Momentum of the Tennis Racket and the Ball

Oct 13, 2025 by windailys.com 18 views

A 0.311 kg Tennis Racket and a 0.0570 kg Ball: An Elastic Collision

In physics, collisions are a fundamental concept that helps us understand the behavior of objects in motion. When two objects collide, they transfer momentum to each other, resulting in a change in their velocities. In this article, we will explore an elastic collision between a tennis racket and a ball. We will use the principles of conservation of momentum and the concept of elastic collisions to determine the velocity of the racket after the collision.

The law of conservation of momentum states that the total momentum of a closed system remains constant over time. In the case of an elastic collision, the total momentum before the collision is equal to the total momentum after the collision. Mathematically, this can be expressed as:

p_{\text{before}} = p_{\text{after}}

where $p$ represents the momentum of an object.

Momentum of the Tennis Racket and the Ball

The momentum of an object is given by the product of its mass and velocity. Let's calculate the momentum of the tennis racket and the ball before the collision.

The momentum of the tennis racket is given by:

p_{\text{racket}} = m_{\text{racket}} \times v_{\text{racket}}

where $m_{\text{racket}}$ is the mass of the tennis racket and $v_{\text{racket}}$ is its velocity.

The momentum of the ball is given by:

p_{\text{ball}} = m_{\text{ball}} \times v_{\text{ball}}

where $m_{\text{ball}}$ is the mass of the ball and $v_{\text{ball}}$ is its velocity.

Given Values

The mass of the tennis racket is $m_{\text{racket}} = 0.311 \, \text{kg}$ .
The velocity of the tennis racket is $v_{\text{racket}} = 30.3 \, \text{m/s}$ .
The mass of the ball is $m_{\text{ball}} = 0.0570 \, \text{kg}$ .
The velocity of the ball is $v_{\text{ball}} = -19.2 \, \text{m/s}$ (note that the velocity is negative because the ball is moving west).

Calculating the Momentum of the Tennis Racket and the Ball

Now that we have the given values, let's calculate the momentum of the tennis racket and the ball.

The momentum of the tennis racket is:

p_{\text{racket}} = 0.311 \, \text{kg} \times 30.3 \, \text{m/s} = 9.43 \, \text{kg m/s}

The momentum of the ball is:

p_{\text{ball}} = 0.0570 \, \text{kg} \times -19.2 \, \text{m/s} = -1.10 \, \text{kg m/s}

Conservation of Momentum in an Elastic Collision

In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision. Mathematically, this can be expressed as:

p_{\text{racket}} + p_{\text{ball}} = p'_{\text{racket}} + p'_{\text{ball}}

where $p'_{\text{racket}}$ and $p'_{\text{ball}}$ are the momenta of the tennis racket and the ball after the collision, respectively.

Solving for the Velocity of the Tennis Racket

Now that we have the momentum of the tennis racket and the ball before the collision, let's solve for the velocity of the tennis racket after the collision.

The total momentum before the collision is:

p_{\text{before}} = p_{\text{racket}} + p_{\text{ball}} = 9.43 \, \text{kg m/s} - 1.10 \, \text{kg m/s} = 8.33 \, \text{kg m/s}

The total momentum after the collision is:

p_{\text{after}} = p'_{\text{racket}} + p'_{\text{ball}}

Since the collision is elastic, the total momentum after the collision is equal to the total momentum before the collision:

p_{\text{after}} = p_{\text{before}} = 8.33 \, \text{kg m/s}

Now, let's solve for the velocity of the tennis racket after the collision. We know that the momentum of the tennis racket after the collision is given by:

p'_{\text{racket}} = m_{\text{racket}} \times v'_{\text{racket}}

where $v'_{\text{racket}}$ is the velocity of the tennis racket after the collision.

Substituting the values, we get:

p'_{\text{racket}} = 0.311 \, \text{kg} \times v'_{\text{racket}}

Since the total momentum after the collision is equal to the total momentum before the collision, we can set up the equation:

p'_{\text{racket}} + p'_{\text{ball}} = p_{\text{before}}

Substituting the values, we get:

0.311 \, \text{kg} \times v'_{\text{racket}} + p'_{\text{ball}} = 8.33 \, \text{kg m/s}

Now, let's solve for the velocity of the tennis racket after the collision. We know that the momentum of the ball after the collision is given by:

p'_{\text{ball}} = m_{\text{ball}} \times v'_{\text{ball}}

where $v'_{\text{ball}}$ is the velocity of the ball after the collision.

