a 1.0kg ball is thrown upward from 1.0m above the ground with a speed of 10m/s reaches a height of 4.5 m. what is the efficiency of the energy transformation?
Well, efficiency is a measure of how well something converts energy into useful work. In this case, the ball is thrown upwards, so let's see how efficient it is in transforming energy.
First, we need to determine the potential energy of the ball at the start and the end. The potential energy at the start is 1.0kg * 9.8m/s^2 * 1.0m = 9.8 joules since it's 1 meter above the ground. The potential energy at the end is 1.0kg * 9.8m/s^2 * 4.5m = 44.1 joules, as it reaches a height of 4.5m.
Now, we can calculate the efficiency by dividing the useful energy output by the total energy input. In this case, the useful energy is the difference in potential energy, which is 44.1 - 9.8 = 34.3 joules. The total energy input is the initial potential energy, which is 9.8 joules.
So, the efficiency of this energy transformation is 34.3 joules divided by 9.8 joules, which is approximately 3.5.
Wow, that's quite inefficient! I guess the ball could use a lesson in energy conservation. Maybe it should attend an efficiency training workshop. Keep practicing, little ball!
To find the efficiency of the energy transformation, we need to calculate the initial potential energy, the final potential energy, and the total energy input.
Step 1: Calculate the initial potential energy (PEi).
The initial potential energy can be calculated using the formula:
PEi = m g h
where m is the mass of the ball, g is the acceleration due to gravity, and h is the initial height.
Given:
m = 1.0 kg
g = 9.8 m/s²
h = 1.0 m
PEi = 1.0 kg * 9.8 m/s² * 1.0 m
PEi = 9.8 Joules (J)
Step 2: Calculate the final potential energy (PEf).
The final potential energy can be calculated using the formula:
PEf = m g h
where h is the final height.
Given:
h = 4.5 m
PEf = 1.0 kg * 9.8 m/s² * 4.5 m
PEf = 44.1 Joules (J)
Step 3: Calculate the total energy input.
The total energy input is the difference between the final potential energy and the initial potential energy:
Total energy input = PEf - PEi
Total energy input = 44.1 J - 9.8 J
Total energy input = 34.3 Joules (J)
Step 4: Calculate the efficiency.
Efficiency is defined as the useful output energy divided by the total energy input, multiplied by 100%:
Efficiency = (PEf - PEi) / PEf * 100%
Efficiency = (34.3 J / 44.1 J) * 100%
Efficiency ≈ 77.7%
Therefore, the efficiency of the energy transformation is approximately 77.7%.
To calculate the efficiency of the energy transformation, we need to determine the initial and final energies involved in the process.
1. First, let's calculate the initial potential energy (U_i) of the ball before it is thrown upward. The formula for potential energy is given by U = m * g * h, where m is the mass of the ball (1.0 kg), g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height above the ground (1.0 m).
U_i = 1.0 kg * 9.8 m/s^2 * 1.0 m
U_i = 9.8 Joules
2. Next, let's calculate the final potential energy (U_f) of the ball at its highest point (4.5 m above the ground). Using the same formula:
U_f = 1.0 kg * 9.8 m/s^2 * 4.5 m
U_f = 44.1 Joules
3. The efficiency (η) of energy transformation is given by the formula:
η = (Useful Energy Output / Total Energy Input) * 100%
In this case, the useful energy output is the change in potential energy (ΔU) from the initial to the final position:
ΔU = U_f - U_i
ΔU = 44.1 J - 9.8 J
ΔU = 34.3 J
Thus, the efficiency is:
η = (34.3 J / Total Energy Input) * 100%
Since the total energy input is the initial potential energy (U_i), we have:
η = (34.3 J / 9.8 J) * 100%
η ≈ 350%
The efficiency of the energy transformation is approximately 350%.