A 1100 kg wrecking ball hangs from a 14m-long cable. The ball is pulled back until the cable makes an angle of 17.0 degrees with the vertical.By how much has the gravitational potential energy of the ball changed?
To calculate the change in gravitational potential energy of the wrecking ball, you need to know the initial and final heights of the ball.
Let's start by determining the initial height of the ball before it is pulled back. Since the cable makes an angle of 17.0 degrees with the vertical, we can use trigonometry to find the vertical component of the cable's length.
The vertical component can be calculated using the equation:
Vertical component = Cable length * sin(angle)
Given that the cable length is 14m and the angle is 17.0 degrees, we can substitute these values into the equation:
Vertical component = 14m * sin(17.0 degrees)
Now, calculate the vertical component:
Vertical component ≈ 14m * 0.2924
Vertical component ≈ 4.0976m
Therefore, the initial height of the wrecking ball is approximately 4.0976m.
Next, we need to determine the final height of the ball after it has been pulled back. When the angle of the cable with the vertical is 17.0 degrees, we can consider the height as the vertical component of the cable's length.
So, the final height is approximately 14m * sin(17.0 degrees) ≈ 4.0976m.
To calculate the change in gravitational potential energy, we subtract the initial height from the final height:
Change in gravitational potential energy = Final height - Initial height
Change in gravitational potential energy = 4.0976m - 4.0976m
Change in gravitational potential energy ≈ 0m
Therefore, the change in gravitational potential energy of the wrecking ball is approximately 0 joules. This implies that there is no change in the gravitational potential energy when the ball is pulled back to an angle of 17.0 degrees with the vertical.
To determine the change in gravitational potential energy of the ball, we first need to calculate the initial and final heights of the ball.
The initial height of the ball can be calculated using the formula:
Initial height = length of the cable * sin(angle)
Initial height = 14m * sin(17.0 degrees)
To calculate the final height, we need to find the vertical component of the cable length. The final height can be calculated as:
Final height = length of the cable * cos(angle)
Final height = 14m * cos(17.0 degrees)
Now, we can calculate the change in gravitational potential energy using the formula:
Change in gravitational potential energy = mass * (final height - initial height) * g
where:
- mass = 1100 kg (mass of the ball)
- g = 9.8 m/s^2 (acceleration due to gravity)
Substituting the values, we have:
Change in gravitational potential energy = 1100 kg * (14m * cos(17.0 degrees) - 14m * sin(17.0 degrees)) * 9.8 m/s^2
By calculating this expression, we can find the change in gravitational potential energy.
Use geometry to find out how much height it went. In my head, I see
height= 14cos17
check that
PE= mgh