Newton's Laws: Forces on Systems

• The worksheets cover forces on systems
• It uses Newton's second law to predict motion changes in systems.
• It applies Newton's third law to ID internal force pairs in a system.

External Force

• This is a force exerted by an object outside the system.

Internal Forces and Newton's Third Law

• Internal forces cancel each other.

Large Internal Forces

• Large internal forces cause deformations.

Pulley in an Elevator System

• Pulleys serve to generate tension in the cable of the elevator system.

Cart and Boxes

• Boxes interact with each other when a cart is pushed.

Motors, Counterweights, Cables, and Pulleys

• The outcome of these elements moving an elevator is that it moves quickly up or down.

Motor's Tension on Elevator Cable

• A motor generating tension in a cable in an elevator system pulls the elevator up.

Apparent Weight in an Elevator

• Apparent weight is the upward/normal force.

Force Opposing Gravity in an Elevator

• Normal force opposes gravity in an elevator.

Acceleration in a System

• Objects connected in a one-dimensional force system share the same acceleration.

Elevator Masses and Acceleration

• With mass and acceleration, the cable tension of an elevator can be determined.

Boat Motion

• When a person walks forward in a boat, the boat accelerates backward.

Two-Dimensional System

• Model by drawing a free-body diagram for each object.

Pulley System Model and Acceleration

• Friction should be ignored when finding acceleration in a pulley system model.

Force in a Pulley System

• Tension in a rope or cable pulls objects in a pulley system.

Pulley System Model Analysis

• Friction is typically ignored when analyzing a pulley system model.

Torque

• Torque is a measure of how effective a force is at producing rotation.
• The magnitude of a torque determined by the size of the force and distance from the point of rotation to the line of action.
• SI unit is Newton•meter (N•m).
• Torque = Force x Lever arm
• Longer lever arm increases torque.
• Normal force doesn't produce torque because the lever arm is zero.
• A common convention assigns positive values to torques causing counterclockwise rotation and negative values to those causing clockwise rotation.

Free Body Diagram

• Boxes A and B experience the same magnitude of acceleration.
• Direction of force is on the right side.
• According to Newton's Third Law, internal forces FBA and FAB are equal and opposite; they cancel each other.
• Forces at different locations on an extended system can cause rotational motion.
• A line of action is a line through the point of application of the force in the direction of its vector.

Static Equilibrium

• Requires forces to sum to zero.
• The center of mass remains stationary.
• A book on a table, with surface force counteracting weight, is an example.
• Applying unbalanced force to an object in static equilibrium makes it accelerate.

Lever Arm

• The perpendicular distance from the point of rotation to the line of action

Shared Acceleration

• When two or more objects are connected and move together in one direction, they share the same acceleration.
• If a hand pushes three 10-kg blocks with an acceleration of 1.0 m/s², the net force on the system, where the force between the blocks are internal, is 30N.
• If a hand pushes three 20-kg blocks with an acceleration of 1.0 m/s², the net force on the system, where the force between the blocks are internal, is 60N.

External forces and torques

• External forces must sum to zero
• External torques must sum to zero

Calculating torque:

• Torque = Force x perpendicular distance.

Static Equilibrium?

• 4000N x 25m = 100,000 N•m (left side)
• 20000N x 5m = 100,000 N•m (right side)
• The forces are in static equilibrium

See-Saw

• Torque 1 = Torque 2
• A boy of weight 600N sits on the see-saw at a distance of 1.5m from the fulcrum.
• To calculate resulting force at the other end do F1 x rperp = F2 x rprep

Calculating resulting force with a wrench:

• Torque = Force x Lever arm
• Ex: 50N x 1.5m = 7.5N m

Pulling boxes

• Find the force where F= (mA+ mB) • а.
• Ex: (5kg.) (2.0m/s²) = 10N