### Understanding Forces in Moving ElevatorsWhen analyzing the forces acting on an elevator in motion, it is crucial to consider the tension in the cable (T) and the weight of the elevator (w). Let's examine different scenarios to understand the relationship between these forces.#### (a) Elevator with Mass (m) Moving UpwardAn elevator with mass \( m \) moving upward has two forces acting on it:- **Upward force of tension in the cable (T)**- **Downward force due to gravity (weight, w)**When the elevator is accelerating upward, **T** is \(\boxed{\text{greater}}\) than **w**.#### (b) Elevator Moving at Constant Velocity UpwardWhen the elevator is moving at a constant velocity upward, which force is greater, **T** or **w**?- \( T \)- \( w \)- **Both forces are equal** \(\boxed{\checkmark}\)At constant velocity, the forces are balanced, so \( T = w \).#### (c) Elevator Moving Upward, Decelerating (Acceleration is Downward)When the elevator is moving upward but decelerating (acceleration is downward), which force is greater, **T** or **w**?- \( T \)- \( w \) \(\boxed{\checkmark}\)- Both forces are equalHere, the force of gravity \( w \) exceeds the tension \( T \).#### (d) Elevator with Mass of 1250 kg and Upward Acceleration of 2.9 m/s²Let's consider an elevator with a mass of 1250 kg experiencing an upward acceleration of \(2.9 \, \text{m/s}^2\). Find \( T \):- \( T \) = \(\boxed{15972.0 \, \text{N}}\)Is this answer consistent with the answer to part (a)?- Yes \(\boxed{\checkmark}\)- No#### (e) Elevator Moving with Constant Upward Velocity of 10 m/sIf the elevator now moves with a constant upward velocity of 10 m/s, find \( T \):- \( T \) = \(\boxed{12250.0 \, \text{N}}\)Is this answer consistent with your answer to part (b)?- Yes \(\boxed{\checkmark}\)- No#### (

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elevator mass m moving upward has two forces acting on it: the upward force of tension in the cable and Ehe downward force aue to gravity. When the elevator is accelerating upward, which Is greater; 7 o Both forces are equal. (b) When the elevator is moving at a constant velocity upward, which is greater, Tor w? ] Both forces are equal. (c) When the elevator is moving upward, but the acceleration is downward, which is greater, Tor w? O Both forces are equal.

elevator mass m moving upward has two forces acting on it: the upward force of tension in the cable and Ehe downward force aue to gravity. When the elevator is accelerating upward, which Is greater; 7 o Both forces are equal. (b) When the elevator is moving at a constant velocity upward, which is greater, Tor w? ] Both forces are equal. (c) When the elevator is moving upward, but the acceleration is downward, which is greater, Tor w? O Both forces are equal.

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Concept explainers

Newton's Second Law

Newton’s laws of motion describe the relationship between the motion of an object and forces acting on it. Newton’s law of motion has two types as follows:

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Question

### Understanding Forces in Moving Elevators

When analyzing the forces acting on an elevator in motion, it is crucial to consider the tension in the cable (T) and the weight of the elevator (w). Let's examine different scenarios to understand the relationship between these forces.

#### (a) Elevator with Mass (m) Moving Upward
An elevator with mass \( m \) moving upward has two forces acting on it:

- **Upward force of tension in the cable (T)**
- **Downward force due to gravity (weight, w)**

When the elevator is accelerating upward, **T** is \(\boxed{\text{greater}}\) than **w**.

#### (b) Elevator Moving at Constant Velocity Upward
When the elevator is moving at a constant velocity upward, which force is greater, **T** or **w**?

- \( T \)
- \( w \)
- **Both forces are equal** \(\boxed{\checkmark}\)

At constant velocity, the forces are balanced, so \( T = w \).

#### (c) Elevator Moving Upward, Decelerating (Acceleration is Downward)
When the elevator is moving upward but decelerating (acceleration is downward), which force is greater, **T** or **w**?

- \( T \)
- \( w \) \(\boxed{\checkmark}\)
- Both forces are equal

Here, the force of gravity \( w \) exceeds the tension \( T \).

#### (d) Elevator with Mass of 1250 kg and Upward Acceleration of 2.9 m/s²
Let's consider an elevator with a mass of 1250 kg experiencing an upward acceleration of \(2.9 \, \text{m/s}^2\). Find \( T \):

- \( T \) = \(\boxed{15972.0 \, \text{N}}\)

Is this answer consistent with the answer to part (a)?

- Yes \(\boxed{\checkmark}\)
- No

#### (e) Elevator Moving with Constant Upward Velocity of 10 m/s
If the elevator now moves with a constant upward velocity of 10 m/s, find \( T \):

- \( T \) = \(\boxed{12250.0 \, \text{N}}\)

Is this answer consistent with your answer to part (b)?

- Yes \(\boxed{\checkmark}\)
- No

#### (

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