Solving Impulse: Why Only 1 Method Works for Determining Change in Velocity

[Nito]

Homework Statement

A ball of mass 0.150 kg is dropped from rest from a
height of 1.25 m. It rebounds from the floor to reach a
height of 0.960 m. What impulse was given to the ball
by the floor?

Homework Equations

Δmv/t =I
vf^2=vo^2 +2aΔy

The Attempt at a Solution

mghi = mghf +1/2mvf^2

vf = 2.38m/s

0.150kg x (2.38-0) = 0.35 Kg m/s

But this did not work. What the answer key did was use kinematics equations to find the velocity before the ball hit the ground and then found the velocity when the ball reached the height 0.960m. They then did change in velocity x mass to find the impulse.

Essentially, I don't see why using the conservation of energy equation to find the change in velocity is wrong. Why does this not work?

 

[Nito]

nvm, there's no kinetic energy when it reaches its peak height. stupid lol!

 

[Chestermiller]

Homework Statement

A ball of mass 0.150 kg is dropped from rest from a
height of 1.25 m. It rebounds from the floor to reach a
height of 0.960 m. What impulse was given to the ball
by the floor?

Homework Equations

Δmv/t =I
vf^2=vo^2 +2aΔy

The Attempt at a Solution

mghi = mghf +1/2mvf^2

vf = 2.38m/s

0.150kg x (2.38-0) = 0.35 Kg m/s

But this did not work. What the answer key did was use kinematics equations to find the velocity before the ball hit the ground and then found the velocity when the ball reached the height 0.960m. They then did change in velocity x mass to find the impulse.

Essentially, I don't see why using the conservation of energy equation to find the change in velocity is wrong. Why does this not work?

Because mechanical energy is not conserved in this collision. Part of the mechanical energy is converted to thermal energy (heat) in the collision, with the temperature of the ball and the temperature of the ground increasing slightly.

 

[pgardn]

Homework Statement

A ball of mass 0.150 kg is dropped from rest from a
height of 1.25 m. It rebounds from the floor to reach a
height of 0.960 m. What impulse was given to the ball
by the floor?

Homework Equations

Δmv/t =I
vf^2=vo^2 +2aΔy

The Attempt at a Solution

mghi = mghf +1/2mvf^2

vf = 2.38m/s

0.150kg x (2.38-0) = 0.35 Kg m/s

But this did not work. What the answer key did was use kinematics equations to find the velocity before the ball hit the ground and then found the velocity when the ball reached the height 0.960m. They then did change in velocity x mass to find the impulse.

Essentially, I don't see why using the conservation of energy equation to find the change in velocity is wrong. Why does this not work?

Like chester said, the ball started off with a certain amount of potential energy mg(1.25) and then ended with mg(0.96). So you would have appeared to "lose" energy.

Often if time is involved in a problem, it will be difficult to use the conservation of mechanical energy alone to solve that problem. If you can use kinematics, cons. of E, and cons. of momentum, you are good on a significant number of mechanics problems. And being able to draw free body diagrams...

 

[Nickie]

I understand your confusion and desire to use the conservation of energy equation to solve for the change in velocity. However, in this specific scenario, it is not the most accurate method for determining the impulse given to the ball by the floor.

The reason for this is because the conservation of energy equation assumes that all the energy in the system (in this case, the ball) is conserved and no external forces are acting on it. However, in reality, there are external forces, such as air resistance and friction, that act on the ball and cause it to lose some of its energy. This means that the energy in the system is not fully conserved, and the resulting velocity calculated using the conservation of energy equation may not be accurate.

On the other hand, the kinematics equations used in the answer key take into account the external forces acting on the ball and provide a more accurate calculation of the change in velocity. This method is known as the impulse-momentum theorem and is based on the principle that the impulse (change in momentum) is equal to the force applied multiplied by the time it acts on the object.

In conclusion, while the conservation of energy equation may seem like a straightforward and convenient method for calculating the change in velocity, it may not always be accurate in real-world scenarios. As scientists, it is important to use the most appropriate and accurate method for solving problems, and in this case, the impulse-momentum theorem is the most reliable approach.