The weight of a person will be greater when the lift

Options

A. accelerates downwards
B. fall with uniform velocity
C. accelerates upwards
D. retards upwards

Answer

To determine when the weight of a person in a lift is greater, we can analyze the forces acting on the person in different scenarios. Here’s how we can approach the problem step by step:

### Step 1: Understand the Concept of Weight
Weight is defined as the force exerted by gravity on an object. It can be calculated using the formula:
\[ W = mg \]
where \( W \) is the weight, \( m \) is the mass of the person, and \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \) on Earth).

### Step 2: Analyze the Forces in the Lift
When a person is in a lift, the apparent weight (normal force \( R \)) experienced by the person can change depending on the lift's motion.

### Step 3: Case 1 - Lift Moving Upward with Acceleration
When the lift is accelerating upwards with an acceleration \( a \):
- The forces acting on the person are:
- The gravitational force downward: \( mg \)
- The normal force upward: \( R \)

Using Newton's second law, we can write:
\[ R - mg = ma \]
Rearranging gives:
\[ R = mg + ma \]
Thus, the apparent weight \( R \) increases when the lift accelerates upwards.

### Step 4: Case 2 - Lift Moving Downward with Uniform Velocity
When the lift is moving downward with uniform velocity (no acceleration):
- The forces are balanced, and the normal force equals the gravitational force:
\[ R = mg \]
In this case, the apparent weight remains the same as the actual weight.

### Step 5: Case 3 - Lift Moving Downward with Acceleration
When the lift is accelerating downwards with an acceleration \( a \):
- The forces acting on the person are the same as before:
\[ R - mg = -ma \]
Rearranging gives:
\[ R = mg - ma \]
Thus, the apparent weight \( R \) decreases when the lift accelerates downwards.

### Conclusion
The weight of a person will be greater when the lift is accelerating upwards. In contrast, the weight will be less when the lift is accelerating downwards. When the lift moves at a constant velocity (either up or down), the weight remains the same.