Unit 4: Newton’s Laws Forces

Force of Gravity

Force:

The units of force are:

There are four fundamental forces that make up all of the forces in the universe: 1) 2) 3) 4)

Force of Gravity:

Mass (kg):

Weight (N):

Mass is ____________ throughout the universe but weight ____________ depending on where you are.

The formula for force of gravity is:

Where:

m =

g =

=

g varies depending on…

For Example:

! On Earth at sea level, g =

! On the moon, g =

! On Jupiter, g =

! On the sun, g =

Determine your weight on Earth, the moon and Jupiter (in Newtons)

Your Mass: ___________ kg (1 kg = 2.2 lbs)

Weight on Earth: Fg = mg =

Weight on the Moon:

Weight on Jupiter:

Activity: Jumping on the Moon

Purpose: To determine how high you could jump on the surfaces of the Moon and the Sun.

Procedure:

1. Have your lab partner measure your best vertical on Earth. 2. Determine the initial velocity of your jump. We will assume that your initial jump velocity will be the

same on the Moon and the Sun. 3. Find your vertical and hang time on the moon using an acceleration = -1.60 m/s2. 4. Find your vertical and hang time on the Sun using an acceleration = -274 m/s2.

Sun

dmax: _______________

t = _________________

Moon

dmax: _______________

t = _________________

Earth

Vertical: ____________

vo = _____________

A Quick Aside on G-Forces

“G-forces” are actually a measurement of acceleration experienced by an object. It is related to the supporting reaction force that an object experiences due to acceleration. While at rest on Earth you are experiencing 1 g.

1 g = 9.80 m/s2

For Example: A car accelerates at 4.9 m/s2, how many g’s is that?

During lift-off a shuttle will accelerate at 28 m/s2. How many g’s are experienced by the astronaut?

A normal human can withstand 4.0 g’s, while a fighter pilot can withstand up to 9.0 g’s. What acceleration would cause each to pass out?

Unit 4: Newton’s Laws Newton’s 1st Law

Newton’s 1st Law: An object in motion will… and an object at rest will… unless…

This is also referred to as the Law of Inertia.

Inertia:

Imagine that you are racing around a track on a go-kart. List three times when you notice your inertia.

1)

2)

3)

Another way of thinking of Newton’s 1st Law is that if there is no net force on an object then it will stay at a constant velocity.

If it is not moving then it has a constant velocity of zero!!!

Ex. Imagine a book sitting on a table. There is a force of gravity pulling down on the book, but there is also a supporting (normal) force pushing up on the book.

Ex. If I drop the book from 2 m, there is only a downwards, gravitational force acting on it. Now that the forces on it are unbalanced, what does the book do?

Examples:

1) While riding a skateboard (or chuckwagon or unicycle, whatever), you fly forward off the board when hitting a curb or rock or other object which abruptly halts the motion of the skateboard.

2) The head of a hammer can be tightened onto the wooden handle by banging the bottom of the handle against a hard surface.

3) While you are sitting in the back seat of the car, it makes a hard right turn. You squish your sister against the side door (CORNERS!!!).

4) Headrests are placed in cars to prevent whiplash injuries during rear-end collisions.

Unit 4: Newton’s Laws Newton’s 2nd Law

Newton’s 2nd Law:

Stated as a formula:

Note that…

Ex. A 5.0 kg block is pushed to the right along a frictionless track with a force of 10.0 N. What is its acceleration?

Ex. A 650 kg car accelerates at 4.0 m/s2 south. What is the net force acting on it?

To find Fnet when two forces work together …

Ex: A 1500 kg ice cream truck accelerates from rest to a top speed of 45 km/h in 8.0 s. What was the net force acting on the truck?

Ex. Stan and Kyle are pushing a 75 kg sled along a frictionless ice rink. Stan pushes with 55 N and Kyle pushes with 45 N. Find the sled’s acceleration.

To find Fnet when many forces act on an object:

Ex: The Batmobile exerts a force of 8.50x103 N east, while friction pulls back on it with a force of 1500 N. If it has a mass of 1250 kg, what is its acceleration?

Worksheet 4.1  Newton’s 2nd Law 

1) For each of the following diagrams determine the magnitude and direction of the net force. 

 

 

 

 

 

 

   

 

 

 

 

 

2) Use the information given for each diagram to fill in all missing blanks. 

