sides,
M1^2 v1^2 = M2^2 v2^2
M1 * M1 v1^2 = M2 * M2 v2^2
M1 * 2 * (1/2) M1 v1^2 = M2 * 2 * (1/2) M2 v1^2
M1 * 2 K1 = M2 * 2 K2
Dividing by 2,
M1 * K1 = M2 * K2
K1/K2 = M2/M1
M2 < M1
Therefore K1 < K2
Therefore K2 i.e. kinetic energy of bullet is greater.
Ans: The bullet has greater kinetic energy.
3. Mass M = 0.42 kg
Initial velocity vi = 12 m/s downfield
Final velocity vf = 18 m/s downfield
a. Change in momentum = M(vf - vi)
= 0.42*(18 - 12)
= 0.42 * 6
= 2.52 kg-m/s downfield
Ans: 2.52 kg-m/s downfield
b. Time t = 0.020 s
Let F = force
F = change in momentum/time = 2.52/0.020 = 126 N downfield
4. Not necessary. For a constant force, change in momentum = force * time
So force alone is not sufficient. Time also matters. If both forces act for equal time, then larger force will produce larger momentum. But if larger force acts for smaller time, then which will produce larger momentum depends on what the values of the forces are and for what time they act.
5. The impulse of a force acting on an object is equal to the change in momentum of the object caused by the force.
Cricket
