# Speed of a ball after collision

• Naldo6
In summary, the conversation discusses the collision between a ball and bat, with the same initial speed of 1.9 m/s. It asks for the final speed of the ball after the collision, assuming an elastic collision with no rotational motion and a much larger mass for the bat. It also mentions finding the factor by which the kinetic energy of the ball increases due to the collision. A hint is provided to solve the problem by considering the masses of the ball and bat and taking the limit as the bat's mass tends to infinity.
Naldo6
1. Homework Statement [/b]

A ball and bat, approaching one another each with the same speed of 1.9 m/s, collide. Find the speed of the ball after the collision. (Assume the mass of the bat is much much larger than the mass of the ball and that this is an elastic collision with no rotational motion).

2. Find the factor by which the KE of the ball increases due to the collision.

Could anyone help me?...

Naldo6 said:
A ball and bat, approaching one another each with the same speed of 1.9 m/s, collide. Find the speed of the ball after the collision. (Assume the mass of the bat is much much larger than the mass of the ball and that this is an elastic collision with no rotational motion).

2. Find the factor by which the KE of the ball increases due to the collision.

Hi Naldo6!

Hint: call the mass of the ball m, and the mass of the bat M, solve in the usual way, and then let M/m tend to infinity.

I would approach this problem by using the principles of conservation of momentum and conservation of kinetic energy. In an elastic collision, these two principles state that the total momentum and total kinetic energy of the system before and after the collision remain constant.

To find the speed of the ball after the collision, we can use the equation for conservation of momentum:

m1v1 + m2v2 = m1v1' + m2v2'

Where m1 and v1 represent the mass and initial velocity of the ball, m2 and v2 represent the mass and initial velocity of the bat, and v1' and v2' represent the final velocities of the ball and bat after the collision. Since the mass of the bat is much larger than the mass of the ball, we can assume that m2 is essentially infinite, making the equation simplify to:

m1v1 + m2v2 = m1v1'

Since the initial velocities of the ball and bat are equal (1.9 m/s), we can substitute that value in the equation and solve for the final velocity of the ball:

m1(1.9 m/s) = m1v1'

v1' = 1.9 m/s

Therefore, the speed of the ball after the collision is also 1.9 m/s.

To find the factor by which the kinetic energy of the ball increases due to the collision, we can use the equation for conservation of kinetic energy:

1/2m1v1^2 + 1/2m2v2^2 = 1/2m1v1'^2 + 1/2m2v2'^2

Again, since the initial velocities of the ball and bat are equal and the mass of the bat is much larger, we can simplify the equation to:

1/2m1v1^2 = 1/2m1v1'^2

v1'^2 = v1^2

v1' = v1

Therefore, the kinetic energy of the ball remains the same before and after the collision. The factor by which the KE increases is 1, meaning there is no change in KE.

In summary, the speed of the ball after the collision remains the same at 1.9 m/s and there is no change in kinetic energy. This is consistent with the principles of conservation of momentum and

## What is the definition of speed of a ball after collision?

The speed of a ball after collision refers to the velocity at which the ball is moving immediately after it collides with another object.

## How is the speed of a ball after collision calculated?

The speed of a ball after collision can be calculated using the equation: v = (m1u1 + m2u2) / (m1 + m2), where v is the final velocity, m1 and m2 are the masses of the colliding objects, and u1 and u2 are the initial velocities of the objects.

## What factors affect the speed of a ball after collision?

The speed of a ball after collision can be affected by factors such as the mass and velocity of the colliding objects, the angle and direction of the collision, and the presence of external forces like friction or air resistance.

## Why is the conservation of momentum important in determining the speed of a ball after collision?

The conservation of momentum states that in a closed system, the total momentum before a collision is equal to the total momentum after the collision. This principle is important in determining the speed of a ball after collision because it allows us to calculate the final velocity of the ball based on the initial velocities and masses of the colliding objects.

## How does the speed of a ball after collision impact real-world scenarios?

The speed of a ball after collision can impact real-world scenarios in various ways, such as in sports where the speed of a ball after collision can determine the outcome of a game, or in car accidents where the speed of a vehicle after collision can determine the severity of the impact and potential injuries. Understanding the speed of a ball after collision can also help engineers design safer products and structures.

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