A 60.8-kg skateboarder starts out with a speed of 1.84 m/s. He does 90.8 J of work on himself by pushing with his feet against the ground. In addition, friction does -278 J of work on him. In both cases, the forces doing the work are non-conservative. The final speed of the skateboarder is 8.12 m/s. (a) Calculate the change (PEf - PE0) in the gravitational potential energy. (b) How much has the vertical height of the skater changed? Give the absolute value.
http://www.jiskha.com/display.cgi?id=1429748458
To solve this problem, we can use the work-energy principle, which states that the work done on an object is equal to its change in kinetic energy.
(a) To calculate the change in gravitational potential energy, we need to find the initial and final potential energies.
The formula for potential energy (PE) is:
PE = m * g * h
Where:
m is the mass (60.8 kg)
g is the acceleration due to gravity (9.8 m/s²)
h is the height above the reference point
Since the reference point is not given, we can assume that the initial height is zero and find the final height based on the change in potential energy.
The initial potential energy (PE0) is zero because the initial height is zero. The final potential energy (PEf) can be calculated using the formula above.
PEf = m * g * h
To find h, we rearrange the equation:
h = PEf / (m * g)
Substituting the given values:
h = (90.8 J - 278 J) / (60.8 kg * 9.8 m/s²)
Calculate:
h = -187 J / (596.48 kg*m²/s²)
h ≈ -0.31 m (taking absolute value)
Therefore, the change in gravitational potential energy (PEf - PE0) is approximately 0.31 m/s².
(b) The absolute value of the change in height can be found by taking the absolute value of the calculated height change:
|0 - (-0.31)| ≈ 0.31 m
Hence, the vertical height of the skater changes by approximately 0.31 meters.