A 55 kg skateboarder comes over the top of a hill at 5.0 m/s and reaches 11 m/s at the bottom. Find the total work done on the skateboarder between the top and bottom of the hill.
To find the total work done on the skateboarder between the top and bottom of the hill, we can use the work-energy principle. The work done on an object can be calculated as the change in its kinetic energy.
The equation for calculating the work done is given by:
Work = Change in Kinetic Energy
The change in kinetic energy can be calculated using the equation:
Change in Kinetic Energy = (1/2) * mass * ((final velocity)^2 - (initial velocity)^2)
Given:
Mass of the skateboarder (m) = 55 kg
Initial velocity (v1) = 5.0 m/s
Final velocity (v2) = 11 m/s
Plugging in the values into the equation:
Change in Kinetic Energy = (1/2) * 55 kg * ((11 m/s)^2 - (5.0 m/s)^2)
Calculating:
Change in Kinetic Energy = (1/2) * 55 kg * (121 m/s^2 - 25 m/s^2)
Change in Kinetic Energy = (1/2) * 55 kg * 96 m/s^2
Change in Kinetic Energy = 2640 J
Therefore, the total work done on the skateboarder between the top and bottom of the hill is 2640 Joules.
To find the total work done on the skateboarder, we need to calculate the change in kinetic energy. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.
The change in kinetic energy can be calculated using the formula:
ΔKE = KE_final - KE_initial
First, let's calculate the initial kinetic energy (KE_initial). The kinetic energy is given by the equation:
KE = (1/2) * m * v^2
where m is the mass of the skateboarder and v is the velocity.
Given:
Mass of the skateboarder (m) = 55 kg
Initial velocity (v_initial) = 5.0 m/s
Final velocity (v_final) = 11 m/s
Calculating the initial kinetic energy:
KE_initial = (1/2) * m * v_initial^2
KE_initial = (1/2) * 55 kg * (5.0 m/s)^2
Now, let's calculate the final kinetic energy (KE_final) using the same formula:
KE_final = (1/2) * m * v_final^2
KE_final = (1/2) * 55 kg * (11 m/s)^2
Now, we can calculate the change in kinetic energy (ΔKE):
ΔKE = KE_final - KE_initial
Finally, the total work done on the skateboarder is equal to the change in kinetic energy (ΔKE).
You can calculate the answer by plugging in the values and performing the calculations.
1/2mv^2(final)-1/2mv^2(initial)
2600J