# Find Minimum Height to Lift 4kg Mass with 0.1kg Block & Pulley

• sal1234
In summary: I don't see how it can be solved if we are not given the duration of the collision or the stretching of the string.But if I understand you, this is a problem you have made by yourself and not found in some book right?

## Homework Statement

Two blocks of mass(4 Kg and 0.1 Kg ) are connected by a mass less string that passes over a friction less pulley.The 4 Kg mass rests on the ground and the 0.1 Kg is hanging above the ground.Find the minimum distance from which the 0.1 Kg mass can be lifted and drop so that it just lifts the 4 Kg mass off the ground.

## The Attempt at a Solution

In order to lift the 4kg mass the tension on the block must be greater than or equal to 40 N. Therefore when i drop the smaller block from a particular height h it should cause an impulse of 40 N along the string
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Delta2
You will need to post your attempt at understanding this before anyone can help you with it.

sal1234 said:
an impulse of 40 N
40 N is a force, not an impulse. What do you know about impulses?

Hmmm, shouldn't we also know the stretching of the string or the time duration of the "collision" (the sort duration process during which the small mass changes its velocity from ##\sqrt {2gh}## to something smaller or even zero (I suppose zero, cause that's what it means by "just lift the 4kg mass"). If the stretching and the time duration are zero, this means that the tension force becomes infinite, doesn't it?

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Delta² said:
Hmmm, shouldn't we also know the stretching of the string or the time duration of the "collision" (the sort duration process during which the small mass changes its velocity from ##\sqrt {2gh}## to something smaller or even zero (I suppose zero, cause that's what it means by "just lift the 4kg mass"). If the stretching and the time duration are zero, this means that the tension force becomes infinite, doesn't it?
Yes, there is something odd here. Maybe it is a trick question, or maybe some fact has been omitted, like a spring constant.

haruspex said:
40 N is a force, not an impulse. What do you know about impulses?
sorry, yes it is the Force.

Delta² said:
Hmmm, shouldn't we also know the stretching of the string or the time duration of the "collision" (the sort duration process during which the small mass changes its velocity from ##\sqrt {2gh}## to something smaller or even zero (I suppose zero, cause that's what it means by "just lift the 4kg mass"). If the stretching and the time duration are zero, this means that the tension force becomes infinite, doesn't it?
say t=0.001
will it be possible to solve the problem if i am not given the time of collission?

sal1234 said:
say t=0.001
will it be possible to solve the problem if i am not given the time of collission?
I don't see how it can be solved if we are not given the duration of the collision or the stretching of the string.
But if I understand you, this is a problem you have made by yourself and not found in some book right?
if ##\Delta t=0.001## then we simply solve the system of equations ##F\Delta t=mv_0## and ##v_0=\sqrt{2gh}## for ##v_0## and ##h##.

Delta² said:
we are not given the duration of the collision or the stretching of the string.
Even knowing the duration would not suffice. The question is the peak tension, so you would have to assume, say, an ideal spring.
Or, if we take it as inextensible, then the answer is any nonzero height.

Delta2
haruspex said:
Even knowing the duration would not suffice. The question is the peak tension, so you would have to assume, say, an ideal spring.
Or, if we take it as inextensible, then the answer is any nonzero height.
Maybe we can assume that the tension remains approximately constant during the "collision", though I know this doesn't look like a very realistic assumption.

## What is the purpose of finding the minimum height to lift a 4kg mass with a 0.1kg block and pulley?

The purpose of finding the minimum height is to determine the minimum amount of force needed to lift the 4kg mass using the given block and pulley system. This information can be useful in designing and optimizing lifting mechanisms.

## What are the factors that affect the minimum height required to lift the 4kg mass?

The minimum height required to lift the 4kg mass is affected by several factors such as the weight of the mass, the weight of the block and pulley, the coefficient of friction between the pulley and the rope, and the gravitational force.

## How can I calculate the minimum height to lift the 4kg mass with the 0.1kg block and pulley?

To calculate the minimum height, you can use the formula F = (m + M)g x h, where F is the minimum force required, m is the mass of the object being lifted, M is the mass of the block and pulley, g is the gravitational acceleration, and h is the minimum height required.

## Can the minimum height to lift the 4kg mass be reduced by using a different pulley system?

Yes, the minimum height can be reduced by using a more efficient pulley system such as a compound pulley or a system with multiple pulleys. These systems can reduce the amount of force required to lift the mass, thus reducing the minimum height needed.

## Are there any safety precautions to consider when lifting a 4kg mass with a 0.1kg block and pulley?

Yes, it is important to ensure that the block and pulley system is securely mounted and can handle the weight of the mass. It is also important to use proper lifting techniques and to be cautious of any potential hazards such as the rope slipping or the pulley breaking under too much force.