a 1100 kg wrecking ball hangs from a16m long cable. the ball is pulled back until the cable makes an angle of 17 with the vertical. By how much has the gravitational potential energy of the ball changed?
height change=17-17cos17deg
PE=mg*heightchange
sds
To calculate the change in gravitational potential energy, we need to find the difference between the initial and final gravitational potential energy.
First, we need to find the height difference between the initial and final positions of the wrecking ball. Since the cable makes an angle of 17 degrees with the vertical, we can use trigonometry to find the vertical height of the ball.
We can use the formula:
h = L * sin(θ)
where:
h = vertical height
L = length of the cable
θ = angle between the cable and the vertical
Let's calculate the initial and final heights:
Initial height:
h_initial = 16m * sin(0°) = 0m
Final height:
h_final = 16m * sin(17°) ≈ 4.63m
Next, we can calculate the change in gravitational potential energy (ΔU) using the formula:
ΔU = m * g * Δh
where:
m = mass of the wrecking ball
g = acceleration due to gravity (approximately 9.8 m/s^2)
Δh = change in height (h_final - h_initial)
Let's substitute the values:
ΔU = 1100 kg * 9.8 m/s^2 * (4.63m - 0m)
ΔU ≈ 51,202 Joules
Therefore, the change in gravitational potential energy of the wrecking ball is approximately 51,202 Joules.
To calculate the change in gravitational potential energy, we need to first find the initial and final heights of the ball.
Initial height:
In the initial position, the cable makes an angle of 17° with the vertical. This means that the height of the ball can be found using trigonometry. We can use the formula:
Initial height = length of the cable * sin(angle)
Plugging in the values, we get:
Initial height = 16 m * sin(17°)
Final height:
When the ball is pulled back, it forms a right-angled triangle with the vertical line. The length of the cable becomes the hypotenuse of this triangle. The vertical side of this triangle represents the final height of the ball.
Final height = length of the cable * cos(angle)
Plugging in the values, we get:
Final height = 16 m * cos(17°)
Change in height:
The change in height is the difference between the initial and final heights of the ball.
Change in height = Final height - Initial height
Now, let's calculate the change in gravitational potential energy:
Change in gravitational potential energy = mass of the ball * acceleration due to gravity * change in height
The mass of the ball is given as 1100 kg, and the acceleration due to gravity is approximately 9.8 m/s².
Change in gravitational potential energy = 1100 kg * 9.8 m/s² * (Final height - Initial height)