A skier (75 kg) goes down a 15* slope. The coefficient of kinetic friction between the skis and the snow is 0.185. The length of the slope is of 500m.
a) What is the work done by gravity?
Answer) Wmg = mgd
= 75kg(9.8N/kg)500m(sin15)
= 354 977 J
Is it cos or sin? And is Work done by both air and friction supposed to be higher than work done by gravity at the end of the slope?
The sine is correct function to use, but you made a mistake in the multiplication.
Work done by friction (on snow) and aerodynamic drag is negative. The skier does the work. The absolute value equals the gravity work only if the kinetic energy does not change.
what is the mistake? And thank you for the information!
and drag and friction work has to be higher at the end than gravity in order to stop the skier at the bottom, right?
oh and I see what you mean, it's 95 116 J, thanks again!
75*9.8*500*(sin15) = 9.516*10^4 J
To calculate the work done by gravity, you need to determine the force of gravity acting on the skier. Since the skier weighs 75 kg, the force of gravity can be calculated as:
Fg = m * g
= 75 kg * 9.8 m/s^2
= 735 N
The angle of the slope is given as 15°. To find the component of gravity that acts parallel to the slope, you can use trigonometry. Since the angle is with respect to the horizontal direction, you will need to use the sine function:
Fg_parallel = Fg * sin θ
= 735 N * sin 15°
Now, to calculate the work done by gravity, you multiply the force parallel to the slope by the distance traveled:
Work done by gravity (Wmg) = Fg_parallel * d
= 735 N * sin 15° * 500 m
≈ 354,977 J
So, the work done by gravity is approximately 354,977 J.
Regarding your second question, the work done by friction and air resistance can vary. Generally, the work done by friction and air resistance is often dissipated as heat, causing a decrease in the kinetic energy of the skier. At the end of the slope, the work done by gravity, friction, and air resistance should sum up to zero, assuming that the skier comes to a stop. In this case, the work done by all the forces, including friction and air resistance, should be equal to the work done by gravity.