Multiple Pulley Problem [SOLUTION]

In summary, the conversation discusses a problem involving the use of pulleys to support a patient's head during healing. The system consists of frictionless pulleys and a rope with an angle of 26.0°. The goal is to determine the weight of the mass needed to support the head, which makes up 7.00% of the patient's body weight. The solution involves using the equation Fnet=ma and determining the tension in the line. The final answer is M = T/g, where T is the tension needed to support half of the head's weight.
  • #1
jumptheair
16
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[SOLVED] Multiple pulley problem

Homework Statement



**Image of apparatus
http://www.learning.physics.dal.ca/library/Graphics/Gtype09/neck.jpg

When a patient's injured neck is healing, it is often desirable to prevent the weight of the head from pushing down on the neck. This can be accomplished with the system of pulleys shown in the figure. The pulleys are small and light and have no appreciable friction. The rope about pulleys 1 and 3 make an angle of θ1 = θ2 = 26.0°; pulleys 1 and 3 are constrained to move only in the vertical direction. Typically, a person's head makes up 7.00 % of the body weight. If the head of a 65.0 kg person is to be supported completely by the apparatus shown, what should the mass M of the weight W be?

Homework Equations



Fnet=ma

The Attempt at a Solution



I started with the head component and determined that pulley 1 and 3 are each responsible for maintaining half of the weight of the head of 44.59N. From then on, I do not know how to draw the FBD of neither pulley 1 or 3 as a system. I would appreciate any help that can hint me on figuring out the answer. Thanks.
 
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  • #2
The weight W puts a tension in the line, and in a static situation T = W =Mg. With frictionless pulleys, the tension in the line must be the same along the length of the line.

Then either pulley 1 or 3 support half the head weight.

For either pulley, the tension pulls upward - one side vertically, and the other side at angle 26.0° from vertical.

Determine the tension T, necessary to support half the head, then M = T/g.
 
  • #3
Got it. Thanks!
 

FAQ: Multiple Pulley Problem [SOLUTION]

What is a multiple pulley problem?

A multiple pulley problem is a physics problem that involves a system of pulleys and the calculation of forces and motion within the system. It typically involves multiple pulleys connected by strings or ropes, and requires the use of principles such as Newton's laws of motion and the conservation of energy.

What are the key concepts involved in solving a multiple pulley problem?

The key concepts involved in solving a multiple pulley problem include understanding the forces acting on each pulley, determining the direction and magnitude of these forces, and applying principles of mechanical equilibrium and energy conservation to find a solution. It is also important to accurately draw a free body diagram of the system to visualize the forces involved.

How do I approach solving a multiple pulley problem?

To solve a multiple pulley problem, it is important to first identify the known and unknown variables, and then determine the forces acting on each pulley. Next, apply Newton's laws of motion to find the equations of motion for the system. Finally, use these equations along with principles of mechanical equilibrium and energy conservation to solve for the unknown variables.

What are some common challenges when solving a multiple pulley problem?

Some common challenges when solving a multiple pulley problem include properly identifying the forces acting on each pulley, correctly setting up the equations of motion, and accurately applying principles of mechanical equilibrium and energy conservation. It is also important to pay attention to the direction and magnitude of forces, as well as any friction or other external factors that may affect the system.

Are there any tips or tricks for solving a multiple pulley problem?

One helpful tip for solving a multiple pulley problem is to start by drawing a clear and accurate free body diagram of the system. This can help visualize the forces involved and make it easier to set up the equations of motion. It is also important to double check all calculations and make sure units are consistent throughout the problem. Additionally, practice and familiarizing oneself with these types of problems can also improve problem solving abilities.

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