Question

A lift with a load of \(1000kg\) is moving up against the frictional force \(2000N\). If the power delivered to it by the operating motor is 36000 W, then the speed of the lift is \((g = 10 m s^{-2})\)

• A. \(2 ms^{-1}\)
• B. \(4 ms^{-1}\)
• C. \(3 ms^{-1}\)
• D. \(6 ms^{-1}\)
• E. \(10 ms^{-1}\)

Hint:

When an object moves at constant speed, the net force is zero. The applied force equals the sum of opposing forces.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This problem relates power, force, and velocity. The power delivered by the motor is used to overcome the downward forces (gravity and friction) and move the lift at a certain speed. Assuming the lift moves at a constant speed, the upward force provided by the motor must balance the total downward force.
Step 2: Key Formula or Approach:
The relationship between power (P), force (F), and velocity (v) is: \[ P = F \cdot v \] To find the speed (v), we can rearrange this to: \[ v = \frac{P}{F} \] Here, F is the total upward force the motor must exert.
Step 3: Detailed Explanation:
First, identify all the forces acting on the lift.
Downward force due to gravity (Weight): \(W = mg\)
Downward frictional force: \(F_{friction} = 2000 \text{ N}\)
Upward force exerted by the motor: \(F_{motor}\)
Calculate the weight of the lift and load: \[ W = (1000 \text{ kg}) \times (10 \text{ m/s}^2) = 10000 \text{ N} \] The total downward force is the sum of the weight and the frictional force. \[ F_{downward} = W + F_{friction} = 10000 \text{ N} + 2000 \text{ N} = 12000 \text{ N} \] Since the power delivered results in the upward motion, the motor must provide an upward force equal to the total downward force to move the lift (assuming constant velocity). \[ F_{motor} = F_{upward} = F_{downward} = 12000 \text{ N} \] Now, we can use the power formula to find the speed (v). We are given:
Power, \(P = 36000 \text{ W}\)
Total upward force, \(F = 12000 \text{ N}\)
\[ v = \frac{P}{F} = \frac{36000 \text{ W}}{12000 \text{ N}} = 3 \text{ m/s} \] Step 4: Final Answer:
The speed of the lift is 3 ms\(^{-1}\). This corresponds to option (C).