Applications of Newton’s Laws Tension and Pulleys

Vector Sum of Forces Equilibrant What is the resultant? (a) Two forces, FA and FB, exerted by workers A and B, act on a crate. (b) The sum, or resultant, of FA and FB is FR. Equilibrant What is the resultant?

Free-Body Diagrams Draw a sketch. For one object, draw a free-body diagram, showing all the forces acting on the object. Make the magnitudes and directions as accurate as you can. Label each force. If there are multiple objects, draw a separate diagram for each one. Resolve vectors into components. Apply Newton’s 2nd law to each component. Solve. Figure 4-19. Caption: Example 4–9:Two force vectors act on a boat. In this example, the net force on the boat has a magnitude of 53.3 N and acts at an 11° angle to the x axis.

What is the resultant magnitude and direction?

Adding force vectors              

Application: Ropes and Pulleys A pulley changes the direction of the tension in the rope. If the pulley is frictionless and massless then the tension in the left rope is the same as the right Module 9 - 7

Example: Two masses hang from a massless, frictionless pulley as shown Example: Two masses hang from a massless, frictionless pulley as shown. Draw free-body diagram for each of the masses. Derive a formula for the acceleration of the masses. Assume m1 = 0.250 kg and m2 = 0.200 kg. Module 9 - 8

Example: Two masses hang from a massless, frictionless pulley as shown Example: Two masses hang from a massless, frictionless pulley as shown. Draw free-body diagram for each of the masses. Calculate the acceleration of the masses and the tension. Assume m1 =0.250 kg and m2 = 0.200 kg. Module 8 - 1