A rock is dropped from the top of a tall tower. Half a second later another rock, twice as massive as the first, is dropped. Ignoring air resistance,
(A) the distance between the rocks increases while both are falling.
(B) the acceleration is greater for the more massive rock.
(C) they strike the ground more than half a second apart.
(D) they strike the ground with the same kinetic energy.
not B: g is constant
bot C: they both take the same time to fall
not D: KE = 1/2 mv^2. Bigger m has bigger KE
Let's dive into this question with a pinch of humor, shall we?
(A) The distance between the rocks increases while both are falling. Well, technically, yes, but at the same time, both rocks are getting closer to the ground. So it's like a long-distance relationship - they might get a little farther apart, but they're ultimately heading towards the same destination.
(B) The acceleration is greater for the more massive rock. Absolutely! The more massive rock is like that friend who never skips leg day at the gym. It has more inertia, so gravity pulls on it harder. Talk about having a "heavy" workout session!
(C) They strike the ground more than half a second apart. Nope! Gravity treats all objects the same, regardless of their mass. Both rocks will fall at the same rate, so they will hit the ground at the same time. Kind of like synchronized falling, if you will.
(D) They strike the ground with the same kinetic energy. You got it! Although the more massive rock has more gravitational potential energy due to its higher mass, both rocks will convert that potential energy into kinetic energy as they fall. So when they hit the ground, they will have the same kinetic energy. It's like they have a fair competition of energy conversion!
So, my final answer here is (D) they strike the ground with the same kinetic energy. Keep on rockin' those physics questions!
(A) The distance between the rocks increases while both are falling.
When two objects of different masses are dropped from the same height, they will both accelerate towards the ground due to the force of gravity. However, the more massive rock will experience a greater force of gravity and thus accelerate at a faster rate. This means that the more massive rock will "catch up" to and eventually pass the less massive rock.
Therefore, the distance between the rocks increases as they fall.
(B) The acceleration is greater for the more massive rock.
According to Newton's second law of motion (F = ma), the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. In this case, the force acting on each rock is the force of gravity, which is the same for both rocks.
Since the more massive rock has a greater mass, it will experience a greater force of gravity and thus a greater acceleration compared to the less massive rock.
(C) They strike the ground more than half a second apart.
The time it takes for an object to fall freely from a given height can be determined using the equation d = 0.5 * g * t^2, where d is the distance, g is the acceleration due to gravity, and t is time.
In this case, the distance fallen by the first rock during the first 0.5 seconds is given by d1 = 0.5 * g * (0.5)^2.
The distance fallen by the second rock during the first 0.5 seconds is given by d2 = 0.5 * g * (0.5)^2 as well, since both rocks were dropped at the same height.
Therefore, both rocks will have fallen the same distance by the time the second rock is dropped. Thus, they will strike the ground at the same time and not more than half a second apart.
(D) They strike the ground with the same kinetic energy.
The kinetic energy of an object is given by the equation K = 0.5 * m * v^2, where K is the kinetic energy, m is the mass, and v is the velocity.
When the rocks strike the ground, they will both have the same velocity as they have fallen the same distance. The velocity is determined by the height from which the rocks were dropped and is independent of mass.
Since both rocks have the same velocity, the kinetic energy will be the same, as the mass is the only variable in the equation.
Therefore, they will strike the ground with the same kinetic energy.
In conclusion, the correct answers are:
- (A) The distance between the rocks increases while both are falling.
- (B) The acceleration is greater for the more massive rock.
- (C) They strike the ground more than half a second apart.
To answer this question, we can apply the laws of motion and the principles of free-fall. Let's analyze each statement separately:
(A) The distance between the rocks increases while both are falling.
This statement is false. When objects are dropped from the same height simultaneously and experience the same acceleration due to gravity, their vertical positions will remain the same throughout their fall. Therefore, the distance between the rocks will not change.
(B) The acceleration is greater for the more massive rock.
This statement is false. In the absence of air resistance, all objects near the Earth's surface fall with the same acceleration due to gravity, which is approximately 9.8 meters per second squared. Thus, the acceleration experienced by both rocks is the same.
(C) They strike the ground more than half a second apart.
This statement is true. The time it takes for an object to fall from a certain height is determined by the formula t = sqrt(2h/g), where t represents time, h represents the initial height, and g is the acceleration due to gravity. Since the second rock is dropped half a second after the first rock, it will have less time to fall before reaching the ground. Therefore, the two rocks will strike the ground more than half a second apart.
(D) They strike the ground with the same kinetic energy.
This statement is false. The kinetic energy of an object is calculated using the formula KE = (1/2)m*v^2, where KE represents kinetic energy, m represents mass, and v represents velocity. Since the second rock is twice as massive as the first rock, it will have more kinetic energy when it reaches the ground due to its greater mass.
In conclusion, the correct answers are (C) They strike the ground more than half a second apart, and (D) They strike the ground with different kinetic energy.