A 1100 wrecking ball hangs from a 10 -long cable. The ball is pulled back until the cable makes an angle of 28.0 with the vertical.By how much has the gravitational potential energy of the ball changed?
To determine the change in gravitational potential energy of the wrecking ball, we need to calculate the initial and final gravitational potential energies and then subtract the initial from the final energy.
The gravitational potential energy of an object is given by the formula:
PE = mgh
Where:
PE is the gravitational potential energy
m is the mass of the object
g is the acceleration due to gravity
h is the vertical height of the object
First, let's calculate the initial gravitational potential energy.
Given:
Mass of the wrecking ball, m = 1100 kg
Height of the ball, h = 10 m (length of the cable)
Acceleration due to gravity, g = 9.8 m/s^2
Initial gravitational potential energy, PE_initial = mgh
Substituting the given values:
PE_initial = (1100 kg)(9.8 m/s^2)(10 m)
Now, let's calculate the final gravitational potential energy.
The final height of the ball can be calculated using basic trigonometry. The vertical height, h, can be determined by multiplying the length of the cable (10 m) by the sine of the angle made by the cable with the vertical (28 degrees).
Final height, h_final = (10 m) * sin(28 degrees)
Now, we can calculate the final gravitational potential energy.
PE_final = mgh_final
Substituting the given values:
PE_final = (1100 kg)(9.8 m/s^2)(h_final)
Finally, we can find the change in gravitational potential energy by subtracting the initial energy from the final energy.
Change in gravitational potential energy = PE_final - PE_initial
Substitute the values of PE_initial and PE_final calculated earlier to find the change in gravitational potential energy.