A 57-gram tennis ball moving at 70 miles per hour is hit with a 110-gram tennis racquet moving at 60 miles per hour.
Which statement best compares the total amounts of mass and energy before and after impact?
A. Because the velocities of the ball and racquet are unequal, there is more mass and energy after impact than there is before impact.
B. Because the velocities of the ball and racquet are unequal, there is less mass and energy after impact than there is before impact.
C. Because neither mass nor energy are conserved, the total amounts of mass and energy are different before and after impact.
D. Because mass and energy are both conserved, the total amounts of mass and energy are the same before and after impact.
I think the Answer is D. because all energy is conserved?
D is correct.
Actually, the correct answer is B. Because the velocities of the ball and racquet are unequal, there is less mass and energy after impact than there is before impact. This is due to the principle of conservation of momentum, which states that momentum is conserved in a closed system. In this case, the momentum of the tennis ball and racquet before impact (which is calculated by multiplying mass with velocity) is greater than the momentum after impact. Some of the energy from the initial velocities is transferred and dissipated as heat, sound, and deformation during the collision, resulting in a decrease in mass and energy after impact.
To determine the correct answer, let's break down the question and analyze the situation step by step.
Before impact:
- The tennis ball has a mass of 57 grams, and it is moving at a velocity of 70 mph.
- The tennis racquet, on the other hand, has a mass of 110 grams and is moving at a velocity of 60 mph.
Now, let's consider the conservation of momentum. Momentum is defined as mass multiplied by velocity. According to the law of conservation of momentum, the total momentum before the impact should be equal to the total momentum after the impact.
Before impact:
Total momentum = (57g * 70 mph) + (110g * 60 mph)
After impact:
The ball and racquet will both have changed their velocities due to the impact, but the total momentum should remain the same.
Now, let's consider the conservation of energy. Energy is a scalar quantity that can be transferred from one object to another. In this case, we can consider the kinetic energy before and after the impact.
Before impact:
Total kinetic energy = (1/2 * mass of ball * velocity of ball^2) + (1/2 * mass of racquet * velocity of racquet^2)
After impact:
Due to the impact, some energy will be lost, but the total energy should still be conserved.
Now, comparing the original question to the available answer choices:
A. This statement is incorrect because, according to the conservation of momentum and energy, the total amounts of mass and energy should be conserved.
B. This statement is also incorrect for the same reason as option A.
C. This statement is incorrect because the conservation laws state that both mass and energy are conserved.
D. This statement is correct because both mass and energy are conserved, so the total amounts of mass and energy should be the same before and after the impact.
Thus, the correct answer is D.