Multiple Masses

Tension in Ropes and Cables When a crane exerts a force on one end of a cable, each particle in the cable, exerts an equal force on the next particle in the cable. This creates tension throughout the cable When a crane exerts a force on one end of a cable, each particle in the cable, exerts an equal force on the next particle in the cable. This creates tension throughout the cable Tension – magnitude of the force exerted on or by a cable, rope, or string Tension – magnitude of the force exerted on or by a cable, rope, or string

Assumptions 1. mass of the rope or cable is very small and therefore we ignore compared to the load and does not affect motion 1. mass of the rope or cable is very small and therefore we ignore compared to the load and does not affect motion 2. tension is the same at every point in a rope or cable 2. tension is the same at every point in a rope or cable 3. If the rope or cable passes over a pulley, the direction of the tension changes but the magnitude stays the same. (pulley is frictionless and its mass is negligible) 3. If the rope or cable passes over a pulley, the direction of the tension changes but the magnitude stays the same. (pulley is frictionless and its mass is negligible)

Connected Objects Elevators are not simply suspended from cables. Instead the supporting cable passes over a pulley and then back down to a heavy, moveable counter-weight. Gravitational forces act downward on the counter-weight creating tension in the cable. The cable then exerts an upward force on the elevator Elevators are not simply suspended from cables. Instead the supporting cable passes over a pulley and then back down to a heavy, moveable counter-weight. Gravitational forces act downward on the counter-weight creating tension in the cable. The cable then exerts an upward force on the elevator

Atwood Machines George Atwood ( ) built a machine he used to determine the value of g George Atwood ( ) built a machine he used to determine the value of g

Assigning Direction to the Motion of Connected Objects With the Atwood machine the masses are moving in different direction but connected objects move as a unit With the Atwood machine the masses are moving in different direction but connected objects move as a unit The connecting coble or rope changes only the direction of the forces acting on the objects and has no effect on the magnitude of the forces. You can assign the direction of the motion as being from one end of the cable or rope to the other The connecting coble or rope changes only the direction of the forces acting on the objects and has no effect on the magnitude of the forces. You can assign the direction of the motion as being from one end of the cable or rope to the other Se figure page 482 Se figure page 482

When working with a group of connected objects we call it a system. The forces exerted through a rope or cable are called internal forces When working with a group of connected objects we call it a system. The forces exerted through a rope or cable are called internal forces The forces that affect the motion of a system are known as external forces (gravity, friction) The forces that affect the motion of a system are known as external forces (gravity, friction)

Objects Connected at an Angle In the lab, a falling weight is often used to provide a constant force to accelerate dynamic carts. Gravitational forces act downward and the string exerts a horizontal force on the cart In the lab, a falling weight is often used to provide a constant force to accelerate dynamic carts. Gravitational forces act downward and the string exerts a horizontal force on the cart

Steps for Problem Solving Analyze the forces on each individual object (FBD) Analyze the forces on each individual object (FBD) Assign a direction to the motion Assign a direction to the motion Draw the connecting string or rope as though it was a straight line Draw the connecting string or rope as though it was a straight line Draw a FBD for the resulting system Draw a FBD for the resulting system Use Newton’s 2 nd Law to calculate acceleration Use Newton’s 2 nd Law to calculate acceleration