a 55 kg skateboarder starts out with a speed of 1.8 m/s. he does +80 J of work on himself by pushing with his feet against the ground. in addition, the friction does -265 J of work on him. in both cases, the forces doing the work are nonconservative. the final speed of the skateboarder is 6 m/s. Calculate the change in the gravitational potential energy. How much has the vertical height of the skater changed, and is the skater above or below the starting point?

Well, well, well! Looks like we have a skateboarder with some interesting physics going on here. Let's break it down, shall we?

To calculate the change in gravitational potential energy, we need to find the change in height. The formula for gravitational potential energy is:

ΔPE = mgh

Where ΔPE is the change in potential energy, m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the change in height. We know the mass of the skateboarder is 55 kg, but we need to find the change in height.

Now, the final speed of the skateboarder is given as 6 m/s, and we know his initial speed is 1.8 m/s. Since the skateboarder is gaining speed, we can infer that the change in height must be positive. So, the skater is above the starting point.

To find the change in height, we can use the conservation of energy principle. The total work done on the skateboarder is equal to the change in potential energy:

Total Work = Work done by the skateboarder + Work done by friction

Since the total work is the sum of the two nonconservative works, we have:

Total Work = +80 J - 265 J = -185 J

Now, we equate this total work to the change in potential energy:

-185 J = ΔPE

Alright, let's plug in the values and solve for ΔPE:

ΔPE = mgh
-185 J = (55 kg) * (9.8 m/s²) * h

Solving for h, we get:

h = -185 J / ((55 kg) * (9.8 m/s²))
h ≈ -0.35 m

Uh-oh! It seems like the change in height is approximately -0.35 meters. So, the skater has actually descended, and he is below the starting point. I hope he doesn't feel too down about it!

To calculate the change in gravitational potential energy, we can use the equation:

ΔPE = m * g * Δh

where ΔPE is the change in gravitational potential energy, m is the mass of the skateboarder (55 kg), g is the acceleration due to gravity (9.8 m/s²), and Δh is the change in vertical height.

First, we need to calculate the initial and final potential energies:

PE_initial = m * g * h_initial
PE_final = m * g * h_final

Since the question states that the forces doing work are nonconservative, we know that the work done on the skateboarder is equal to the change in total mechanical energy:

Work_total = Work_push + Work_friction
Work_total = ΔKE + ΔPE

We can rearrange this equation to solve for the change in potential energy:

ΔPE = Work_total - ΔKE

Given that ΔKE = KE_final - KE_initial and the final speed of the skateboarder (6 m/s), we can find ΔKE:

KE_final = 0.5 * m * v_final²
KE_initial = 0.5 * m * v_initial²

Now we can calculate ΔKE:

ΔKE = KE_final - KE_initial

To calculate the change in gravitational potential energy, we can substitute the known values into the equation:

ΔPE = Work_total - ΔKE

Finally, we can calculate the change in vertical height (Δh) by rearranging the equation for ΔPE:

Δh = ΔPE / (m * g)

To determine if the skater is above or below the starting point, we need to compare the initial and final potential energies. If the final potential energy is greater than the initial potential energy, then the skater is above the starting point. If the final potential energy is less than the initial potential energy, then the skater is below the starting point.

To calculate the change in gravitational potential energy for the skateboarder, we can first calculate the initial and final kinetic energy.

The initial kinetic energy (KEi) of the skateboarder can be calculated using the formula:
KEi = (1/2) * mass * initial velocity^2

Substituting the given values:
mass = 55 kg
initial velocity = 1.8 m/s

KEi = (1/2) * 55 kg * (1.8 m/s)^2 = 88.2 J

The final kinetic energy (KEf) of the skateboarder can be calculated using the formula:
KEf = (1/2) * mass * final velocity^2

Substituting the given values:
final velocity = 6 m/s

KEf = (1/2) * 55 kg * (6 m/s)^2 = 990 J

The change in kinetic energy (ΔKE) is the difference between the final and initial kinetic energies:
ΔKE = KEf - KEi = 990 J - 88.2 J = 901.8 J

Since the forces doing work on the skateboarder are nonconservative, the work done by these forces is equal to the change in kinetic energy.

Therefore, the work done on the skateboarder can be calculated as:
Work = Work by the skateboarder on himself + Work by friction
Work = 80 J + (-265 J) = -185 J

As we know that work equals the change in kinetic energy, we can write:
Work = ΔKE
-185 J = 901.8 J

Since the change in gravitational potential energy (ΔPE) is negative, we can conclude that the skater is below the starting point.

The change in gravitational potential energy is given by the formula:
ΔPE = -Work

Substituting the value of work:
ΔPE = -(-185 J) = 185 J

Therefore, the change in gravitational potential energy is 185 J.

To calculate the change in vertical height (Δh), we can use the formula:
ΔPE = m * g * Δh

Rearranging the formula, we get:
Δh = ΔPE / (m * g)

Substituting the given values:
mass = 55 kg
ΔPE = 185 J
g (acceleration due to gravity) = 9.8 m/s^2

Δh = 185 J / (55 kg * 9.8 m/s^2) = 0.345 m

Therefore, the vertical height of the skater has changed by 0.345 meters, and the skater is below the starting point.

Initial total energy-friction force=final energy.

Let the final energy be KE only, set PE to zero, after all, that point is arbritary.

1/2 m 1.8^2+mgh-frictionwork=1/2 m 6^2
solve for h

1/2 m 1.8^2-265=1/2 m*26

solve for h. If h is negative, then the skater is above the starting point.