A heavy rifle initially at rest fires a light bullet.
Which of the following statements about these objects is true?
A. The bullet and rifle both gain the same magnitude of momentum.
B. The bullet and rifle are both acted upon by the same average force during the firing.
C. The bullet and rifle both have the same acceleration during the firing.
D. The bullet and the rifle gain the same amount of kinetic energy.
To determine which statement is true, let's analyze the situation using the principles of momentum, force, acceleration, and kinetic energy.
Momentum: Momentum is defined as the product of an object's mass and velocity. If we consider the initial state of the rifle and bullet as a system at rest, the total momentum is initially zero. When the rifle is fired, the bullet is accelerated forward, acquiring momentum in one direction, while the rifle experiences a backward momentum.
Force: According to Newton's third law of motion, for every action, there is an equal and opposite reaction. When the bullet is propelled forward by the force of the exploding gunpowder, the rifle experiences an equal and opposite backward force. Therefore, the average forces acting on the bullet and rifle are indeed the same.
Acceleration: Acceleration is defined as the change in velocity per unit time. Since the bullet is accelerated forward by the explosion, it gains velocity and leaves the rifle at a high speed. The rifle, however, tends to move backward due to the equal and opposite reaction. The bullet experiences a relatively higher acceleration than the rifle.
Kinetic Energy: Kinetic energy is given by the equation KE = (1/2)mv^2, where m is the mass and v is the velocity of the object. Since the bullet leaves the rifle at a high velocity, it gains kinetic energy during the firing. The rifle, on the other hand, may experience a negligible change in kinetic energy as it moves backward at a slower speed compared to the bullet.
Based on this analysis, the correct statement is:
D. The bullet and the rifle gain a different amount of kinetic energy.
Thus, the bullet gains more kinetic energy than the rifle due to its higher velocity.