A 350 N child is in a swing attached to rope 1.75m long. Find the gravitational PE associated with the child relative to her lowest position when the ropes make a 30 degree angle with the vertical
Gravitational potential energy is given by mgh
where h=difference in elevation
m=mass
For the given case,
radius,r =1.75m
θ=30°
h=r(1-cos(θ))
Can you take it from here?
To find the gravitational potential energy (PE) associated with the child in the swing, we need to consider the change in height and the gravitational force acting on the child.
The formula for gravitational potential energy is:
PE = m * g * h
Where:
PE = Gravitational Potential Energy
m = Mass of the object (in this case, the child)
g = Acceleration due to gravity (approximately 9.8 m/s² on Earth)
h = Change in height
In this case, we are given the weight of the child, which is 350 N. Weight (W) is given by the formula:
W = m * g
Since weight can be substituted as mg, we can rewrite the formula for PE as:
PE = W * h
To find the height (h), we need to consider the geometry of the situation. The swing is attached to a rope that is 1.75 m long, making a 30-degree angle with the vertical. This forms a right triangle.
Using trigonometry, we can find the vertical component of the rope length (height) using the formula:
h = rope length * sin(angle)
Here, the angle is 30 degrees and the rope length is 1.75 m. Thus,
h = 1.75 m * sin(30°)
Calculating sin(30°), we get:
h = 1.75 m * 0.5
h = 0.875 m
Now we have the height (h = 0.875 m) and weight (W = 350 N). We can substitute these values into the PE formula:
PE = W * h
PE = 350 N * 0.875 m
Calculating this, we get:
PE = 306.25 Joules
Therefore, the gravitational potential energy associated with the child relative to her lowest position in the swing is 306.25 Joules.