Question

In the figure above, each pulley added to the pulley system after Pulley A reduces the amount of force required to lift an object to \(50 \%\) of the original amount. If the system has three additional pulleys, what would be the approximate force, in Newtons, that is exerted to lift a weight that normally requires 200 pounds of force to lift? ( 1 Newton \(=0.224\) pounds) A) \(5.6\) B) \(11.2\) C) \(111.6\) D) \(223.2\) $$ Q=17.6 T $$

Short answer

The approximate force exerted to lift the weight using the pulley system is \(111.6\) Newtons. The correct answer is C) \(111.6\).

Step-by-step solution

Calculate the force required with three additional pulleys

Since every additional pulley reduces the force required to 50% of the original amount, we can calculate the force required after adding three additional pulleys using the following formula: Force with additional pulleys = Original Force * (0.5)^number of additional pulleys In this case, the original force is 200 pounds, and there are three additional pulleys. So: Force with additional pulleys = 200 * (0.5)^3

Calculate the force in Newtons

Now we have the force required in pounds, which needs to be converted to Newtons using the conversion factor: 1 Newton = 0.224 pounds To convert the force in pounds to Newtons, we will divide the force by the conversion factor: Force in Newtons = Force in pounds / 0.224 But, first, we need to calculate the force with additional pulleys.

Calculate the force with additional pulleys

Using the formula from Step 1: Force with additional pulleys = 200 * (0.5)^3 Force with additional pulleys = 200 * 0.125 Force with additional pulleys = 25 pounds

Convert the force to Newtons

Now we can convert 25 pounds of force to Newtons using the conversion factor from Step 2: Force in Newtons = 25 / 0.224 Force in Newtons = 111.6 So, the approximate force exerted to lift the weight using the pulley system is 111.6 Newtons. The correct answer is C) \(111.6\).

Key concepts

Force Calculation

Calculating force is a crucial part of solving physics problems, especially when dealing with pulley systems. It allows us to determine how much effort is needed to move or lift an object. In the context of this exercise, the original force required to lift an object is given as 200 pounds.

When additional pulleys are introduced into the system, they can significantly reduce the needed force by distributing the load. To calculate the new force required, we use the equation:

• Force with additional pulleys = Original Force * (0.5)^(number of additional pulleys)

This equation takes the original force and reduces it by half for each additional pulley. In this problem, three additional pulleys reduce the force to 12.5% of the original, resulting in a force of 25 pounds.

Pulley Systems

Pulley systems are mechanical devices used to lift or move loads with reduced force. Each pulley in a system can change the direction of the applied force or reduce the amount of force required. Pulley systems are often referred to in terms of their efficiency in terms of mechanical advantage.

The setup in this problem involves multiple pulleys. The inclusion of three additional pulleys helps to lessen the lifting force significantly. This is because each pulley adds to the mechanical advantage, spreading the load more and decreasing the required effort. Whenever a pulley is added, the system becomes more efficient, enabling the same load to be lifted with less force.

Unit Conversion

Unit conversion is vital in ensuring that all measurements are in the same system for effective calculations. In physics, we often convert between different units of force, such as pounds and Newtons. The problem gives us a scenario where the weight to be lifted is initially measured in pounds.

Conversion is straightforward when the conversion factor is known. Here, we have:

• 1 Newton = 0.224 pounds

To convert from pounds to Newtons, we divide the force in pounds by the conversion factor. For this problem, once we have calculated the required force in pounds as 25, converting to Newtons follows:

• Force in Newtons = 25 pounds / 0.224 = 111.6 Newtons

This ensures our final answer is in the universally standard SI units for force.

Mechanical Advantage

Mechanical advantage describes how a machine, such as a pulley system, can multiply force. This makes it easier to accomplish tasks with less input effort by distributing the load more evenly. Such principles are essential when calculating the effects of each added pulley on the force required to lift an object.

Essentially, mechanical advantage is the factor by which a machine multiplies the force put into it. In this problem, each additional pulley doubles the mechanical advantage, thereby cutting the required force by half each time. With three pulleys, the mechanical advantage becomes significant, resulting in a reduction to only 12.5% of the initial force needed to lift the load. This exemplifies why understanding mechanical advantage is crucial for practical applications of physics in designing efficient systems.