A 54.5-kg skateboarder starts out with a speed of 1.95 m/s. He does +80.0 J of work on himself by pushing with his feet against the ground. In addition, 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 5.95 m/s.
a) Calculate the change (ΔPE = PEf - PE0) in the gravitational potential energy.
b)How much has the vertical height of the skater changed?
c)Is the skater above or below the starting point?
initial Ke = (1/2)(54.5)(1.95)^2
= 104 J
energy added = 80-265 = - 185 J
so
if no change in elevation final ke would be
104-185 = - 81 J
actual final ke = (1/2)(54.5)(5.95)^2
= 965 J
so the gravitational PE loss (dropped down to gain speed)
= 965 + 81 = 1046 J
or
delta PE = -1046 J
if height drop = h
m g h = 1046
h = 1046 / (9.81*54.5) = 1.96 meters drop
the height went down below the start of course
First find the initial change in kinetic energy = 1/2 * m * v(initial)^2
1/2 * 54.5 * 1.95^ 2 = 103.6J
Find final kinetic energy = 1/2 * m * v(final)^2
1/2 * 54.5 * 5.95^2 = 964.7J
We know that with non-conservative energy the equation:
Net External Work = change in kinetic energy - (-change in potential energy)
the external work is 80-265 = -185J
so, using the equation above, DPE = change in potential Energy
-185 = (964.7 - 103.6) - (-DPE)
a.) DPE = -1046.1
DPE = PE(final) - PE(initial)
Because the state boarder starts at height 0 (on the ground), PE(initial) is 0
PE(final) = mgh(final) = DPE
-1046.1 = 54.5 * 9.8 * h
b.) h = -1.96m, (this is the final height)
c.) because the final height is less than the initial, the skater is below where he started with respect to height
a) Well, since we're dealing with a nonconservative force, I can't help but wonder if the skateboarder had some questionable dance moves while doing that work on himself. Anyway, to calculate the change in gravitational potential energy, we need to find the initial and final values. Since no height is mentioned, let's assume the skateboarder is on a flat surface (unless they've invented anti-gravity skateboards, then I'm definitely late to the party). So, in this case, the change in gravitational potential energy is zero. We defy physics once again!
b) Ah, the vertical height change. This poor skateboarder didn't get any airtime, huh? Well, if there's no change in gravitational potential energy, then there's no change in height either. The skater is stuck in a land where gravity is just playing hard to get.
c) Since there's no change in height, we can safely say that the skater is neither above nor below the starting point. They're stuck in a state of purgatory, forever destined to skate on an eternal flat surface. It’s like an infinite treadmill, but with wheels and less sweat.
Keep on skateboardin', my friend! Just remember to watch out for those nonconservative forces, they always tend to mess with our physics calculations.
a) To calculate the change in gravitational potential energy (ΔPE = PEf - PE0), you need to determine the initial and final potential energy.
The formula for gravitational potential energy is PE = mgh, where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height.
Since the question does not provide information about the height, we need to assume that there is no change in height. Therefore, the initial and final potential energies will be the same, and the change in gravitational potential energy (ΔPE) will be zero.
b) As mentioned in part a), since there is no change in height, the vertical height of the skater does not change.
c) Since there is no change in height (Δh = 0), the skater is neither above nor below the starting point. The skater remains at the same height throughout.