A 22kg child on a 1.75m long swing is released from rest when the swing supports make an angle of 35 degrees with the vertical.

1.What is the child's maximum potential energy?
2.Disregarding friction, find the child's theoretical speed at the lowest point.
3.If the actual speed of the child at the lowest point is 2.2m/s, how much mechanical energy is lost to friction?

I do not understand what to do.

height above bottom of swing = 1.75 *(1-cos 35)

= .316 meters up

so potential energy relative to bottom of swing
= m g h
= 22 (9.81)(.316) = 68.3 Joules

(1/2) m v^2 = 68.3
so
v^2 = 2 * 68.3 /22
v = 2.49 m/s

loss = 68.3 - (1/2)(22)(2.2)^2

To solve these questions, we'll need to use the principles of potential energy, kinetic energy, and the conservation of mechanical energy.

1. To find the child's maximum potential energy, we need to determine the height at which the child is released. Given the length of the swing (1.75m) and the angle with the vertical (35 degrees), we can use trigonometry to find the vertical height (h) using the equation:

h = length of swing * sin(angle)

So, plugging in the values:

h = 1.75m * sin(35 degrees) = 1.00m (rounded to two decimal places)

Now, we can calculate the potential energy (PE) using the equation:

PE = mass * gravity * height

Given that the mass of the child (m) is 22kg and the acceleration due to gravity (g) is approximately 9.8 m/s^2:

PE = 22kg * 9.8 m/s^2 * 1.00m = 215.6 J (rounded to one decimal place)

Therefore, the child's maximum potential energy is 215.6 J.

2. To find the child's theoretical speed at the lowest point, we can equate the gravitational potential energy at the highest point (maximum potential energy) to the kinetic energy at the lowest point using the equation:

PE = KE

Since the gravitational potential energy is given by PE = mass * gravity * height and the kinetic energy is given by KE = (1/2) * mass * velocity^2, we can rearrange the equation to solve for velocity:

velocity = sqrt(2 * gravity * height)

Plugging in the known values:

velocity = sqrt(2 * 9.8 m/s^2 * 1.00m) = sqrt(19.6) m/s = 4.43 m/s (rounded to two decimal places)

Therefore, the child's theoretical speed at the lowest point is 4.43 m/s.

3. To find the amount of mechanical energy lost to friction, we can subtract the actual kinetic energy at the lowest point from the maximum potential energy.

First, let's find the kinetic energy (KE) at the lowest point using the equation:

KE = (1/2) * mass * velocity^2

Plugging in the known values:

KE = (1/2) * 22kg * (2.2 m/s)^2 = 13.64 J (rounded to two decimal places)

To find the energy lost to friction (EF), we subtract the kinetic energy from the maximum potential energy:

EF = maximum potential energy - kinetic energy
= 215.6 J - 13.64 J
= 201.96 J (rounded to two decimal places)

Therefore, the amount of mechanical energy lost to friction is 201.96 J.