Calculating Average Power of a Ski Lift in 2.0 Minutes Using Tension in Cable

[neoking77]

In 2.0 minutes, a ski lift raises four skiers at constant speed to a height of 140 m. The average mass of each skier is 65kg. What is the average power provided by the tension in the cable pulling the lift?

t= 2.0min(60s/1min) = 120s
m = 65kg x 4 = 260kg

Wnc = △Ek + △Ep
Wnc = Ekf - Eki + Epf - Epi
Wnc = -mv^2 + mghf
Wnc = -1/2(v)^2 + 356720J


P = [-1/2(v)^2 + 356720J]/ 120s

i do not know v so i don't know how to solve this. have i made any errors? thanks in advance

 

[GregA]

From what I can see..the velocity 'v' is irrelevant as there is no change in mechanical energy (constant speed)...you have almost solved it

 

[quicknote]

Your calculations and approach seem to be correct. However, to find the average power, you will need to know the average velocity of the ski lift. This can be calculated by dividing the total displacement (140m) by the time taken (120s). Once you have the average velocity, you can substitute it into the formula for work done, W = Fd, where F is the force (tension in the cable) and d is the displacement. Then, to find the average power, you can divide the work done by the time taken (120s). This will give you the average power provided by the tension in the cable pulling the lift.

 

[kyle8921]

Your calculations seem correct, but you are missing the value for the velocity (v) in order to calculate the average power. To find the velocity, you can use the equation v = √(2gh), where g is the acceleration due to gravity (9.8 m/s^2) and h is the height (140 m). Once you have the value for v, you can plug it into your equation for power (P) and solve for the average power provided by the tension in the cable. This will give you the answer in watts (W), which is the standard unit for power. I hope this helps!