Question

Once in the hospital, the doctors rush him into an elevator. The elevator and everything in it has a mass of 1,808kg. If the elevator starts accelerating upward at

1.11m/s2, what is the tension in the cable?

Mr. Frey is 90kg

Use 9.8 for acceleration

Answer 1

T ≈ 19725 N

Step-by-step explanation:

To solve for the tension in the elevator cable, we need to consider two forces acting on the elevator: the force due to gravity (which is the weight of the elevator and its contents) and the force due to the elevator's upward acceleration.

Given:

• m = 1,808 kg

• a = 1.11 m/s²
• g = 9.8 m/s²

Using the free-body diagram I have attached to the answer, we can create a sum of forces:

`\Longrightarrow \sum \vec F_y: \vec T-\vec w=m\vec a`

Solving for 'T':

`\Longrightarrow \vec T=m \vec a + \vec w`

The weight 'w' is the mass of the elevator and its contents times the acceleraction due to gravity:

`\Longrightarrow \vec T=m \vec a + mg\\\\\\\\\therefore \vec T = m(\vec a + g)`

Plugging in our values:

`\Longrightarrow T=(1808 \ kg)(1.11 \ m/s^2 + 9.8 \ m/s^2)\\\\\\\\\therefore \boxed{\vec T = 19725 \ N }`

The tension in the elevator cable, when it starts accelerating upward at

1.11 m/s² is approximately 19725 N.