Application of Newton's forces

In summary, a system of pulleys can be used to prevent the weight of a healing neck from pushing down on the neck. The pulleys are light and have no friction, and typically a person's head makes up 7.00% of their body weight. In order to support a 77.0 kg person's head completely, the mass of W must be determined. The tension in the rope, T, must be found in order to calculate the force exerted by the apparatus on the head. This can be done by finding the vertical components of the tension at each of the four points where it exerts a force on the wheels.
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Homework Statement



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 all small and extremely light in weight and have no appreciable friction. Typically, a person’s head makes up 7.00% of his or her body weight.

If the head of a 77.0 kg person is to be supported completely by the apparatus shown, what should the mass of W be? Start with a free-body diagram of the head.

I drew out a free body diagram, but don't know where to go from there.
 
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Where is the figure?
 
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If the tension in the rope is T, what is the force exerted by the apparatus on the head?
 
  • #5
dx said:
If the tension in the rope is T, what is the force exerted by the apparatus on the head?

mg? With T pointing upward.
 
  • #6
T points along the rope. There are four places where the tension exerts forces on the wheels. At two of these places, T points upward, and at the other two it points at an angle of 37 degrees to the vertical. You have to find the vertical componets of all these and add them up to find the total vertical force exerted on the head.
 

1. How is Newton's first law of motion applied in everyday life?

The first law, also known as the law of inertia, states that an object will remain at rest or in motion at a constant velocity unless acted upon by an external force. This can be seen in everyday life, such as a book remaining on a table unless someone picks it up or a car continuing to move forward unless the brakes are applied.

2. What is Newton's second law of motion and how is it used in scientific experiments?

The second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This law is often used in scientific experiments to calculate the force needed to move an object or the mass of an object based on its acceleration.

3. Can you explain the concept of Newton's third law of motion?

Newton's third law states that for every action, there is an equal and opposite reaction. This means that when one object exerts a force on another object, the second object will exert an equal but opposite force back. For example, when you jump, your feet push down on the ground and the ground pushes back up on your feet, causing you to move upwards.

4. How does the application of Newton's laws of motion impact our understanding of the universe?

Newton's laws of motion are fundamental principles that help us understand the motion of objects in our universe. They have been used to explain everything from the movement of planets in our solar system to the behavior of atoms and subatomic particles. Without these laws, our understanding of the physical world would be limited.

5. How do forces play a role in Newton's laws of motion?

Forces are an essential component of Newton's laws of motion. They are the external influences that cause objects to accelerate or move in a certain direction. Without forces, an object would remain at rest or in motion at a constant velocity, as stated in the first law. The second law relates the net force acting on an object to its acceleration, and the third law explains the equal and opposite forces acting between two objects in an interaction.

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