Energy, work, power and efficiency when throwing a ball upward

[danielsmith123123]

Homework Statement

A 1.0-kg ball thrown upward from 1.0 m above the ground with a speed of 10 m/s reaches a height of 4.5 m. What was the efficiency of this energy transformation?

Relevant Equations

Efficiency

I don't have an idea of where to start. I tried to do
Ein = 1/2 mv^2 ------ (1/2)(1)(10)^2 ----------- 50
but i don't know where to go from here

 

[kuruman]

Homework Statement:: A 1.0-kg ball thrown upward from 1.0 m above the ground with a speed of 10 m/s reaches a height of 4.5 m. What was the efficiency of this energy transformation?
Relevant Equations:: Efficiency

I don't have an idea of where to start. I tried to do
Ein = 1/2 mv^2 ------ (1/2)(1)(10)^2 ----------- 50
but i don't know where to go from here

"Efficiency" is not an equation.

How high would the ball rise if the energy transformation were 100% efficient? What about if the energy transformation were 50% efficient?

 

[danielsmith123123]

"Efficiency" is not an equation.

How high would the ball rise if the energy transformation were 100% efficient? What about if the energy transformation were 50% efficient?

Mass: 1 kg Initial height: 1 m Final height : 4.5 m Initial velocity: 10 m/s, assumption that final velocity is 0m/s

E-in= mgh + 1/2 * mv^2. = 1 kg * 9.81 * 1 m + 1/2 * 1 kg * (10 m/s)^ 2 = 9.81 + 50 = 59.81 Joules

E-out= mgh = 1 kg * 9.81 * 4.5 m = 44.145 Joules.

44.145/59.81 * 100% = 73.8%

I reviewed this with my classmates and they said it is correct but the textbook says the answer is 69%

 

[Delta2]

I think your book wants you to consider the zeroth level of gravitational potential energy to be at the height of 1m. It is because it asks for the efficiency of transformation of kinetic energy to potential energy, you shouldn't take the additional 9.81 potential energy as part of the input(or output) energy because it is not transformed from kinetic energy, it just exists there.

 

[Orodruin]

I think your books wants you to consider the zeroth level of gravitational potential energy to be at the height of 1m. It is because it asks for the efficiency of transformation of kinetic energy to potential energy, you shouldn't take the additional 9.81 potential energy as part of the input energy because it is not transformed.

This really. If you are allowed to arbitrarily include energy that was already potential energy in the original energy, you can get any answer you want by selecting different zero levels.