It takes 16s to raise a 2800lb car and the supporting 650lb hydraulic car-lift platform to a ht of 6.5 ft. Knowing that the overall conversion efficiency from electric to mechanical power for the system is 82% determine a) the average power output delivered by the hydraulic pump to lift the system b) the avg electric power required
To determine the average power output delivered by the hydraulic pump (part a) and the average electric power required (part b), we need to use the following formulas:
a) Power output = Work done / Time taken
b) Power input = Power output / Efficiency
Given information:
Mass of car (m) = 2800 lb
Mass of hydraulic lift platform (m_plat) = 650 lb
Height (h) = 6.5 ft
Time taken (t) = 16 s
Efficiency (η) = 82% = 0.82
Step 1: Convert the masses to kilograms:
Mass of car (m) = 2800 lb * 0.4536 kg/lb ≈ 1270.08 kg
Mass of hydraulic lift platform (m_plat) = 650 lb * 0.4536 kg/lb ≈ 294.84 kg
Step 2: Convert the height to meters:
Height (h) = 6.5 ft * 0.3048 m/ft ≈ 1.981 m
Step 3: Calculate the work done:
Work done (W) = Force * Distance
Force = gravitational force = (mass of car + mass of platform) * acceleration due to gravity
Distance = height
Force = (1270.08 kg + 294.84 kg) * 9.8 m/s^2 ≈ 15709.37 N
Work done (W) = 15709.37 N * 1.981 m ≈ 31098.17 J
Step 4: Calculate the average power output delivered by the hydraulic pump (part a):
Power output = Work done / Time taken
Power output = 31098.17 J / 16 s ≈ 1943.63 W
Therefore, the average power output delivered by the hydraulic pump is approximately 1943.63 Watts.
Step 5: Calculate the average electric power required (part b):
Power input = Power output / Efficiency
Power input = 1943.63 W / 0.82 ≈ 2370.27 W
Therefore, the average electric power required is approximately 2370.27 Watts.
To find the average power output delivered by the hydraulic pump to lift the system, we first need to calculate the work done on the car-lift system.
The work done (W) on an object is given by the equation:
W = force × distance
In this case, the force is equal to the weight being lifted, which is the sum of the car's weight and the platform's weight:
Total weight = car weight + platform weight
Total weight = 2800 lb + 650 lb
Now, we can determine the work done by finding the force exerted by the system:
W = Total weight × distance
W = (Total weight) × (height)
W = (2800 lb + 650 lb) × 6.5 ft
Now that we have the work done, we can calculate the power using the formula:
Power (P) = Work / Time
First, we need to convert the time from seconds to hours:
Time = 16 s × (1 hour / 3600 s)
Now, we can calculate the power output:
Power = Work / Time
To find the power output, we need to consider the conversion efficiency of the system. Let's denote the power output as P_output, and the power input (electric power required) as P_input.
P_output = P_input × Efficiency
Given that the efficiency is 82%, we can write:
P_output = 0.82 × P_input
Now, let's determine the average electric power required (P_input):
P_input = P_output / Efficiency
First, calculate the power output (P_output) using the previously calculated work and time:
P_output = Work / Time
Finally, substitute the known values into the equations to find the answers to parts (a) and (b).