Th e motor of an elevator develops power at a rate of 2500 W. a Calculate the speed that a 1200 kg load is being raised at. b In practice it is found that the load is lifted more slowly than indicated by your answer to a. Suggest reasons why this is so.

Let's break this down step by step.

### Part (a) Calculate the speed at which the 1200 kg load is being raised.

The power developed by the motor is given as 2500 W, and the mass of the load is 1200 kg. The power required to lift the load is related to the gravitational force acting on the load and the speed at which the load is raised.

#### Formula:
Power \( P = F \cdot v \)

Where:
- \( P \) is the power (in watts),
- \( F \) is the force (in newtons),
- \( v \) is the velocity (in meters per second).

The force \( F \) required to lift the load is the gravitational force, which is:
\[ F = m \cdot g \]
Where:
- \( m = 1200 \, \text{kg} \) is the mass of the load,
- \( g = 9.8 \, \text{m/s}^2 \) is the acceleration due to gravity.

Substitute the values:
\[
F = 1200 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 11760 \, \text{N}
\]

Now, using the power formula:
\[
P = F \cdot v
\]

Rearrange to solve for \( v \):
\[
v = \frac{P}{F}
\]

Substitute the known values:
\[
v = \frac{2500 \, \text{W}}{11760 \, \text{N}} \approx 0.213 \, \text{m/s}
\]

Thus, the speed at which the 1200 kg load is being raised is approximately **0.213 m/s**.

---

### Part (b) Reasons why the actual lifting speed is slower:

In practice, the actual speed might be slower than calculated due to several reasons:

1. **Friction**: There is friction in the pulleys, cables, and other mechanical parts of the elevator, which reduces the efficiency of the system.
2. **Air resistance**: Although it may be minimal, air resistance could slightly decrease the lifting speed.
3. **Energy losses in the motor**: The motor may lose energy due to inefficiencies, such as electrical resistance or heat generation, reducing the actual power delivered.
4. **Start-up and inertia**: The elevator takes time to accelerate from rest due to the inertia of the load.
5. **Safety mechanisms**: Elevators often operate at slower speeds than their theoretical maximum to ensure safety, smooth operation, and to prevent sudden jerks or damage to the system.

---

Would you like any additional explanations or further clarification on this problem?

### 5 Related Questions:
1. How does friction affect the efficiency of an elevator system?
2. What is the role of pulley systems in reducing the required force to lift a load?
3. How can we improve the efficiency of a motor-driven elevator?
4. What other factors could influence the power requirements of an elevator system?
5. How would a change in gravitational acceleration (e.g., on another planet) affect the lifting speed?

### Tip: 
Always consider friction and mechanical inefficiencies in practical problems, as ideal calculations often neglect these real-world factors.

The motor of an elevator develops power at a rate of 2500 W. a) Calculate the speed that a 1200 kg load is being raised at. b) In practice, it is found that the load is lifted more slowly than indicated by your answer to a. Suggest reasons why this is so.

Learn how to calculate the speed of a 1200 kg load being raised by an elevator motor with 2500 W power. Understand the step-by-step process using key physics formulas, including power and force relationships. Explore factors that reduce actual speed, like friction and energy loss.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation