Chapter 4Forces

Newton’s Laws of Motion

ForcesForce – A vector quantity that changes the velocity vector of an object. When you hit a baseball, the velocity of the ball changes.

Can be a push or a pull on an object.

Contact forces – Result from physical contact with an object. (pulling a trailer, friction forces, normal force)

Field forces – Interactions where contact is not necessary. (electric force, gravitational force)

Figure 4.2 shows examples

4 Fundamental types of forces

• Strong nuclear force – subatomic particles, hold nucleus together

• Electromagnetic forces – forces between charges

• Weak nuclear force – radioactive decay

• Gravitational force – attraction between objects with mass (Why a dropped ball falls down.)

Newton’s Laws

3 Laws that govern the motion of a particle.

When a force is applied, these laws describe how the velocity responds.

Also explains how objects interact when a force is applied by one on another.

• 1st Law• 2nd Law• 3rd Law

Mass and Inertia

Inertia – The tendency of an object to continue in its original state of motion.

Mass – Measurement of an object’s resistance to change in motion due to a force.

The more massive an object, the more inertia the object will have.

An 18-wheeler has a lot more inertia than a small car. It’s harder to stop the 18-wheeler.

Determining the Inertia/Mass

We measure the mass of an object.The U.S. unit is the slug.The SI unit is kilogram. (kg)

We will exclusively use the SI units.mass of a small car ~1000 kgmass of my cat ~8 kgmass of a penny ~1 gm

The more mass an object has, the more force is needed to change it’s velocity. (accelerate the object).

Kick a volleyball – It will move a lot.

Kick a bowling ball – It won’t move as much.

The bowling ball resists changing its velocity more than the volleyball. The bowling ball has more inertia. (a higher mass)

Newton’s 2nd Law

Book’s definition:The acceleration, a, of an object is directly proportional to the net force acting on it and inversely proportionally to its mass.

Newton’s 2nd LawRemember that ΣF= ma, is a vector equation.

The 2nd Law is to be applied in the 3 dimensions individually.(Remember the rule to keep vector components in different dimensions separated.)

If there is no net force in a direction, the acceleration is zero, then the velocity in that direction, is constant.

Newton’s 3rd LawBook definition:

If object 1 and object 2 interact, the force F12 exerted by object 1 on object 2, is equal in magnitude but opposite in direction to the force F21 exerted by object 2 on object 1.

Law of equal and opposite reaction.Forces always occur in pairs.

Example: If you push on a wall, the wall pushes back onto you.

Units of forces

Units of forces are the pound (US) and the newton(SI). We will use the newton.

1 N = 1 kg m/s2

To convert: 1 N = 0.225 lb 1 lb = 4.45 NAlso of use: 1 kg of mass weighs 2.2 lbs.

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Examples of forces we will work with

• Gravitational force – due to gravity

•Normal force – due to contact

•Friction forces – surfaces sliding against each other

•Spring forces – compressing or stretching a spring

•Tensions – involving ropes, cables, tendons…

Gravitational force

Gravitational force is the mutual attraction between any two objects in the Universe.

Determined by: 𝐹𝐹𝑔𝑔 = 𝐺𝐺𝑚𝑚1𝑚𝑚2𝑟𝑟2

(r is the separation between the two objects.)

Gravitation constant G = 6.67 x 10-11Nm2/kg2

We will use this more later.

Gravitational Force

𝐹𝐹𝑔𝑔 = 𝐺𝐺𝑚𝑚1𝑚𝑚2𝑟𝑟2

let m1 equal the mass of the Earth and r the radius of the Earth we get:

𝐹𝐹𝑔𝑔 = 6.67𝑥𝑥10−11𝑁𝑁𝑚𝑚2/𝑘𝑘𝑔𝑔2 5.98𝑥𝑥1024𝑘𝑘𝑔𝑔 𝑚𝑚26.38𝑥𝑥106𝑚𝑚 2

• Fg= (9.8 m/s2)m2= m2g• Weight• w = mg, where g = GME/r2

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(220.46 lbs)

Mt. Everest: r = re+ 104m

Normal Forces

Normal forces, are contact forces that are normal, or perpendicular, to the surface in contact.

