Calculate the power needed from the motor of an elevator for it to be able to lift a 1x10^4kg mass a distance of 20m in 5s. (Enter your answer in scientific notation utilizing "e" format and rounding the decimal value to one decimal place.)
I used the equation p = w/t
1e4kg(20m)/5s = 40,000J --> 4.0e4
My answer was incorrect. Please help!
F = m*g = 1*10^4kg * 9.8N/kg = 9.8*10^4N
P = F*d/t = 9.8*10^4 * 20/5 = 3.92*10^5
J/s = 3.92*10^5 Watts. = 3.92e5 Watts.
Note: Your Eq should have been m*g * d/t
You omitted g(9.8m/s^2).
Well, first of all, I have to say that your equation p = w/t is correct. Good job on that! However, let's double-check your calculation.
The work done is given by the formula: w = mgh, where m is the mass being lifted, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height through which the mass is lifted.
So, w = 10^4 kg * 9.8 m/s^2 * 20 m = 1.96e6 J.
Now, let's substitute this value into the power equation:
p = w/t = 1.96e6 J / 5 s = 3.92e5 W.
Therefore, the power needed from the motor would be 3.92e5 W.
To calculate the power needed to lift the mass, we can use the formula:
Power (P) = Work (W) / time (t)
The work done in lifting the mass can be calculated using the formula:
Work (W) = Force (F) x Distance (d)
The force required to lift the mass can be calculated using the formula:
Force (F) = mass (m) x acceleration due to gravity (g)
The acceleration due to gravity is approximately 9.8 m/s^2.
Let's calculate the force first:
Force (F) = 1e4 kg x 9.8 m/s^2 = 9.8e4 N
Now, let's calculate the work done:
Work (W) = Force (F) x Distance (d) = 9.8e4 N x 20 m = 1.96e6 J
Finally, let's calculate the power:
Power (P) = Work (W) / time (t) = 1.96e6 J / 5 s = 3.92e5 W
Therefore, the power needed from the motor of the elevator is 3.92e5 watts.
To correctly calculate the power needed from the motor of the elevator, you need to use the equation:
Power (P) = Work (W) / Time (t)
Work (W) is calculated by multiplying the force applied (F) by the distance (d) over which the force is applied:
Work (W) = Force (F) * Distance (d)
In this case, the force required to lift the mass would be the weight of the mass, which is calculated using:
Force (F) = Mass (m) * Gravitational acceleration (g)
Gravitational acceleration (g) is approximately 9.8 m/s^2 on Earth.
So, let's break down the calculation:
Mass (m) = 1x10^4 kg
Gravitational acceleration (g) = 9.8 m/s^2
Distance (d) = 20 m
Time (t) = 5 s
First, calculate the force:
Force (F) = Mass (m) * Gravitational acceleration (g)
F = (1x10^4 kg) * (9.8 m/s^2)
F = 9.8x10^4 N
Next, calculate the work:
Work (W) = Force (F) * Distance (d)
W = (9.8x10^4 N) * (20 m)
W = 1.96x10^6 J
Finally, calculate the power:
Power (P) = Work (W) / Time (t)
P = (1.96x10^6 J) / (5 s)
P = 3.92x10^5 W
Therefore, the power needed from the motor of the elevator is 3.92x10^5 Watts.