A surfer is catching a wave. Suppose she starts at the top of the wave with a speed of 1.3 m/s and moves down the wave until her speed increases to 8.0 m/s. The drop in her vertical height is 2.8 m. If her mass is 59 kg, how much work is done by the (nonconservative) force of the wave?

ΔKE =W(wave)+W(gravity)

W(wave)= ΔKE- W(gravity)= m•v²/2 - m•v₀²/2 – m•g•Δh =
=59(8²-1.3²)/2 - 59•9.8•2.8 =219 J.

To find the work done by the nonconservative force of the wave, we first need to find the change in potential energy and kinetic energy of the surfer.

The work done by a force is given by the formula:

Work = Change in Potential Energy + Change in Kinetic Energy

Since the surfer starts at the top of the wave and moves down, the change in potential energy is negative (decreasing height) and the change in kinetic energy is positive (increasing speed).

1. Change in Potential Energy:
The potential energy can be calculated using the formula: Potential Energy = mass * gravitational acceleration * height

Given that the drop in the surfer's vertical height is 2.8 m and the mass is 59 kg, we can calculate the change in potential energy as follows:

Change in Potential Energy = mass * gravitational acceleration * change in height
= 59 kg * 9.8 m/s^2 * (-2.8 m)
= -1629.04 J (Joules) [Negative because potential energy decreases]

2. Change in Kinetic Energy:
The kinetic energy can be calculated using the formula: Kinetic Energy = 1/2 * mass * velocity^2

The initial velocity is 1.3 m/s, and the final velocity is 8.0 m/s. Using these values, we can calculate the change in kinetic energy as follows:

Change in Kinetic Energy = 1/2 * mass * (final velocity^2 - initial velocity^2)
= 1/2 * 59 kg * (8.0 m/s)^2 - 1.3 m/s)^2
= 1/2 * 59 kg * (64 - 1.69) m^2/s^2
= 1536.95 J (Joules) [Positive because kinetic energy increases]

Finally, we can calculate the work done by the nonconservative force of the wave:

Work = Change in Potential Energy + Change in Kinetic Energy
= -1629.04 J + 1536.95 J
= -92.09 J (Joules)

Therefore, the work done by the nonconservative force of the wave is -92.09 Joules.

To find the work done by the nonconservative force of the wave, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.

The surfer starts with a speed of 1.3 m/s at the top of the wave and ends with a speed of 8.0 m/s after moving down the wave. The change in kinetic energy can be calculated using the formula:

ΔK = (1/2)mvf^2 - (1/2)mvi^2

Where:
ΔK - Change in kinetic energy
m - Mass of the surfer (59 kg)
vf - Final velocity (8.0 m/s)
vi - Initial velocity (1.3 m/s)

ΔK = (1/2)(59 kg)(8.0 m/s)^2 - (1/2)(59 kg)(1.3 m/s)^2
ΔK = (1/2)(59 kg)(64 m^2/s^2) - (1/2)(59 kg)(1.69 m^2/s^2)
ΔK = 1903.8 J - 29.94 J
ΔK = 1873.86 J

The work done by the nonconservative force of the wave is equal to the change in kinetic energy, so the work done is 1873.86 Joules.