a boy on a swing is pulled to a position 2.34m off the ground and released.at the fastest and lowest pointof the swing the boy is 0.50m off the ground and travelling 3.0m/s.the percent efficiency of this swing system?
To determine the efficiency of the swing system, we need to compare the potential energy lost during the swing with the initial potential energy.
First, let's calculate the initial potential energy when the boy is pulled to a position 2.34m off the ground. The potential energy (PE) is given by the equation:
PE = mgh
Where m is the mass of the boy, g is the acceleration due to gravity (9.8 m/s²), and h is the height above the reference point (ground).
Next, we need to find the potential energy at the lowest point of the swing when the boy is 0.50m off the ground. The potential energy at the lowest point is zero since it is at the reference point.
Now, we can calculate the potential energy lost during the swing. The potential energy lost is the difference between the initial potential energy and the potential energy at the lowest point.
Plugging in the values into the equation, we have:
Potential Energy Lost = PE_initial - PE_lowest
Potential Energy Lost = mgh_initial - mgh_lowest
Potential Energy Lost = mg(h_initial - h_lowest)
Since the mass is canceled out, we don't need it to calculate the efficiency.
Next, let's calculate the initial potential energy:
PE_initial = mgh_initial
And the potential energy at the lowest point:
PE_lowest = mgh_lowest
Therefore:
Potential Energy Lost = mgh_initial - mgh_lowest = mgh_initial
The efficiency of the swing system is given by the ratio of the actual potential energy lost to the initial potential energy:
Efficiency = (Potential Energy Lost / Initial Potential Energy) * 100
Substituting in the values, we have:
Efficiency = (mgh_initial / mgh_initial) * 100
Efficiency = 100%
Therefore, the efficiency of this swing system is 100%.