Problem 30 - College Physics

Question

A tennis ball traveling horizontally at 22 \(\mathrm{m} / \mathrm{s}\) suddenly hits a vertical brick wall and bounces back with a horizontal velocity of 18 \(\mathrm{m} / \mathrm{s}\) . Make a free-body diagram of this ball (a) just before it hits the wall, (b) just after it has bounced free of the wall, and (c) while it is in contact with the wall.

Step-by-Step Solution

Answer

The forces are gravity before impact, gravity after rebound, and both gravity and a normal force during contact with the wall.

Step 1: Determine the Forces on the Ball Just Before Impact

Before the tennis ball hits the wall, it is only subjected to the force of gravity acting downward. Therefore, the free-body diagram will simply show a force vector pointing downward, labeled as weight (W), due to gravity.

Step 2: Identify Forces After the Ball Bounces Off the Wall

Once the ball has bounced off the wall, it still experiences gravity pulling it downward. Additionally, the ball now moves horizontally in the opposite direction. The only force is the weight due to gravity, so the free-body diagram is the same as before impact: a force vector pointing downward labeled as weight (W).

Step 3: Analyze Forces While the Ball is in Contact with the Wall

During impact with the wall, and while the ball is in contact, two forces act on it: the normal force exerted by the wall (horizontally opposite to the ball's velocity) and the gravitational force acting downward. In the free-body diagram, show a downward force vector labeled as weight (W) and a horizontal force vector pointing back from the wall labeled as normal force (N).

Key Concepts

Forces in Physics

Forces are fundamental to understanding motion and dynamics in physics. They can be described as interactions that change the motion of an object. In the case of a tennis ball, several critical forces are at play, and understanding these helps to create an accurate free-body diagram.

• Gravitational Force: This is a constant force acting downward on the ball, proportional to its mass and acceleration due to gravity. It is represented in all scenarios, whether the ball is in motion or at rest.
• Normal Force: This force comes into play when the ball contacts a surface, such as the wall in this scenario. It acts perpendicular to the surface, counteracting the inward motion or keeping the ball from penetrating the wall.

Understanding these forces helps in solving problems related to motion and predicting future movement. They set the groundwork for building more complex physics concepts like energy, momentum, and force interactions.

Impact Dynamics

Impact dynamics focuses on the study of collisions and interactions between objects, like the ball hitting the wall. When the tennis ball hits the wall, several processes occur instantaneously.

During the impact:

• The ball's horizontal velocity rapidly changes direction – from moving towards the wall to rebounding away from it.
• This change in direction is due to the normal force exerted by the wall. It's crucial to note that the impact doesn't affect the vertical component of the motion, which is still influenced by gravity.

The analysis of impact dynamics involves understanding how forces like the normal force influence the ball's motion direction and speed. This knowledge is essential for applications ranging from simple games to complex vehicle safety systems.

Motion Analysis

Motion analysis involves studying an object's movement through space and understanding how different forces impact this movement. In our example of the tennis ball, motion analysis helps us track its trajectory before, during, and after contact with the wall.

Some key points about analyzing the ball’s motion:

• Pre-impact Motion: The ball is moving horizontally with a uniform velocity of 22 m/s while being pulled downward by gravity.
• Impact Motion: While in contact with the wall, the ball experiences a sudden change in horizontal velocity but maintains a constant downward velocity due to gravity.
• Post-impact Motion: After bouncing off the wall, the horizontal velocity direction changes, and the speed reduces to 18 m/s. Gravity continues to act on the ball.

Analyzing these motions provides insights into how forces modify velocity and how energy is transferred during collisions. This analysis is vital for designing protective gear, optimizing sports techniques, and enhancing robotics dynamics.