Say you have a 10 N brick sitting on a table. The Earth pulls down on the brick with a force of 10 Newtons. If there was no normal force, the brick would fall through the table. The table exerts a 10 N normal force up onto the brick.

Normal Forces

Example: My weight is 880 N pressing down on the floor. The floor exerts a normal force of 880 N up on me.

Normal Forces

Normal forces are always perpendicular to the direction of the surface the object is pressed against.

Fn is equal to the adjacent (normal) component of the weight.Normal force balances out this component of weight.

Free Body Diagrams

A free body diagram is a picture that includes an object, and ALL the forces that are exerted on the object.

We will use these a lot because they are very handy.

If you set up the diagram correctly, the equations needed for using Newton’s 2nd Law can be visualized.

Book

Desk

Fnb= -mbg = -(10 kg)(-9.8m/s2) = 98 N upward.Fnd= -mbg-mdg = -(10 kg +20 kg) )(-9.8m/s2) = 294 N upward

Notice that to find the normal force the ground exerts on the desk, you use the weight of the book and the desk.

Fnd

Fnd+

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Fp

As the angle of inclination increases:FN decreases FP increases

As the slope increases, gravity has a greater effect on the object.

When incline is vertical,Object resembles falling bodyFP= weight = mg

Free body diagram

Fnet is the total, or resultant force. It is directed along the plane.

Applying the 2nd LawFnet = ma = (50kg)aa = Fnet/ma = (50kg)g (sin 30)/(50 kg)a = 4.9 m/s2

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First we use the force to find acceleration:

a

“What is the tension in the rope?”

Friction• Friction is due to surfaces not being perfectly smooth.

•Friction force ALWAYS opposes the direction of motion.

•The result of friction forces is energy. (heat)

•Two types of friction:Static friction force keeps the object at rest, and is needed to be overcome so the object can begin motion.Kinetic friction occurs when one object is sliding against another surface.

Friction

When is friction used is ordinary life?-car brakes-making a car move forward-driving around a turn-walking- Holding objects together/up-rubbing your hands together to make warmth

Friction

How to calculate frictional force.Frictional force, Ff , depends on the material of the two surfaces involves. Given by coefficient of friction (µ). See table on page 109 for examples.

There are two coefficients:

See figure 4.21 on page 108.

the weight.

Fs balances out Fp

From earlier we know FP= mg sin θWhen the box is about to slide down:Ff= µsFN= µsmg cos θ

You hang a mass from a scale.

When you jerk the scale upwards, what does the scale read?

When you accelerate the scale downward, what does it read?

When you jerk the scale upwards, the reading will increase.

When you jerk the scale down, the reading decreases.

Conclusions:If you want to give an object an upwards positive acceleration, you need to apply more force than the weight of the object.

If you are lifting an object but it is slowing down, you are applying a force that is less than the weight.

https://youtu.be/Bo2mwavmQko

See example 4.11 Atwood’s Machine

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Atwood’s Machine continued.Once the acceleration is found, we can find the time it takes for the heavier block to fall 2 meters.

Use: ∆y = vot + ½ a t2

∆y = -2 mv0 = 0 m/sAcceleration is from previous slide. Acceleration of heavier block is downward, so it is negative. (Same sign as ∆y.)

Example of Atwood Machine at the CPA

https://youtu.be/ubJ58i9X8fA

t

k

k

t

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A 70 kg person jumps off a 5 meter ledge. Once the person comes in contact with the ground, it takes 0.8 seconds to come to a complete stop. Find the magnitude of the force, the ground exerts on the person during this time.

First find the speed that the person hits the ground.Use: 𝑣𝑣𝑓𝑓2 = 𝑣𝑣02 + 2𝑎𝑎∆𝑥𝑥 = 02 + 2𝑔𝑔(5𝑚𝑚)

vf= 9.9 m/s

Methods of developing mechanical advantage

Use an incline. Unless there is a huge amount of friction, it takes less force to slide something up a ramp, than it does to lift an object straight up.

Use a pulley system to multiply the tension in a rope. (Snatch blocks).

https://www.youtube.com/watch?v=M2w3NZzPwOM

https://www.youtube.com/watch?v=PriqHStVhL0