A chair lift takes skiers to the top of a mountain that is 320 m high. The average mass of skiers complete with equipment is 85 kg . The chair lift can deliver three skiers to the top of the mountain every 36 s
Determine the power required to carry out this task
If friction increases the power by 25% what power must the motor running the lift be able to deliver
massrate= 85/36 kg/second
power= force*distance/time= force/time *distance
= massrate*g*distance
I am not certain what the last question states.
To determine the power required to carry out the task, we can use the formula:
Power = Work / Time
First, let's calculate the work done to lift one skier to the top of the mountain. This can be calculated using the formula:
Work = Force * Distance
The force can be calculated using Newton's second law of motion:
Force = Mass * Acceleration
Acceleration due to gravity is approximately 9.8 m/s^2. Thus, the force can be calculated as:
Force = Mass * 9.8
So, for one skier, the force will be:
Force = 85 kg * 9.8 m/s^2 = 833 N
Now, let's calculate the work done to lift one skier to the top of the mountain:
Work = Force * Distance = 833 N * 320 m = 266,560 J
To determine the power required to carry out this task, we need to divide the work by the time taken for three skiers to reach the top of the mountain, which is 36 s:
Power = Work / Time = 266,560 J / 36 s = 7398.89 W (or 7.4 kW)
Therefore, the power required to carry out this task is approximately 7.4 kilowatts.
If friction increases the power by 25%, the total power needed will be 125% of the original power. Let's calculate the new power:
New Power = 1.25 * 7.4 kW = 9.25 kW
Therefore, if friction increases the power by 25%, the motor running the lift must be able to deliver approximately 9.25 kilowatts of power.
To determine the power required to carry out the task of taking skiers to the top of the mountain, we can use the formula:
Power = Work/Time
First, let's calculate the work done.
Work = Force * Distance
Since the work done against gravity is equal to the weight of the skiers multiplied by the height of the mountain, we have:
Work = weight * height
Weight = mass * acceleration due to gravity
Given that the average mass of skiers is 85 kg and the height of the mountain is 320 m, we can calculate the weight and work done:
Weight = 85 kg * 9.8 m/s^2 (acceleration due to gravity) = 833 N
Work = 833 N * 320 m = 266,560 J
Next, let's calculate the time taken for one skier to reach the top:
Time = 36 s / 3 skiers = 12 s
Now, we can calculate the power required:
Power = Work / Time = 266,560 J / 12 s = 22,213.33 W or 22.21 kW (rounded to two decimal places)
If the friction increases the power required by 25%, we need to calculate the new power:
New Power = Power + (Power * 25%) = Power * (1 + 25%)
New Power = 22.21 kW * (1 + 0.25) = 22.21 kW * 1.25 = 27.76 kW
Therefore, the power that the motor running the lift must be able to deliver, considering the increased friction, is 27.76 kilowatts (kW).