 

 

 

 

   

 

 

 

 

 

FN = 100 N

Ff = 20 N 

Fg = 100 N 

Fapp = 20 N 

T = 400 N

Fg = 150 N 

FN = 600 N

Ff = 75 N 

Fg = 600 N 

Fapp = 250 N

FN = 150 N

Fg = 150 N 

Fapp = 60 N 

FN = 200 N

Ff = 80 N 

Fg = 200 N

Fapp = 120 N

Fapp = 60 N

FN = 200 N

Ff = 55 N 

Fg = 200 N

FN = 300 N 

Ff = 20 N 

Fg = 300 N 

Fapp = 70 N 

m = 5 kg a = _______ m/s

2 

m = ______ a = _______ m/s

2 m = 40 kga = 4 m/s

2 right 

m = 8 kg a = _______ m/s

2 

m = _________a = 4 m/s

2 right m = 12 kga = _______ m/s

2 

FN = _____

Ff = 20 N

Fg = ______

Fapp = 20 N

FN = _____

Ff = 80 N 

Fg = _____ 

Fapp = 240 N

FN = 160 N 

Fg = _____ 

FN = _____

Ff = ______

Fg = ______

Fapp = 200 N

FN = 500 N

Ff = 125 N 

Fg = ______

1. A book is at rest on a table top. 2. A girl is suspended motionless from a bar which hangs from the ceiling by two ropes.

3. An egg is free-falling from a nest in a tree. Neglect air resistance.

4. A plane flies at a constant velocity (Note: there will be an applied force generated by the engines as well as a lift force provided by the wings).

5. A rightward force is applied to a book in order to move it across a desk with a rightward acceleration. Consider frictional forces. Neglect air resistance.

6. A rightward force is applied to a book in order to move it across a desk at constant velocity. Consider frictional forces. Neglect air resistance.

7. A college student rests a backpack upon his shoulder. The pack is suspended motionless by one strap from one shoulder.

8. A skydiver is descending with a constant velocity. Consider air resistance.

9. A force is applied to the right to drag a sled across loosely-packed snow with a rightward acceleration.

10. A football is moving upwards towards its peak after having been booted by the punter.

11. A car is coasting to the right and slowing down. Diagram the forces acting upon the car.

Unit 4: Newton’s Laws - FBDs

Force Description

Ex 1: A box is pushed across a rough floor at a constant velocity. Ex 2: A hockey player glides on frictionless ice at a constant velocity.

Unit 4: Newton’s Laws Newton’s 3rd Law

Newton’s 3rd Law:

Any interaction involves two forces that we call…

1) You hit a baseball with a bat.

2) A sprinter starts running.

3) A fish swims through water.

Imagine a bug hitting the windshield of a semi trailer.

What force pair occurs?

Which force is bigger?

Which object has a greater acceleration?

Example 1: Recoil Example 2: Bricks Example 3: Rockets

Unit 5: Forces Force of Friction 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Friction is created whenever… 

On the microscopic level… 

 

Friction is given by the equation: 

          Where:         FN  =               =         µ   =                =                = 

Ex 1: A 3.75 kg block is pushed along a tabletop with a force of 45.0N.  The coefficient of friction is 0.65. 

a) Find the force of friction. 

b) Find the acceleration.  

 

Ex 2: A 0.200 kg puck is pushed along a sheet of ice with a force of 0.240 N.  If it moves at a constant velocity, find the coefficient of friction.  

  

Ex 3: A 1.1 kg textbook is held against a vertical wall with a force of 45 N. What is the coefficient of friction between the book and the wall?  

  

Static Friction: 

 

Kinetic Friction: 

 

Frictionstatic    Frictionkinetic 

μ static      μkinetic  

 1) A 7.6 kg object is resting on a horizontal surface. What is the normal force on the object?      2) A 7.6 kg object is pulled along a horizontal surface. If the coefficient of friction is 0.20, what is the force of friction?      4) A 9.6 kg object is pulled along a horizontal surface. If the coefficient of friction is 0.11 what is the force of friction?      5) A 20.0 N object is pulled along a horizontal surface at a constant velocity by a 3.0 N force, what is the coefficient of friction?     6) A 16.2 kg object is pulled along a frictionless surface by an applied force of 10.2 N, what is the normal force acting on it?       7) A 6.2 kg object is pulled along a horizontal surface by a force of 22.0 N. If its acceleration is 1.1 m/s2, what is the coefficient of friction between the two surfaces?       

 8) A 1250 kg car traveling at 60.0 km/h comes to a sudden stop in 35 m. What is the coefficient of friction acting on the brakes?           9) A 950 kg car traveling at a constant velocity of 28 m/s, has a coefficient of friction of 0.125 acting on its axle. How much force is required by the engine to maintain its speed?            10) A 1425 kg dragster exerts 13900 N of force and accelerates from 0 to 100.0 km/h in 3.25 s. What is the coefficient of friction acting on the car?  

Worksheet 5.3 ‐ Force of Friction  

1) 74 N  2) 15 N  3) 137 N  4) 10. N  5) 0.15  6) 159 N  7) 0.25  8) 0.40  9) 1200 N  10) 0.123

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Tension occurs within a material that 

It is an internal force that acts ___ ___

Consider two carts attached by a rope b

If m1 is pulled to the right by a force of 4

a) The acceleration of the carts. 

