**Chapter 5**

**Basic Physics-Force**

**The Big Idea**

Acceleration is caused by force. All forces come in pairs because they arise in the interaction of two objects — you can’t hit without being hit back! The more force applied, the greater the acceleration that is produced. Objects with high masses are difficult to accelerate without a large force. In the absence of applied forces, objects simply keep moving at whatever speed they are already going. In formal language1: 1

*Principia in modern English, Isaac Newton, University of California Press, 1934***Key Concepts**

• An object will not change its state of motion (i.e., accelerate) unless an unbalanced force acts on it. Equal and oppositely directed forces do not produce acceleration.

• If no unbalanced force acts on an object the object remains at constant velocity or at rest.

• The force of gravity is called weight and equals

*mg*, where*g*is the acceleration due to gravity of the planet (*g*= 9.8 m/s2 ∼ 10 m/s2, downward, on Earth).• Your mass does not change when you move to other planets, because mass is a measure of how much

*matter*your body contains, and not how much gravitational force you feel.• Newton’s 3

*rd*Law states for every force there is an equal but opposite reaction force. To distinguish a third law pair from merely oppositely directed pairs is difficult but very important. Third law pairs must obey three rules: they must be of the same type of force, they are exerted on two different objects and they are equal in magnitude and oppositely directed.*Example:*A block sits on a table. The Earth’s gravity on the block and the force of the table on the block are equal and opposite.**But these are not third law pairs,**because they are both on the same object and the forces are of different types. The proper third law pairs are: (1) earth’s gravity on block/block’s gravity on earth and (2) table pushes on block/ block pushes on table.•

**Pressure**is often confused with force. Pressure is force spread out over an area; a small force exerted on a very small area can create a very large pressure; ie, poke a pin into your arm!2 Ultimately, many of these “contact” forces are due to attractive and repulsive electromagnetic forces between atoms in materials.

**Problem Solving for Newton’s Laws, Step-By-Step**

1.

*Figure out which object is “of interest.”*If you’re looking for the motion of a rolling cart, the cart is the object of interest. Draw a sketch! This may help you sort out which object is which in your problem.2.

*Using your object as the “origin”, draw an**x*−*y**coordinate system on your sketch.*This will help you properly place the directions of all your forces. Label to the right the +x direction and up as the +

*y*direction. Label the mass.3.

*Identify all the forces acting on the object and draw them on object.(This is a free-body diagram –FBD)**LABEL**all forces – not with numbers, but with the symbol representing the force; ie,**T**is tension, mg is weight,**N**is normal, etc. Be careful - If you can’t identify a force it may not really exist!*INERTIA IS NOT A FORCE!a. If the object has mass and is near the Earth, the easiest (and therefore first) force to write down is the force of gravity, pointing downward, with value ′′

*mg*′′.b. If the object is in contact with a surface, it means there is a normal force acting on the object. This normal force points

*away*from and is perpendicular to the surface.c. There may be more than one normal force acting on an object. For instance, if you have a bologna sandwich, remember that the slice of bologna feels normal forces from both the slices of bread!

d. If a rope, wire, or cord is pulling on the object in question, you’ve found yourself a tension force. The direction of this force is in the same direction that the rope is pulling (you can’t push on a rope!). Don’t worry about what’s on the OTHER end of the rope – it’s just “tension”.

e. Remember that Newton’s 3

*rd*Law, calling for “equal and opposite forces,” does not apply to a single object. Only include forces acting on the ONE object you have identified.f. Recall that scales (like a bathroom scale you weigh yourself on) read out the normal force acting on you, not your weight. If you are at rest on the scale, the normal force equals your weight. If you are accelerating up or down, the normal force had better be higher or lower than your weight, or you won’t have an unbalanced force to accelerate you.

g. Never include “m

**a**” as a force acting on an object. “m**a**” is the*result*for which the net force*F**net*is the*cause*.4.

*Identify which forces are in the**x*−*direction, which are in the**y*−*direction, and which are at an angle*.a. If a force is upward, make it in the

*y*−direction and give it a positive sign. If it is downward, make it in the y-direction and give it a negative sign.b. Same thing applies for right vs. left in the

*x*−direction. Make rightward forces positive.5.

*“Fill in” to Newton’s second law*:a. Remember that all the rightward forces add with a plus (+) sign, and that all the leftward forces add with a minus (–) sign.

b. Now repeat, but for the

*y*−*forces*and this will be equal to the mass multiplied by the acceleration in the ′′*y*′′– direction.Example: FBD - Rocket accelerating upward,

*F*= 500 N,*M*= 10 kg.*a*= ?Use FBD to “fill in” Newton’s second law equation:

Î£

*F**individual f orces*=*m*a or, in this case,Î£*F**y*−*direction f orces*=*ma**y**F*–

*Mg*=

*Ma*

500N − 10kg(10 m/s2) = 10kg (

*a*)*a*= 40m/s2

**Newton’s Laws Problem Set**

1. Is there a net force on a hammer when you hold it steady above the ground? If you let the hammer drop, what’s the net force on the hammer while it is falling to the ground?