Substituting the values, we get:

p'_{\text{ball}} = 0.0570 \, \text{kg} \times v'_{\text{ball}}

Since the collision is elastic, the velocity of the ball after the collision is given by:

v'_{\text{ball}} = -v_{\text{racket}} \times \frac{m_{\text{racket}} - m_{\text{ball}}}{m_{\text{racket}} + m_{\text{ball}}}

Substituting the values, we get:

v'_{\text{ball}} = -30.3 \, \text{m/s} \times \frac{0.311 \, \text{kg} - 0.0570 \, \text{kg}}{0.311 \, \text{kg} + 0.0570 \, \text{kg}}

Simplifying the expression, we get:

v'_{\text{ball}} = -30.3 \, \text{m/s} \times \frac{0.254 \, \text{kg}}{0.368 \, \text{kg}}

Evaluating the expression, we get:

v'_{\text{ball}} = -20.8 \, \text{m/s}

Now that we have the velocity of the ball after the collision, let's substitute the value into the equation:

0.311 \, \text{kg} \times v'_{\text{racket}} + 0.0570 \, \text{kg} \times -20.8 \, \text{m/s} = 8.33 \, \text{kg m/s}

Simplifying the equation, we get:

0.311 \, \text{kg} \times v'_{\text{racket}} - 0.59 \, \text{kg m/s} = 8.33 \, \text{kg m/s}

Adding 0.59 kg m/s to both sides of the equation, we get:

0.311 \, \text{kg} \times v'_{\text{racket}} = 8.33 \, \text{kg m/s} + 0.59 \, \text{kg m/s}

Evaluating the expression, we get:

0.311 \, \text{kg} \times v'_{\text{racket}} = 8.92 \, \text{kg m/s}

Dividing both sides of the equation by 0.311 kg, we get:

v'_{\text{racket}} = \frac{8.92 \, \text{kg m/s}}{0.311 \, \text{kg}}

Evaluating the expression, we get:

v'_{\text{racket}} = 28.7 \, \text{m/s}

In this article, we explored an elastic collision
A 0.311 kg Tennis Racket and a 0.0570 kg Ball: An Elastic Collision - Q&A

In our previous article, we explored an elastic collision between a tennis racket and a ball. We used the principles of conservation of momentum and the concept of elastic collisions to determine the velocity of the racket after the collision. In this article, we will answer some frequently asked questions related to the topic.

Q: What is an elastic collision?

A: An elastic collision is a type of collision in which the total kinetic energy of the system is conserved. In an elastic collision, the objects involved in the collision do not lose any energy, and the total kinetic energy before the collision is equal to the total kinetic energy after the collision.

Q: What is the law of conservation of momentum?

A: The law of conservation of momentum states that the total momentum of a closed system remains constant over time. In the case of an elastic collision, the total momentum before the collision is equal to the total momentum after the collision.

Q: How do you calculate the momentum of an object?

A: The momentum of an object is given by the product of its mass and velocity. Mathematically, this can be expressed as:

p = m \times v

where $p$ represents the momentum of the object, $m$ is its mass, and $v$ is its velocity.

Q: What is the difference between an elastic collision and an inelastic collision?

A: In an elastic collision, the total kinetic energy of the system is conserved, whereas in an inelastic collision, some of the kinetic energy is lost as heat or sound. In an elastic collision, the objects involved in the collision do not lose any energy, whereas in an inelastic collision, the objects involved in the collision lose some energy.

Q: Can you give an example of an elastic collision?

A: Yes, an example of an elastic collision is a collision between two billiard balls. When two billiard balls collide, they bounce off each other, and the total kinetic energy of the system is conserved.

Q: Can you give an example of an inelastic collision?

A: Yes, an example of an inelastic collision is a collision between a car and a wall. When a car collides with a wall, some of the kinetic energy is lost as heat or sound, and the car is damaged.

Q: How do you determine the velocity of an object after an elastic collision?

A: To determine the velocity of an object after an elastic collision, you need to use the principles of conservation of momentum and the concept of elastic collisions. You can use the following equation to determine the velocity of an object after an elastic collision:

v' = \frac{m \times v + m' \times v'}{m + m'}

where $v'$ is the velocity of the object after the collision, $m$ is the mass of the object, $v$ is its velocity before the collision, $m'$ is the mass of the other object, and $v'$ is its velocity after the collision.

Q: What is the significance of the concept of elastic collisions?

A: The concept of elastic collisions is significant because it helps us understand the behavior of objects in motion. Elastic collisions are an important aspect of physics, and they have many practical applications in fields such as engineering, mechanics, and materials science.

In this article, we answered some frequently asked questions related to the topic of elastic collisions. We hope that this article has helped you understand the concept of elastic collisions and its significance in physics. If you have any further questions, please feel free to ask.