A 48.4 N child is in a swing that is attached to ropes 1.24 m long. Find the gravitational potential energy associated with the child relative to her lowest position when (a) the ropes are horizontal
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To find the gravitational potential energy associated with the child relative to her lowest position when the ropes are horizontal, we can use the formula:
Gravitational Potential Energy = mass * gravity * height
In this case, we are given the weight of the child which is 48.4 N. To find the mass of the child, we can use the formula:
Weight = mass * gravity
Rearranging the formula, we have:
mass = Weight / gravity
The acceleration due to gravity (g) is approximately 9.8 m/s².
Let's calculate the mass of the child first:
mass = 48.4 N / 9.8 m/s² = 4.94 kg
Now we can calculate the gravitational potential energy:
Gravitational Potential Energy = mass * gravity * height
height in this case would be the distance the child is above her lowest position when the ropes are horizontal, which is half the length of the ropes.
height = 1.24 m / 2 = 0.62 m
Gravitational Potential Energy = 4.94 kg * 9.8 m/s² * 0.62 m = 29.25 J
Therefore, the gravitational potential energy associated with the child relative to her lowest position when the ropes are horizontal is 29.25 J.
To find the gravitational potential energy associated with the child when the ropes are horizontal, we need to understand the concept of gravitational potential energy and know the formula to calculate it.
Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. It depends on the object's mass, the acceleration due to gravity, and its height relative to a reference point.
The formula to calculate gravitational potential energy is:
Potential Energy = mass * acceleration due to gravity * height
In this case, the child's mass is not given, but we are given the force applied on the child, which is 48.4 N. By using Newton's second law of motion (force = mass * acceleration), we can solve for the child's mass.
48.4 N = mass * acceleration due to gravity
The acceleration due to gravity is approximately 9.8 m/s^2, so we can rearrange the equation to solve for mass:
mass = 48.4 N / 9.8 m/s^2
Now we can proceed to calculate the gravitational potential energy.
Potential Energy = mass * acceleration due to gravity * height
Since the ropes are horizontal, the height of the child can be taken as the length of the ropes, which is 1.24 m.
Substituting the values we have:
Potential Energy = (48.4 N / 9.8 m/s^2) * 9.8 m/s^2 * 1.24 m
The acceleration due to gravity cancels out, simplifying the equation to:
Potential Energy = 48.4 N * 1.24 m
Now we can calculate the value:
Potential Energy = 60.0168 J
Therefore, the gravitational potential energy associated with the child relative to her lowest position when the ropes are horizontal is 60.0168 Joules.