Kelli weighs 392 N, and she is sitting on on a playground swing that hangs 0.4 m above the ground. Her mom pulls the swing back and releases it when the seat is 1.1 m above the ground. If Kelli moves through the lowest point at 1.5 m/s, how much work was done on the swing by friction?

To find the work done on the swing by friction, we first need to calculate the gravitational potential energy at the lowest point of Kelli's swing.

The gravitational potential energy is given by the formula:

PE = mgh

Where:
PE is the potential energy,
m is the mass (which we can find from the weight, W),
g is the acceleration due to gravity (approximately 9.8 m/s²),
h is the height.

We are given Kelli's weight (W = 392 N) and the height at the lowest point (h = 1.1 m). We can calculate the mass of Kelli using the formula:

W = mg

Rearranging the formula, we get:

m = W / g

Substituting the values, we have:

m = 392 N / 9.8 m/s²
m = 40 kg

Now that we have the mass of Kelli, we can calculate the gravitational potential energy at the lowest point of the swing:

PE = mgh
PE = 40 kg * 9.8 m/s² * 1.1 m
PE = 431.2 J

Since we know that kinetic energy is conserved and no external work is done on the system (ignoring air resistance), we can calculate the work done by friction by subtracting the initial kinetic energy from the final potential energy:

Work = PE - KE

At the lowest point, the swing has no potential energy (PE = 0), and the kinetic energy is given by:

KE = 1/2 * m * v²

We are given the speed of Kelli at the lowest point, v = 1.5 m/s.

Calculating the initial kinetic energy:

KE = 1/2 * 40 kg * (1.5 m/s)²
KE = 45 J

Now we can calculate the work done on the swing by friction:

Work = PE - KE
Work = 431.2 J - 45 J
Work = 386.2 J

Therefore, the work done on the swing by friction is 386.2 joules.