A small ball is set in horizontal motion by rolling it with a speed of 3.00 m/s across a room 12.0m long, between two walls. Assume that the collisions made with each wall are perfectly elastic and that the motion is perpendicular to the two walls. (a)Show that the motion is perpendicular, and determine its period. (B) Is this motion simple harmonic? explain
The motion is not harmonic, as the velocity is constant, and acceleration for most of the time is zero.
Period? How long does it take to travel 12 m? That is one half the period, right/
To determine the period of the motion, we need to first understand the motion of the ball between the two walls.
(a) To show that the motion is perpendicular, we can use the fact that the collisions with the walls are perfectly elastic. This implies that the angle of incidence is equal to the angle of reflection.
Assuming the ball starts from one wall and moves towards the other, it will collide with the second wall and bounce back towards the first wall. During this process, the motion of the ball is perpendicular to the walls, as the angle of incidence and reflection are equal.
Now, let's proceed to determine the period of the motion.
The distance traveled by the ball between the two walls is 12.0m, and we know that the speed of the ball is 3.00 m/s.
The time taken to travel a certain distance can be calculated using the formula:
Time = Distance / Speed
Therefore, the time taken for the ball to travel from one wall to the other is:
Time = 12.0 m / 3.00 m/s = 4.00 s
Since the period of motion is the time taken for one complete cycle, half of the time between the two walls is considered one-half period.
Thus, the period of the motion of the ball is:
Period = 2 * Time = 2 * 4.00 s = 8.00 s
(b) No, this motion is not simple harmonic. Simple harmonic motion (SHM) is characterized by the oscillation of an object between two extreme positions, with a restoring force proportional to the displacement from the equilibrium position.
In this case, the motion of the ball between the two walls is not oscillatory but rather a linear motion back and forth. The velocity of the ball is constant, and there is no restoring force acting on it. Therefore, it does not exhibit the characteristics of simple harmonic motion.