How much rope would need to be pulled through a pulley with a mechanical advantage of 2 to lift a load 4 ft?
2 answers:
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Complete Question
The diagram for this question is shown on the first uploaded image
Answer:
The distance traveled in horizontal direction is
Explanation:
From the question we are told that
The length of the string is
The mass of the ball is
The height of ball is
Generally the work energy theorem can be mathematically represented as
Where PE is the loss in potential energy which is mathematically represented as
Where h is the difference height of ball at A and at B which is mathematically represented as
So
While KE is the gain in kinetic energy which is mathematically represented as
Where is the velocity of the of the ball
Therefore we have from above that
Making the subject we have
substituting values
Considering velocity of the ball when it hits the floor in terms of its vertical and horizontal component we have
The time taken to travel vertically from the point the ball broke loose can be obtained using the equation of motion
Where s is distance traveled vertically which given in the diagram as
The negative sign is because it is moving downward
Substituting values
solving for t we have
Now the distance traveled on the horizontal is mathematically evaluated as
