A tennis ball of mass= 0.058 kg and speed= 19 m/s strikes a wall at a 45 degree angle and rebounds with the same speed at 45 degrees.
1. What is the magnitude of the impulse given to the ball?
2. What is the direction of the impulse given to the ball?
To find the magnitude and direction of the impulse given to the ball, we need to understand the concepts of impulse and momentum.
1. Impulse is defined as the change in momentum of an object. Momentum is the product of an object's mass and its velocity. The equation for impulse is given by:
Impulse = Change in momentum = Final momentum - Initial momentum
Since the mass and speed of the ball remain the same in this situation, the final and initial momenta will have the same magnitude. Therefore, the magnitude of the impulse given to the ball is equal to the magnitude of its initial momentum, which can be calculated using the equation:
Momentum = mass * velocity
Initial momentum = 0.058 kg * 19 m/s
Therefore, the magnitude of the impulse is 1.102 N·s.
2. The direction of the impulse given to the ball is perpendicular to the direction of the change in momentum. In this case, the ball strikes the wall at a 45-degree angle and rebounds with the same speed at a 45-degree angle. As the direction of the velocity changes during the collision, the direction of the impulse will be opposite to the initial momentum. Since the initial momentum points towards the wall, the direction of the impulse will be away from the wall.
Therefore, the direction of the impulse given to the ball is away from the wall.
To find the magnitude of the impulse given to the ball, we can use the principle of conservation of momentum.
1. First, let's find the initial momentum of the ball before it strikes the wall. The initial momentum is given by the product of the mass and velocity:
Initial momentum = mass x velocity
= 0.058 kg x 19 m/s
= 1.102 kg·m/s
2. Next, let's find the final momentum of the ball after it rebounds off the wall. Since the ball rebounds with the same speed and at the same angle, the magnitude of the final momentum is the same as the initial momentum, but the direction is reversed:
Final momentum = -1.102 kg·m/s
3. The impulse given to the ball can be calculated by subtracting the initial momentum from the final momentum:
Impulse = Final momentum - Initial momentum
= -1.102 kg·m/s - 1.102 kg·m/s
= -2.204 kg·m/s
The magnitude of the impulse given to the ball is 2.204 kg·m/s.
Now let's find the direction of the impulse given to the ball.
4. The direction of the impulse is given by the direction of the change in momentum. Since the momentum changes from positive (initial momentum) to negative (final momentum), the direction of the impulse is in the opposite direction.
Therefore, the direction of the impulse given to the ball is opposite to the direction of its initial motion, which is the angle of approach (45 degrees).
Note: The negative sign in the magnitude indicates a change in direction.
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