Gravitation, Friction, and Net Force Physics-Unit IV, Part C

I. Newton’s Universal Law of Gravitation A. General Info First thought of by Newton as he pondered why an apple falls directly to the earth He realized that the apple fell because it was attracted to the earth He also realized that this attraction (force) would increase as the object got closer to the earth. Applying his 3rd law, he also knew that the earth was attracted to the apple.

More… He went on to state that this force between earth and other objects would extend to the earth and other planets, and eventually to all bodies in the universe This law would come to be known as Newton’s Universal Law of Gravitation This Law reads: The force of attraction between any two bodies is directly proportional to their mass and inversely proportional to the square of the distance between them.

Mathematically: This law is stated: Fg=Gm1m2 r2 Fg= Gravitational Force G=Gravitational Constant (6.7*10-11N * m2/kg2) m1= mass of 1st object m2= mass of 2nd object r = distance between the centers of the objects Fg=Gm1m2 r2

B. Statements concerning this law As the mass of an object increases, the force increases As the distance between two objects increases, the force decreases if I double the mass of one object, the force doubles. if two objects are brought twice as close together the force between them increases by a factor of 4.

C. Graphs concerning this law F vs. m F vs. r

D. Sample Problem What is the force of attraction between two objects, one with mass 8 kg, the other 6 kg, if they are 5 m apart? Fg=Gm1m2 r2 Fg= Fg=(6.7*10 -11N * m2/kg2 )(8kg)(6kg) (5m)2

More Sample Problems What happens to the force of attraction between 2 objects if the mass of one doubles, the other triples and the distance between them triples? Masses are multiplied (2*3=6) Then divided by the square of the distance (3*3=9) 6/9= two thirds as large

II. Friction A. General Info Friction is defined as any force that opposes motion. Friction may act when a body is sliding (moving left or right) or it may act when an object is moving up or down. Friction that acts when a body is in free fall is termed air resistance. Friction is also known as the force that opposes motion when two surfaces are in contact.

B. Static Friction Consider a heavy box sitting on a floor: FN Fg This box will be difficult to push along the floor

Continued… The box will be difficult to push because of the static friction, the force that opposes the initial motion of the box. Static friction exists because of the attraction the molecules of both surfaces have for each other. The rougher the surface(s), or the more alike the two surfaces, the higher the static friction

A microscopic look at static friction 1.) Wood/Cardboard Box (a closer look) cardboard wood Both the wood and the cardboard have rough surfaces, these surfaces have a high level of attraction, and therefore a high static friction.

More…… Glass Pane/Marble: Both surfaces are relatively smooth, therefore there is little attraction and a small amount of static friction.

Static friction continued…. Various surfaces can be looked at to see how much static friction they will produce. A constant, indicating how much static friction a surface can create, can be calculated. This calculation is known as the coefficient of static friction (μs) Values for static friction will be given to you.

Equation!!! Based on these values, you can also calculate the frictional force or the normal force you need to generate to overcome friction. The formula is: Ff= Force of friction μ = coefficient of friction FN = normal force Ff =μ FN

Sample Problem A car tire sits on a dry highway. It has a weight of 500N. What frictional force will be produced as the object begins to move?

C) Sliding (Kinetic) Friction Once an object begins to move on a surface, it is relatively easy to keep it moving. Friction will still act on the surfaces, however this kinetic friction will be less than the static friction if the object was at rest. Both kinetic + static friction depend only on the nature of the surfaces and DO NOT depend on how much surface area is in contact.

Kinetic Friction Values for the coefficient of kinetic friction (μk) will also be given to you. The same formula (Ff= μFN) can be used when dealing with kinetic friction

Sample Problem: A 5000 kg car moves along a highway with a constant velocity. What frictional force must the car overcome in order to keep moving with this speed? Peter You NEED TO SOLVE THIS! NOW!

III. Net Force A. General Info You must take friction into account when calculating the forces acting on objects In order to calculate net force, you must first describe all the forces acting on an object Forces involved include friction (FF), weight (Fg), the normal force (FN) + the sliding force (Fs) This allows us to draw force diagrams for objects moving and at rest:

Net Force a) Force diagram for a block at rest: 1 2 NOTE: Forces are always drawn from the center of the object We know force #2 is the weight. Force #1 is called the “normal force,” it works opposite the weight. If it didn’t exist we would be “pounded” into the ground by gravity

b) Force Diagram Force diagram for a block sliding across the table (to the right) 1 4 3 2 Normal- FN 3. Sliding Force- Fs Weight- Fg 4. Friction- FF

More Diagrams… These same diagrams can be drawn for objects moving down hill 2 1 3 4 FN Fg Fs Ff

More on that diagram Note the angle between the weight and the sliding force. This angle is equal to the angle of the incline. This means the weight and the normal forces aren’t equal, this will cause the block to slide. 2 1 3 4

B. Net force and equilibrium If an object is at rest, but has forces acting on it, we say it’s at equilibrium. It will no longer be in equilibrium if an unbalanced force acts on it. A force may act to bring an object to equilibrium. The force that does this is called the equilibrant. An object is in equilibrium if all the forces acting on it add up to zero. (The object may be at rest or moving at constant velocity) If an object is not at equilibrium, the equilibrant will be the one that makes all the forces add up to zero.

Examples What is the equilibrant of a force going 60N South? In the diagram, is the object in equilibrium? FN= 10 Fg= 10 Ff= 5 Fs= 10 Which way is the object moving? What force can you add to cause equilibrium?

Net Force We must always account for friction in our calculations. It will act against objects moving horizontally, eventually causing them to stop. It also works against objects moving up. In this case, its called “air resistance” For objects moving upward, the air resistance would be equal to the objects weight.

More… For objects moving horizontally: For objects moving vertically: Air resistance also works against objects in free-fall. These objects will accelerate, then eventually not go any faster. This is called terminal velocity For objects moving horizontally: Net Force = Applied Force – Friction For objects moving vertically: Net Force = Applied Force – Weight

Examples An unbalanced force acts on an object with a magnitude of 75N. The frictional force works against the 5kg object at a rate of 2m/s2. What is the net force? You load a 60kg person into a hot air balloon. It rises with a force of 4500N. If the balloon weighs 40N: What is the total weight of the balloon + object? What net force is acting on the balloon? After 10 sec, what speed is the balloon traveling at?

D. Forces acting at an angle When a force is applied to an object at an angle, some of the force will be wasted. We need to be able to calculate both the ‘use-less’ and ‘use-ful’ amount of force when an angle is involved, we will use our trig functions to do this. Ex. A box is being hauled by putting a 70N tension on a rope at an angle of 60º. What are the useful and useless forces acting on the box? 60º 70N

Cont. To solve this problem you must resolve your force vector into its vertical and horizontal components. 60º 70N b a To calculate force b you will use cosine To calculate force a you will use sine In this case force a is useless, force b is useful.

Examples A person is pushing a lawnmower with a force of 70N at an angle of 45º. What actual useful force is she pushing with? A piano is being hauled to the 3rd floor of a building by a rope/pulley system. The rope is pulled with a force of 120N at a 45º angle. What is the useful force?