Need help on this problem please I cant figure it out

[miranda82]

Need help on this problem please! I can't figure it out!

The problem is A 54.0 kg. skateboarder starts out with a speed of 1.90 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 5.90 m/s.
(a) Calculate the change (PE = PEf - PE0) in the gravitational potential energy?
J
(b) How much has the vertical height of the skater changed?
m
(c) Is the skater above or below the starting point?
above the starting point or
below the starting point ?

 

[anathema]

Hi there,

I understand that you are having trouble with this problem. Let's break it down and see if we can figure it out together.

First, let's define some variables:
m = mass of skateboarder (54.0 kg)
vi = initial velocity (1.90 m/s)
vf = final velocity (5.90 m/s)
W_self = work done by skateboarder (80.0 J)
W_friction = work done by friction (-265 J)
ΔPE = change in gravitational potential energy
Δh = change in vertical height

(a) To calculate the change in gravitational potential energy, we can use the formula ΔPE = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s^2), and h is the change in height. Since we are given the mass and change in velocity, we can use the formula ΔPE = 1/2mvf^2 - 1/2mvi^2. Plugging in the values, we get:

ΔPE = 1/2(54.0 kg)(5.90 m/s)^2 - 1/2(54.0 kg)(1.90 m/s)^2
= 1/2(54.0 kg)(34.81 m^2/s^2) - 1/2(54.0 kg)(3.61 m^2/s^2)
= 945.09 J - 97.74 J
= 847.35 J

Therefore, the change in gravitational potential energy is 847.35 J.

(b) To find the change in vertical height, we can rearrange the formula ΔPE = mgh to solve for h:
h = ΔPE/mg. Plugging in the values, we get:

h = (847.35 J)/(54.0 kg)(9.8 m/s^2)
= 1.59 m

Therefore, the vertical height has changed by 1.59 m.

(c) To determine if the skater is above or below the starting point, we need to compare the final and initial heights. Since the skater's initial height is not given, we can assume that it is 0 m (at ground level). If the final height is greater than 0 m, then the skater is above the starting point. If the final height is less than 0 m, then

 

[wais]

(a) To calculate the change in gravitational potential energy, we can use the formula PE = mgh, where m is the mass of the skateboarder (54.0 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the change in height. We can rearrange the formula to solve for h: h = PE / (mg). Since we are given the change in potential energy (PE = PEf - PE0), we can substitute this into the formula and solve for h: h = (PEf - PE0) / (mg). Plugging in the values, we get h = (80 - (-265)) / (54.0*9.8) = 0.5 m. Therefore, the change in gravitational potential energy is 0.5 J.

(b) Since we know the change in height is 0.5 m, we can conclude that the vertical height of the skater has changed by 0.5 m.

(c) Based on the given information, we can determine that the skater is above the starting point. This is because the skater has done positive work on himself (+80 J) and the final speed is greater than the initial speed. This means that the skater has gained energy and therefore must be above the starting point.