2. If an object is moving at constant velocity or at rest, what is the minimum number of forces acting on it (other than zero)?

3. If an object is accelerating, what is the minimum number of forces acting on it?

4. You are standing on a bathroom scale. Can you reduce your weight by pulling up on your shoes? (Try it.) Explain.

5. When pulling a paper towel from a paper towel roll, why is a quick jerk more effective than a slow pull?

6. A stone with a mass of 10 kg is sitting on the ground, not moving.

a. What is the weight of the stone?

b. What is the normal force acting on the stone?

7. For a boy who weighs 500 N on Earth what are his mass and weight on the moon (where

*g*=1.6 m/s2)?8. The man is hanging from a rope wrapped around a pulley and attached to both of his shoulders. The pulley is fixed to the wall. The rope is designed to hold 500 N of weight; at higher tension, it will break. Let’s say he has a mass of 80 kg. Draw a free body diagram and explain (using Newton’s Laws) whether or not the rope will break.

9. Now the man ties one end of the rope to the ground and is held up by the other. Does the rope break in this situation? What precisely is the difference between this problem and the one before?

10. Draw arrows representing the

**forces**acting on the cannonball as it flies through the air. Assume that air resistance is small compared to gravity, but not negligible. 11. Draw free body diagrams (FBDs) for all of the following objects involved (in

**bold**) and label all the forces appropriately. Make sure the lengths of the vectors in your FBDs are proportional to the strength of the force: smaller forces get shorter arrows!a. A

**man**stands in an elevator that is accelerating upward at 2 m/s2.b. A boy is dragging a

**sled**at a constant speed. The boy is pulling the sled with a rope at a 30◦ angle.c. The

**picture**shown here is attached to the ceiling by three wires.d. A

**bowling ball**rolls down a lane at a constant velocity.e. A

**car**accelerates down the road. There is friction f between the tires and the road.12. Mary is trying to make her 70.0 − kg St. Bernard to out the back door but the dog refuses to walk. The force of friction between the dog and the floor is 350 N, and Mary pushes horizontally.

a. Draw a FBD for the problem, labeling all forces.

b. How hard must Mary push in order to move the dog with a constant speed? Explain your answer.

c. If Mary pushes with a force of 400 N, what will be the dog’s acceleration?

d. If her dog starts from rest, what will be her dog’s final velocity if Mary pushes with a force of 400 N for 3.8 s ?

13. A crane is lowering a box of mass 50 kg with an acceleration of 2.0 m/s2.

a. Find the tension

*F**T*in the cable.b. If the crane lowers the box at a constant speed, what is the tension

*F**T*in the cable?14. A rocket of mass 10, 000 kg is accelerating up from its launch pad. The rocket engines exert a vertical upward force of 3 × 105 N on the rocket.

a. Calculate the weight of the rocket.

b. Draw a FBD for the rocket, labeling all forces.

c. Calculate the acceleration of the rocket (assuming the mass stays constant).

d. Calculate the height of the rocket after 12.6 s of acceleration, starting from rest.

e. In a REAL rocket, the mass decreases as fuel is burned. How would this affect the acceleration ofthe rocket? Explain briefly.

15. It’s a dirty little Menlo secret that every time the floors in Stent Hall are waxed, Mr. Colb likes to slide down the hallway in his socks. Mr. Colb weighs 950 N and the force of friction acting on him is 100 N.

a. Draw a FBD for Mr. Colb.

b. Calculate Mr. Colb’s acceleration down the hall.

c. Oh no! There’s an open door leading nowhere at the end of the second floor hallway! Mr. Colb is traveling at 2.8 m/s when he becomes a horizontally launched projectile and plummets to the ground below (don’t worry, he lands on a pile of backpacks and only his pride is injured). If the window is 3.7 m high, calculate how far from the base of the wall Mr. Colb lands.

16. A physics student weighing 500 N stands on a scale in an elevator and records the scale reading over time. The data are shown in the graph below. At time

*t*= 0, the elevator is at rest on the ground floor.a. Draw a FBD for the person, labeling all forces.

b. What does the scale read when the elevator is at rest?

c. Calculate the acceleration of the person from 5-10 sec.

d. Calculate the acceleration of the person from 10-15 sec. Is the passenger at rest?

e. Calculate the acceleration of the person from 15-20 sec. In what direction is the passenger moving?