Calculating Impulse & Kinetic Energy of Collision

[dbb2112]

A 5 kilogram ball initally rests at the edge of a 2 meter long, 1.2 meter high frictionless table. A hard plastic cube of mass .5 slides across the table at a speed of 26 meters per second and strikes the ball, causing the ball to leave the table in the direction in which the cube was moving.

a. Determine the total impulse given to the ball.
b.Determine the horizantal velocity of the ball immediately after the collission.
c.Determine the following for the cuble immediatley after the collision.
i. its speed
i. its direction of travel if moving
d determine the kinetic energ dissipated in the collision
e. determine the distance beween the two points of impact of the objects with the floor

 

[tiny-tim]

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Hi dbb2112! Welcome to PF!

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[thomate1]

a. The total impulse given to the ball can be calculated using the formula Impulse = Change in Momentum. In this case, the change in momentum is equal to the mass of the ball (5 kg) multiplied by the final velocity of the ball after the collision. Since the ball leaves the table with a horizontal velocity, the total impulse can be calculated as follows:

Impulse = 5 kg * (final velocity of the ball)

b. The horizontal velocity of the ball immediately after the collision can be calculated using the formula Momentum = Mass * Velocity. Since the only force acting on the ball is the impulse from the collision, the final momentum of the ball will be equal to the impulse calculated in part a. Therefore, the horizontal velocity of the ball can be calculated as:

Momentum = 5 kg * (final velocity of the ball)

c. After the collision, the cube will continue to move in the same direction as it was before the collision. Therefore, its direction of travel will remain the same. The speed of the cube can be calculated using the formula Momentum = Mass * Velocity. Since the momentum before and after the collision will be the same, the speed of the cube can be calculated as:

Momentum = 0.5 kg * 26 m/s = 13 kg m/s

d. The kinetic energy dissipated in the collision can be calculated using the formula Kinetic Energy = 1/2 * Mass * Velocity^2. The initial kinetic energy of the cube can be calculated as:

Kinetic Energy = 1/2 * 0.5 kg * (26 m/s)^2 = 169 J

After the collision, the kinetic energy of the cube will be dissipated and transferred to the ball. Therefore, the kinetic energy dissipated in the collision can be calculated as:

Kinetic Energy Dissipated = 169 J - Final Kinetic Energy of the ball

e. The distance between the two points of impact of the objects with the floor can be calculated using the formula Distance = 1/2 * Acceleration * Time^2. Since the objects are falling due to gravity, the acceleration can be taken as 9.8 m/s^2. The time can be calculated using the formula Time = Square Root (2 * Height / Acceleration). Therefore, the distance between the two points of impact can be calculated as:

Distance = 1/2 * 9.8 m/s^2 * (