Force in Mechanical Systems Overview
Force in Mechanical Systems What is a force? Created by a push/pull How is a force transmitted? For example by: Chains and sprockets Belts and wheels Spur gears Rods
Force in Mechanical Systems How is force measured? Using a device such as a beam balance, spring balance What are the units of force? English Metric (SI) > pound (lb) > Newton (N)
What are balanced forces? All forces acting on a body cancel each other out, resulting in no net (or zero) force The body remains in a state of constant motion (or rest) Newton s 1 st Law Law of Inertia
What is equilibrium? The result of balanced forces on a body If the body is at rest, it remains at rest If the body is in motion, that motion does not change
What are unbalanced forces? All forces acting do not cancel out, resulting in a net (non-zero) force. The body changes its speed, direction or shape Newton s 2 nd Law
How are forces described? Forces are quantities that are described in terms of 2 parameters: Magnitude of the force (ex. 10 lbs, 100N) Direction of the force (ex. Left, up, north) Any quantity that is described thus is called a VECTOR quantity Ex. 10 lbs NE, or 50N left Examples of other vectors Velocity Acceleration Momentum
If not a VECTOR, then? A quantity that is described by its magnitude only is called a SCALAR quantity Examples of scalars Temperature Mass Pressure
How are forces represented? Drawn as an arrow Arrow length is magnitude Ex. 10 ft.lb Arrow heading is direction NE Ex. 10 ft.lb NE
Force (vector) arithmetic in line Adding forces acting on a line If the forces are acting in the same direction ADD to get the total force (resultant) on the body Ex. 5N right + 10N right = 15 N right If the forces are acting in the opposite direction SUBTRACT to get the total force on the body Ex. Tug of war 500N to right 1000N 1500N
Adding forces acting at a right angle (20N right and 10 N up) Cannot add arithmetically to find the total force (resultant) Use graph paper Draw the 1 st force (A) scaled appropriately with an arrow head to show direction (ex. 1 square = 2N) at the head of the arrow draw the 2nd force (B) at right angles to the 1st using the same scale as the 1st. connect the tail of the 1st force with the head of the C A B 2nd force to represent the resultant (or total) force (C). measure this resultant using the same scale and measure the heading of the resultant (angle between A and C) with a protractor.
Practice Use the graph paper to draw the 2 vectors (40lb right and 30lb up) and the resultant. Use a scale such as 1 cm = 5lb Draw the 40lb (A) Draw the 30lb (B) starting from the tip of A Connect the start and finish points = resultant (C) Measure the resultant length (C) using the scale above Measure the resultant angle using a protractor C A B
Weight vs Mass? Weight is a representation of the effect of gravity on an object vector quantity Weight is the gravitational force with units of pounds (lbs) or Newtons (N) Mass is the amount of matter a body contains with units of pounds mass (lbm) or kilograms (kg) scalar quantity At the same location on earth, the greater the mass the greater the weight. Conversion 1 kg = 2.2 lb (so: 220 lbs = 100 kg)
What is torque? Torque is a forcelike quantity in the rotational mechanical system, or a turning force resulting from applying a force at some distance from the axis of rotation of the body Torque examples: wrenches, gears, flywheels or screws, rope starter on chainsaw
Torque Can be clockwise (cw) or counterclockwise (ccw) Formula for calculating torque Torque = applied force times length of the lever arm T = F x L, where F = force, in lbs or newtons L = lever arm length, in feet or meters T = applied torque, in lb-ft or N.m
Examples of torque in action Gears Driving gear teeth mesh with Driven gear teeth Radius of the gear is the lever arm Wrench (torque or crescent) A force is applied at a distance (moment arm) from the axis of rotation (pivot point). Opposing torque If the clockwise and counterclockwise torques cancel each other out, then the system is in equilibrium and its rotational state does not change. If the opposing torques do not cancel each other out, then the net torque will cause a change in the rotational speed of the system.
Practice A torque wrench has a lever arm of 1.5 ft. A force of 40 lbs is applied at the end of the wrench to tighten the bolt. What is the torque in lb-ft? Torque = force x lever arm Torque = 40 x 1.5 = 60 lb-ft