An elevator weighing 4.56 N is supported by a steel cable. What is the tension in the cable when the elevator is accelerated upward at a rate of 3 m/s2?
An elevator weighing 4.56 N is supported by a steel cable. What is the tension in the cable when the elevator is accelerated upward at a rate of 3 m/s2?
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Question
![**Problem Statement:**
An elevator weighing 4.56 N is supported by a steel cable. What is the tension in the cable when the elevator is accelerated upward at a rate of 3 m/s²?
**Explanation:**
This problem involves calculating the tension in a cable supporting an elevator. The weight of the elevator is given as 4.56 N. When the elevator is accelerated upwards, the tension in the cable will increase due to this additional force.
To find the tension in the cable, use the formula:
\[ T = W + ma \]
Where:
- \( T \) is the tension in the cable,
- \( W \) is the weight of the elevator (4.56 N),
- \( m \) is the mass of the elevator, which can be found by rearranging the weight formula \( W = mg \) (where \( g = 9.8 \, \text{m/s}^2 \)),
- \( a \) is the acceleration of the elevator (3 m/s²).
Calculate the tension using these values to understand the forces at play when accelerating an elevator upwards.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff4116597-78e6-477d-91b2-9fa4cad4d0f7%2F2caa1518-89a3-416a-bac8-92d0714e91ad%2Ffc4i1bm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
An elevator weighing 4.56 N is supported by a steel cable. What is the tension in the cable when the elevator is accelerated upward at a rate of 3 m/s²?
**Explanation:**
This problem involves calculating the tension in a cable supporting an elevator. The weight of the elevator is given as 4.56 N. When the elevator is accelerated upwards, the tension in the cable will increase due to this additional force.
To find the tension in the cable, use the formula:
\[ T = W + ma \]
Where:
- \( T \) is the tension in the cable,
- \( W \) is the weight of the elevator (4.56 N),
- \( m \) is the mass of the elevator, which can be found by rearranging the weight formula \( W = mg \) (where \( g = 9.8 \, \text{m/s}^2 \)),
- \( a \) is the acceleration of the elevator (3 m/s²).
Calculate the tension using these values to understand the forces at play when accelerating an elevator upwards.
Expert Solution
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Step 1
When an object moves upwardswith acceleration 'a' , effective value of g is
g' = g+ a
Giventhat a = 3.0m/s2
g' = 9.8+ 3.0 = 12.8m/s2
Mass of elevator = weight /g
= 4.59 /9.8
m = 0.468 kg
Step by step
Solved in 2 steps
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