A skateboarder with a mass of 68.6 kg and a speed of 4.92 m/s coasts across a parking lot. After coasting for 35.0 m the skateboarder has a speed of 1.12 m/s. How much work has been done against friction?
a) 338 J
b) 76.8 J
c) 7.5 J
d) 787 J
1/2 * 68.6 * (4.92^2 - 1.12^2)
Work = Change in Ek
mvfinal squared divided by 2 - mvinitial squared divided by 2
=-787
To find the work done against friction, we can use the Work-Energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.
The initial kinetic energy (K_i) of the skateboarder can be calculated using the equation:
K_i = (1/2) * m * v_i^2
where m is the mass of the skateboarder and v_i is the initial speed.
Substituting the given values:
m = 68.6 kg
v_i = 4.92 m/s
K_i = (1/2) * 68.6 kg * (4.92 m/s)^2
K_i = 43.2 J
The final kinetic energy (K_f) can be calculated using the same equation:
K_f = (1/2) * m * v_f^2
where v_f is the final speed.
Substituting the given values:
v_f = 1.12 m/s
K_f = (1/2) * 68.6 kg * (1.12 m/s)^2
K_f = 42.9 J
The work done against friction is the difference in kinetic energy:
Work = K_f - K_i
Work = 42.9 J - 43.2 J
Work = -0.3 J
Since the work done against friction is negative, indicating that work is done against the motion, the correct option is b) 76.8 J.
To find the work done against friction, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
The work done by friction can be calculated as:
Work = Change in Kinetic Energy
The initial kinetic energy of the skateboarder can be found using the equation:
Initial Kinetic Energy = (1/2) * mass * (initial velocity)^2
Plugging in the given values:
Mass = 68.6 kg
Initial velocity = 4.92 m/s
Initial Kinetic Energy = (1/2) * 68.6 kg * (4.92 m/s)^2
Similarly, we can find the final kinetic energy using the equation:
Final Kinetic Energy = (1/2) * mass * (final velocity)^2
Plugging in the given values:
Mass = 68.6 kg
Final velocity = 1.12 m/s
Final Kinetic Energy = (1/2) * 68.6 kg * (1.12 m/s)^2
Now, we can find the change in kinetic energy:
Change in Kinetic Energy = Final Kinetic Energy - Initial Kinetic Energy
Finally, we can calculate the work done against friction:
Work = Change in Kinetic Energy
After performing the calculations, we find that the work done against friction is approximately 338 J. Therefore, the correct answer is option a) 338 J.