MCAT Physical : Forces
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Example Question #71 : Forces
A 2kg mass is suspended on a rope that wraps around a frictionless pulley attached to the ceiling with a mass of 0.01kg and a radius of 0.25m. The other end of the rope is attached to a massless suspended platform, upon which 0.5kg weights may be placed. While the system is initially at equilibrium, the rope is later cut above the weight, and the platform subsequently raised by pulling on the rope.
If, instead of using one pulley to raise the platform after it falls, we decided to use two, how would the force required to lift the platform change?
Increase by 1/2
Decrease by 4 times
Decrease by 1/2
Increase by 4 times
Decrease by 1/2
One-half of the force will be required to pull the platform up in the new scenario. In the diagram below, now notice that the box has two upward tension forces due to the pulley attached directly to the box. These two tension forces act against the weight of the box, meaning that each tension force is one half of the weight of the box. Because tension is transmitted unchanged over the length of the rope, the tension a person would need to pull against would be half the weight of the box. This leads us to determine that half the force would be required to lift the box if two pulleys were used.
Example Question #72 : Forces
Two students (student X and student Y) lift a boulder vertically from point A to point B. Student X directly lifts the boulder from point A to point B, whereas student Y uses a pulley to lift the boulder. This allows student Y to apply a force (
The vertical distance between point A and point B is 
Student Z uses a frictionless inclined plane to lift the boulder and has to apply only a third of 
The pulley has a greater mechanical advantage than the inclined plane
The inclined plane has a greater mechanical advantage than the pulley
The pulley and the inclined plane have the same mechanical advantage
More information is required to determine the relative mechanical advantage
The pulley and the inclined plane have the same mechanical advantage
The question states that:
Recall that the passage states that 
The force exerted by student Y and student Z is the same.
Mechanical advantage is defined as:
The weight of the object is the same for both students because both of them are lifting the same boulder. The force applied is also the same; therefore, mechanical advantage for both machines is the same.
Example Question #73 : Forces
Two students (student X and student Y) lift a boulder vertically from point A to point B. Student X directly lifts the boulder from point A to point B, whereas student Y uses a pulley to lift the boulder. This allows student Y to apply a force (
The vertical distance between point A and point B is
If the pulley has a mechanical advantage of 
The definition of mechanical advantage is:
Rearranging this equation and solving for weight gives:
Mechanical advantage is a unitless quantity. Remember the difference between weight and mass. Weight is a measure of force and has units of Newtons, whereas mass has units of kilograms.
Example Question #71 : Forces
A 2kg object falls from a height of 3m onto a spring, which compresses 20cm. What is the spring constant?
Conservation of energy is the key here. Initial energy is all gravitational potential energy:
Note that the final height change is equal to the height above the spring added to the displacement of the spring.
This is equal to the final energy, which is all spring potential energy:
Set these equations equal and solve for the spring constant.
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