a superball of mass .125 kg is dropped onto a concrete floor from a height of 1m it bounces back at a height of .9m. What is the net force acting on the ball before and after its released? Work done by the net force while the ball is falling until just before it hits the floor. What is the change in potential energy during the fall? What is the kenetic energy of the ball just before it hits? Find the potential energy of the ball at the top of its bounce? How much mechinical energy is lost during the bounce? The the momentum of the ball just before it hits the floor? find the momentum of the ball just after it leaves the floor on the return bounce. What is the impulese delivered to the floor by the ball? What is the impulse delivered to the ball by the floor?
To answer these questions, let's break it down step by step:
1. Net force before release: When the ball is held at a height of 1m, the net force acting on it is equal to its weight. The weight can be calculated using the formula: weight = mass * gravity. Considering the mass of the ball is 0.125 kg and gravity is approximately 9.8 m/s^2, the net force before release is given by: net force = weight = 0.125 kg * 9.8 m/s^2.
2. Net force after bounce: After bouncing back at a height of 0.9m, the net force will again be equal to the weight of the ball, as there is no vertical movement at the top of the bounce. Therefore, the net force is the same as before release.
3. Work done by net force during fall: The work done by the net force while the ball is falling is equal to the change in potential energy. The potential energy formula is: potential energy = mass * gravity * height. The change in potential energy can be calculated as the difference between the potential energy at the starting height and the potential energy just before hitting the floor.
4. Change in potential energy during the fall: The change in potential energy can be found using the above formula for potential energy by subtracting the final potential energy from the initial potential energy.
5. Kinetic energy just before hitting: The kinetic energy of the ball just before it hits the floor is equal to the potential energy it had just before release. This is due to the conservation of mechanical energy, as there is no work done by forces other than gravity.
6. Potential energy at the top of its bounce: The potential energy at the top of its bounce is equal to the kinetic energy it had just before hitting the floor. This once again follows the principles of conservation of mechanical energy.
7. Mechanical energy lost during the bounce: The mechanical energy lost during the bounce can be calculated by finding the difference between the potential energy at the top of the bounce and the potential energy just before release.
8. Momentum just before hitting the floor: The momentum just before hitting the floor can be calculated using the formula: momentum = mass * velocity. The velocity can be found using the equation for conservation of mechanical energy by substituting the value of potential energy just before hitting the floor into the formula for potential energy.
9. Momentum just after leaving the floor on the return bounce: The momentum just after leaving the floor on the return bounce can be found using the same formula as above. However, instead of using the potential energy just before hitting the floor, we use the potential energy at the top of the bounce.
10. Impulse delivered to the floor: Impulse is defined as the change in momentum. The impulse delivered to the floor is equal to the change in momentum of the ball just before hitting the floor.
11. Impulse delivered to the ball: Similarly, the impulse delivered to the ball by the floor is equal to the change in momentum of the ball just after leaving the floor on the return bounce.
By following these steps and performing the necessary calculations, all the quantities you asked for can be determined.
To find the net force acting on the ball before and after it is released, we can use Newton's second law:
F = m * a
where F is the force, m is the mass of the ball, and a is the acceleration.
1. Before the ball is released:
Since the ball is just about to be released, the only force acting on it is its weight (mg), where g is the acceleration due to gravity (approximately 9.8 m/s^2). Therefore, the net force acting on the ball before it is released is:
F = m * g
F = 0.125 kg * 9.8 m/s^2
F ≈ 1.225 N (Newtons)
2. After the ball is released:
When the ball is released, it starts falling under the force of gravity. The net force acting on the ball while falling is the weight of the ball minus the force of air resistance (which we'll assume is negligible). So, the net force can be calculated as:
F = m * (g - a)
F = 0.125 kg * (9.8 m/s^2 - 0 m/s^2)
F ≈ 1.225 N
The work done by the net force while the ball is falling until just before it hits the floor can be calculated using the formulas:
Work = Force * Distance * cos(θ)
Since the ball is falling downward, the angle θ between the direction of force and displacement is 180 degrees. The distance is the height the ball falls, which is 1m. Plugging in the values:
Work = 1.225 N * 1 m * cos(180 degrees)
Work = -1.225 joules
Note that the negative sign indicates that work is done against the force of gravity.
The change in potential energy during the fall can be calculated using the formula:
ΔPE = m * g * Δh
where ΔPE is the change in potential energy, m is the mass of the ball, g is the acceleration due to gravity, and Δh is the change in height. In this case, the ball falls from a height of 1m to 0m. Plugging in the values:
ΔPE = 0.125 kg * 9.8 m/s^2 * (0.9 m - 1 m)
ΔPE = -0.1225 joules
Again, the negative sign indicates a decrease in potential energy.
The kinetic energy of the ball just before it hits can be calculated using the formula:
KE = 0.5 * m * v^2
where KE is the kinetic energy and v is the velocity of the ball. At the moment just before it hits, the velocity of the ball can be calculated using the equation for free-fall motion:
v = sqrt(2 * g * h)
where h is the height from which the ball is dropped. Plugging in the values:
v = sqrt(2 * 9.8 m/s^2 * 1 m)
v ≈ 4.43 m/s
Now, calculate the kinetic energy:
KE = 0.5 * 0.125 kg * (4.43 m/s)^2
KE ≈ 0.309 joules
The potential energy of the ball at the top of its bounce can be calculated using the formula:
PE = m * g * h
where PE is the potential energy and h is the height of the bounce. In this case, the height of the bounce is 0.9m. Plugging in the values:
PE = 0.125 kg * 9.8 m/s^2 * 0.9 m
PE ≈ 1.1025 joules
The mechanical energy lost during the bounce can be calculated by taking the difference between the initial mechanical energy and the final mechanical energy. Since no energy is lost during the fall, the initial mechanical energy is equal to the potential energy at the top of the bounce. Therefore:
Lost Mechanical Energy = PE (top of bounce) - KE (just before hitting)
Lost Mechanical Energy = 1.1025 joules - 0.309 joules
Lost Mechanical Energy ≈ 0.7935 joules
The momentum of the ball just before it hits the floor can be calculated using the formula:
p = m * v
where p is the momentum and v is the velocity. Plugging in the values:
p = 0.125 kg * 4.43 m/s
p = 0.55375 kg*m/s
The momentum of the ball just after it leaves the floor on the return bounce can be calculated using the same formula:
p = m * v
Since the ball bounces back with the same speed, the velocity will be the same as when it hit the floor. Plugging in the values:
p = 0.125 kg * 4.43 m/s
p = 0.55375 kg*m/s
The impulse delivered to the floor by the ball can be calculated using the formula:
Impulse = Δp = p(final) - p(initial)
In this case, the impulse delivered to the floor is equal to the change in momentum of the ball just before and just after it hits the floor:
Impulse = p(after hitting) - p(before hitting)
Impulse = 0.55375 kg*m/s - (-0.55375 kg*m/s)
Impulse ≈ 1.1075 kg*m/s
The impulse delivered to the ball by the floor is equal in magnitude but opposite in direction:
Impulse = -1.1075 kg*m/s
Note: Sometimes impulse is referred to as the change in momentum (Δp) of the object.