A train is traveling along a straight, horizontal track at a constant speed of 20 mph (i.e.,a non-relativistic speed). An observer on the train places paint cans at the front and back of one of the cars. She then detonates the cans. Due to a malfunction, the can at the front explodes 0.1 seconds before the can at the back.
The distance between the paint marks on the train is
A. greater than the length of the train car
B. less than the length of the train car
C. equal to the length of the train car
The distance between the paint marks on the track is
A. greater than the length of the train car
B. equal to the length of the train car
C. less than the length of the train car
1 C
2 less, maybe you run over the mark from the first one on the track just as the rear can explodes, and the two marks on the track are together :)
To solve this problem, let's first analyze the situation.
Since the train is moving at a constant speed, we can assume that any event that occurs inside the train is observed as if the train were at rest. This is due to the principle of relativity in classical mechanics.
Given that the detonation time difference is 0.1 seconds, we need to determine how far the train travels in that time.
The distance traveled by an object moving at a constant speed can be calculated using the formula:
Distance = Speed x Time
In this case, the distance traveled by the train in 0.1 seconds is:
Distance = 20 mph x 0.1 seconds
To ensure that our units are consistent, let's convert the speed from mph to feet per second:
1 mph = 1.47 ft/s
Substituting this value, we have:
Distance = 20 mph x 1.47 ft/s x 0.1 seconds
Simplifying the expression:
Distance = 2.94 ft
Therefore, in 0.1 seconds, the train travels a distance of 2.94 feet.
Given that the observer places paint cans at the front and back of one of the cars, the distance between these two paint marks on the train is equal to the length of the train car.
Therefore, the distance between the paint marks on the train is equal to the length of the train car, which means the answer is Option C.
Now let's consider the distance between the paint marks on the track.
Since the observer in the train perceives the train as being at rest, the time difference between the detonation at the front and back of the train is purely due to the time it takes for sound to travel from the front to the back of the train car.
The speed of sound in air is approximately 1,125 ft/s. Using this value, we can calculate the distance the sound wave travels during the 0.1-second time difference:
Distance = Speed x Time = 1,125 ft/s x 0.1 seconds = 112.5 ft
Therefore, the distance between the paint marks on the track is equal to the distance the sound wave travels, which is 112.5 feet.
Based on this calculation, the answer is Option A, as the distance between the paint marks on the track is greater than the length of the train car.