A motor is rated to deliver 10.0kW. At what speed can this motor raise a mass of 2.75x10^4kg?
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To find the speed at which the motor can raise a mass, we need to make use of the power and weight of the mass.
Step 1: Convert the power rating from kilowatts (kW) to watts (W).
Given: Power (P) = 10.0 kW
1 kW = 1000 W
So, P = 10.0 kW * 1000 = 10,000 W
Step 2: Calculate the force needed to lift the mass.
The weight (W) of an object is given by W = m * g, where m is the mass and g is the acceleration due to gravity. In this case, the mass is 2.75 x 10^4 kg.
Given: m = 2.75 x 10^4 kg, g = 9.8 m/s^2
W = 2.75 x 10^4 kg * 9.8 m/s^2 = 2.695 x 10^5 N
Step 3: Calculate the speed (v) at which the motor can raise the mass.
Power (P) is defined as P = F * v, where F is the force and v is the velocity (speed).
Substituting the values, we get F * v = 10,000 W and F = 2.695 x 10^5 N.
Rearranging the equation to solve for v, we have v = P / F.
v = 10,000 W / 2.695 x 10^5 N ≈ 0.0371 m/s
Therefore, the speed at which the motor can raise the mass of 2.75 x 10^4 kg is approximately 0.0371 m/s.
To determine the speed at which the motor can raise a mass of 2.75x10^4 kg, we need to use the power equation, which relates power (P), force (F), and speed (v). The equation is given by:
P = F * v
Where:
P is the power in watts (W)
F is the force in newtons (N)
v is the speed in meters per second (m/s)
Rearranging the formula, we get:
v = P / F
First, we need to determine the force required to raise the mass. The force can be calculated using Newton's second law of motion:
F = m * g
Where:
m is the mass in kilograms (kg)
g is the acceleration due to gravity (approximated as 9.8 m/s^2)
Substituting the given values:
m = 2.75x10^4 kg
g = 9.8 m/s^2
F = (2.75x10^4 kg) * (9.8 m/s^2)
F ≈ 2.696x10^5 N
Now, we have the force (F) and the power (P) given as 10.0 kW, but we need to convert it to watts:
10.0 kW = 10,000 W
Substituting the values into the equation:
v = (10,000 W) / (2.696x10^5 N)
Simplifying:
v ≈ 0.037 m/s
Therefore, the motor can raise a mass of 2.75x10^4 kg at a speed of approximately 0.037 m/s.