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.
A. is correct
B. would also be correct, except that the equal-magnitude forces are in opposite drections
Well, let's break this down! When the heavy rifle fires a light bullet, there are a few things to consider.
A. The bullet and rifle both gain the same magnitude of momentum. - Not really, my friend. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. The bullet and rifle will have equal magnitudes of momentum, but since the bullet has much less mass, it will have a much greater velocity.
B. The bullet and rifle are both acted upon by the same average force during the firing. - Nope! The force exerted on the bullet may be the same as the force exerted on the rifle, but since the bullet has much less mass, it will experience a larger acceleration.
C. The bullet and rifle both have the same acceleration during the firing. - Ha! Definitely not. Due to the difference in mass, the bullet will experience a greater acceleration. Remember, acceleration is directly proportional to force and inversely proportional to mass.
D. The bullet and the rifle gain the same amount of kinetic energy. - Almost got it! The kinetic energy of an object is given by (1/2)mv^2, where m is the mass and v is the velocity. Since the bullet has a much greater velocity, it will gain more kinetic energy compared to the rifle.
So, my dear friend, the correct answer is D. The bullet and the rifle do not gain the same amount of kinetic energy. Keep those questions coming!
The correct statement is D. The bullet and the rifle gain the same amount of kinetic energy.
Explanation:
According to the law of conservation of momentum, the sum of the initial momenta of the bullet and the rifle is equal to the sum of their final momenta. Since the rifle is initially at rest, its initial momentum is zero. Therefore, the momentum gained by the rifle is equal in magnitude but opposite in direction to the momentum gained by the bullet.
From this, we can conclude that the bullet and the rifle both gain the same amount of momentum but in opposite directions.
However, when it comes to the average force, acceleration, and kinetic energy, the statement is not true.
A. The bullet gains a larger magnitude of momentum than the rifle since the bullet is much lighter and moves with a higher velocity.
B. The average force acting on the bullet is much larger than the average force acting on the rifle, due to its smaller mass and higher acceleration.
C. The acceleration of the bullet is significantly larger than the acceleration of the rifle, again due to the difference in mass.
Therefore, only statement D is true.
To determine which statement is true, let's analyze each option:
A. The bullet and rifle both gain the same magnitude of momentum.
Momentum is defined as the product of an object's mass and velocity. In this scenario, the rifle is much heavier than the bullet and initially at rest. When the rifle fires the bullet, the bullet gains momentum in one direction, while the rifle gains an equal but opposite momentum to conserve the overall momentum of the system. Therefore, statement A is correct.
B. The bullet and rifle are both acted upon by the same average force during the firing.
To determine the average force experienced by an object, we need to consider the change in momentum and the time over which it occurs. Since the bullet gains a significant velocity within a short timeframe, it experiences a larger average force compared to the rifle, which has a smaller velocity change. Thus, statement B is incorrect.
C. The bullet and rifle both have the same acceleration during the firing.
Acceleration is defined as the change in velocity divided by time. Since the bullet and the rifle have different masses, and the same force acts on both objects during the firing, according to Newton's second law of motion (F = ma), their accelerations will be different. Consequently, statement C is incorrect.
D. The bullet and the rifle gain the same amount of kinetic energy.
Kinetic energy is dependent on an object's mass and velocity. Since the bullet gains a higher velocity than the rifle, it will have a greater change in kinetic energy. Therefore, statement D is incorrect.
In conclusion, the only true statement is A. The bullet and rifle both gain the same magnitude of momentum.