# Boulder being pulled up by a chain. Find max acceleration

• Wobble
In summary: So t=sqrt(2X/a). So t=sqrt(2*150/2.14)= 8.81 secondsIn summary, the maximum force that the chain can support is 16483.6 (in penguins/cubic banana units) and the weight of the system is 13524. To find the maximum acceleration, we can use the equation F=ma and solve for a, which gives us a value of 2.14 in penguins/cubic banana units. To find the time it takes for the boulder to be lifted out at maximum acceleration, we can use the equation X=1/2*a*t^2 and solve for t, giving us a value of 8.81 seconds.
Wobble

## Homework Statement

A 800 kg boulder is raised from a quarry 150 m deep by a long uniform chain having a mass of 580 kg. This chain is of uniform strength, but at any point it can support a maximum tension no greater than 2.90 times its weight without breaking.

What is the maximum acceleration the boulder can have and still get out of the quarry?

How long does it take to be lifted out at maximum acceleration if it started from rest?

THE MAX ACCELERATION IS 2.14

How do I find time?

## Homework Equations

f=ma, one of the kinematic equations for the second question

## The Attempt at a Solution

The max force is is the weight of the chain*2.9 = 16483.6

The weight of the system is (chain*9.8)+(boulder*9.8) = 13524

I'm not sure where to go with these numbers. The weight of the system would be pointing down. So something with the tension would be the force going up. How do I find the tension, and then move to acceleration?
EDIT EDIT EDIT: The tension to hold up the boulder = the weight of the boulder and chain. So I did (Max tension - tension value)=18483.6 - 13524=2959.6

2959.6 is the force you can have for the system to work. So 2959.6/(mass of the boulder and chain) = 2959.6/1380 = 2.14

Is 2.14 right?

Last edited:
In one place you write that the maximum force is 16483.6 (no units given so I suppose we are in penguins/cubic banana as usual).
Later on we use the value 18483.6. So a little discrepancy has crept in.

Wobble said:
How do I find time?

You can use the equation X=X0 + V0*t + 1/2*a*t2
Since you know the initial distance and initial velocity are 0, you solve for just X=1/2*a*t2

You know X and a. Just rearrange and solve for t.

delta X = Vot + 1/2 at^2. Vo is 0.

## 1. How is a boulder being pulled up by a chain different from being pulled up by a rope?

A chain is typically stronger than a rope, so it can withstand a higher maximum tension force without breaking. Additionally, a chain has less give and stretch than a rope, so it can provide a more stable and controlled movement when pulling up the boulder.

## 2. What factors determine the maximum acceleration of a boulder being pulled up by a chain?

The maximum acceleration of a boulder being pulled up by a chain depends on the strength and weight of the chain, the weight of the boulder, and the force being applied to pull the boulder up. Friction and the angle of the chain can also affect the maximum acceleration.

## 3. How does the angle of the chain affect the maximum acceleration of the boulder?

The angle of the chain can affect the maximum acceleration of the boulder by changing the direction of the force being applied. If the chain is at a steeper angle, more force will be directed towards pulling the boulder up rather than against the ground, resulting in a higher maximum acceleration.

## 4. Can the maximum acceleration of a boulder being pulled up by a chain be greater than the acceleration due to gravity?

Yes, it is possible for the maximum acceleration of a boulder being pulled up by a chain to be greater than the acceleration due to gravity. This can occur if the force being applied to pull the boulder up is greater than the force of gravity pulling the boulder down.

## 5. How can the maximum acceleration of a boulder being pulled up by a chain be calculated?

The maximum acceleration of a boulder being pulled up by a chain can be calculated by dividing the maximum force that the chain can withstand by the mass of the boulder. This will give the maximum acceleration that the boulder can experience without breaking the chain.

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