Forces in Mechanical Systems 1.1

Objectives Define force and describe how forces are measured. Describe what happens when forces on an object are balanced and when they are unbalanced. Explain the meaning of Newton’s first law of motion. Define scalar, vector, weight, mass and torque. Determine the resultant force on an object when two or more forces act on it. Solve problems involving force, lever arm, and torque.

Force A push or a pull In Mechanical Systems forces change an object’s motion. Forces can be transmitted to a variety of mechanical parts

Bicycle

Measuring Forces Metric System Based on powers of 10

The SI base units for seven basic quantities: Quantity Unit Symbol Length ( l ) meter m Mass ( m ) kilogram kg Time ( t ) second s Electric Current ( I ) ampere A Temperature ( T ) Kelvin K Amount of Substance ( n ) mole mol Luminous intensity candela cd

Derived units – unit made from a combination of base units. SI unit of speed is m/s (length / time) Acceleration is m/s2 (speed / time) Force is the Newton (N) which is actually kg m/s2

Comparison of English and SI Units Length Time Mass Force English foot (ft) second (s) slug pound (lb) SI meter (m) kilogram (kg) Newton (N)

Weight and Mass Conversions 1 pound = 16 ounces 1 kilogram weighs 9.80 N or 2.2 lb 1 pound = 4.45 newtons 1 slug weighs 32.2 lb 1 kilogram = 1000 grams 1 slug = 14.59 kg

Force can be measured with a spring scale. Spring stretch is directly proportional to force Weight is the force due to gravity.

Make sure units match before calculations are run on values.

Force is a Vector The effect of force on an object depends on two things magnitude direction

Vector is a quantity that must be described by both magnitude and direction. Force is a vector quantity. Displacement, velocity, acceleration, and momentum are also vector quantities1. 1 We will cover these later.

Scalars – quantities described by magnitude only. Temperature elapsed time Pressure mass

How to Represent Forces Vector drawing – arrows are proportional to magnitude and point in the direction of the vector. (Figs 1.4 and 1.5, p. 9)

Balanced and Unbalanced Forces

Net force – the sum of all forces acting on an object Fnet = F = F1 + F2 ……

Balanced forces – when the net force on an object is equal to zero. Motion of object stays the same – called equilibrium. Speed and direction stays the same.

Unbalanced forces – when the net force on an object is not equal to zero. Motion of the object changes

Falling objects and terminal velocity Figure 1.7a Fgravity > Fdrag Figure 1.7b Fgravity = Fdrag Terminal velocity – final velocity reached when gravity and drag are balanced.

Newton’s First Law of Motion An object at rest remains at rest, acted upon by an unbalanced force. Likewise an object in motion will keep its velocity, unless an unbalanced force acts on it. Sometimes called the law of inertia.

Example 1-1 A yo-yo weighing 0.25 lb hangs motionless at the end of a string. Draw the forces acting on the yo-yo.

Adding Forces That Act Along a Line Forces are added to find net force (Fnet) on an object. Easy if in the same direction. Sign can be used to indicate direction Forces in the up or to the right directions are in the positive. Forces in the downward or the left directions are negative.

Example 1-2 Tug-of-War Problem Five people compete in a tug-of-war. Three people on the left side each pull with 230 N of force. Two people on the right side each pull with 300 N of force. Who will win the tug-of-war?

Adding Forces That Do Not Act Along a Line Forces can’t be added if they do not act along a straight line. Example in Figure 1.11 To solve we use a graphing method Vectors are drawn “head-to-tail.”

Step 1: Draw first vector Step 2: Draw second vector “Head-to-tail” Step 3: Draw the resultant force Resultant force – single vector representing the sum of two or more vectors. Step 4: Determine the magnitude and direction of the resultant. Pythagorean Theorem for right triangles Step 5: Make some conclusions

Weight and Mass Aren’t the Same Thing! Unbalanced force acts on object at rest, it will move. Two books have twice the mass, and require twice the force to get them to move. Since the amount of inertia depends on the amount of matter, two books have twice the inertia.

Torque and Rotation Torque – a quantity that causes rotation in mechanical systems. The effect of a force applied on a body at some distance from the axis of rotation. Can be: Clockwise (cw) Or, counterclockwise (ccw)

Torque = applied force x lever arm Line of action – line along the applied force that extends in both directions. Torque = applied force x lever arm  = F  L

What are the English units for torque? SI units?

Gear Teeth Shaft Teeth of one gear mesh with another gear. Driving gear Driven gear

Example 1-3 Calculation of Torque Applied by a Torque Wrench A torque wrench has a lever arm of 1.5 ft. A force of 40 lb is applied to the end of the wrench to tighten a bolt. Find the torque applied to the bolt in a.) lb·ft and b.) N·m.

Example 1-4 Torques in a Belt-Driven System The motor pulley in a belt-driven system has a radius of 5 cm (0.05 m). The large pulley attached to the shaft of a machine has a radius of 20 cm (0.20 m). The dragging or pulling force of the belt is 40 N. Assume that the belt doesn’t slip as the motor and belt drive the load pulley. What is the torque applied to each pulley?

Opposing Torques Opposing torques, like forces, can be in equilibrium. (torques cancel each other out) If system at rest, it stays at rest. If in motion, it continues to rotate. If unbalanced, the net torque will cause a change in the rotational speed. It speeds up or slows down.

Example 1-5 Truck Scales Involve Opposing Torques A 48 000 lb truck sits on the platform of truck-weighing scales. The truck weight acts on a 0.5 ft lever arm about the pivot point. A 1000 lb balancing weight is hung on the opposite side of the pivot point, 20 ft away. Find: (a.) Torque of truck about pivot point. (b.) Torque of balance weight about the pivot point. (c.) Whether or not the torques are balanced.