Draw separate free-body diagrams of the forces on objects A, B, and C. Is there a difference between the force on mass B and at point P? Assign symbols to all of the forces, and define what they represent next to your diagram. It is also useful to put the force vectors on a separate coordinate system for each object (force diagram). Remember that on a force diagram, the origin (tail) of all vectors is at the origin of the coordinate system.
Draw separate free-body diagrams of the forces on objects A, B, and C. Is there a difference between the force on mass B and at point P? Assign symbols to all of the forces, and define what they represent next to your diagram. It is also useful to put the force vectors on a separate coordinate system for each object (force diagram). Remember that on a force diagram, the origin (tail) of all vectors is at the origin of the coordinate system.
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*PLEASE SOLVE #2*
The system consists of a central object, B, suspended halfway between two pulleys by a string. The whole system is in equilibrium. The counterweight objects A and C, which have the same mass, allow you to determine the force exerted on the central object by the string.
- Draw a picture of the setup similar to the one in the Equipment section. Be sure to include symbols for the horizontal distance L, and the mass of object B and objects A and C. Label the angle that the string sags below the horizontal as theta () and the displacement of point P as “d”. Use trigonometry to show how the vertical displacement (d) of object B is related to the angle theta and the horizontal distance L.
- Draw separate free-body diagrams of the forces on objects A, B, and C. Is there a difference between the force on mass B and at point P? Assign symbols to all of the forces, and define what they represent next to your diagram. It is also useful to put the force vectors on a separate coordinate system for each object (force diagram). Remember that on a force diagram, the origin (tail) of all vectors is at the origin of the coordinate system.
- Since this is a static situation, what is the acceleration for each object? For each force diagram break all forces into their x and y components and write down Newton's 2nd law along each coordinate axis.
- Solve your equations for the vertical displacement (d) of object B in terms of the mass (M) of object B, the mass (m) of objects A and C, and the horizontal distance (L) between the pulleys. Your final equation should not depend on angles.
- Use your equation to sketch the shape of the graph of the vertical displacement (d) versus mass of object B.
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