 

 

 

NOTE: tension… 

b) The tension in the string connect

 

 

NOTE: Since it cancels out of the total F

NOTE: Since tension acts on both masses eq

Consider two equal masses hanging fro

Diagram the forces acting on the entir

With pulley problems it is sometime ea

 

Unit 4: Newton’s Laws Tension 

 

is being… 

__ _________ along a rope (string, chain, etc

being pulled along a flat surface. (Friction is n

40.0 N find: 

ting them. 

net equation, we will only consider the forces

qually we can use…  

om a pulley. 

e system. 

asier to “unfold” the rope as shown. 

) in _____ ____________. 

negligible.) 

s acting... 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ex: The two masses shown hanging fro

a) The acceleration of the system

 

 

b) The tension in the string.  

 

NOTES: 1. When solving for accelerati

 2. When finding T we only use

Ex: A mass on a frictionless table is att

a) The acceleration of the masses

 

 

b) The tension in the rope. 

 

Ex2: If the same system has a friction f

a) The acceleration of the masses

 

 

b) The tension in the rope. 

 

om a frictionless pulley are released at rest. F

. 

ion of the whole system we consider ______

e ______ __________. 

ached to a hanging mass over a frictionless p

s. 

force of 25 N acting on the 8.0 kg mass find:

s. 

Find 

________ 

pulley as shown. Find: 

Dynamics Notes 1 – Newton’s Laws

Newton’s 1st Law: An object… and an object… unless…

Newton’s 2nd Law: As a formula:

Newton’s 3rd Law: For every… As a formula:

Free Body Diagrams: (Draw one for EVERY force question) 1) Represent the object as a box and, 2) Represent all forces as arrows

• The arrows are vectors so their direction is critical

• Start in the center and draw outwards

• The size of the arrow represents the magnitude of the force

1. A puck slides along frictionless ice.

2. A dragster accelerates from rest.

3. A block of wood slides down an incline

Ex. A student pulls straight upwards with a force of 650 N on their 15 kg backpack. What is the backpack’s acceleration?

Ex. A 1200kg car accelerates at 5.85 m/s2. If the coefficient of friction acting on the car is roughly 0.24, how much force does the engine exert?

Ex: A boy pulls his 8.0 kg toboggan by a rope that angles 32o above the horizontal. If his 36.0 kg sister sits on the toboggan, how much force does he need to exert to accelerate them at 2.25 m/s2?

Ex: A 1.12 kg textbook is pushed horizontally against a wall with a coefficient of friction of 0.465. What is the least amount of force required to keep the book from slipping?

Ex: Two blocks (m1 = 2.0 kg and m2 = 3.0 kg) are connected by a rope as shown. m1 is pulled to the right with a force of 18 N. What is the tension in the rope connecting the two masses?

Ex: A 65 kg student stands on a bathroom scale in an elevator and notices that it reads 520 N. Determine the magnitude and direction of the acceleration of the elevator.

Dynamics Notes 2 – Forces in 2-D

Ex 3: Two children pull a third child on a toboggan (shown from the top, assume up is north). Assuming that they pull on ropes that are parallel to the ground determine the magnitude of the force exerted on the toboggan.

Ex Two students push a crate across a frictionless surface. Student A pushes with 75 N East and Student B pushes with 48 N South. What is the resultant force acting on the box?

As with any vectors, forces must be resolved with consideration to both their ____________ and ____________.

If there are more than two forces then it is best to solve for the resultant using the... Ex Resolve these force vectors into their x and y components

F1 = 35 N

20o

F2 = 45 N

50o

F3 = 65 N

Ex 2 - Determine the resultant force if all three forces in the last example are applied to a single body.

F1 F2

F3

FR

Dynamics Notes 3 – Inclines

Although the Fg pulls straight down at all times…

A ball sitting on a level surface will not roll because the

forces on it are balanced (Fnet = 0).

However, when the ball is

placed on an inclined plane it will roll down the

plane.

FN is always…

For inclined plane questions our first step should always be

to resolve the object’s Fg into two components:

Two important things to notice:

1) Only the ___________________ ___________________________ pulls down the ramp.

2) The ______________________ __________________________ is equal and opposite to

__________________________.

Ex

An 8.0 kg block slides down the

frictionless inclined plane shown.

What is its acceleration?

35o

Ex

How much force is required to push

an 11 kg block up the frictionless ramp

shown at a constant velocity?

Ex

A 15 kg block sits on an inclined ramp

whose coefficient of friction is 0.21. Find

the block’s acceleration.

58o

40o

Dynamics Notes 4 – Two Objects and Tension

There are a number of common force problems that involve 2 objects, that you will be expected to be able to solve. We will focus on 3 of these.

Atwood’s Machine: Two masses suspended by a pulley Diagram: Include all forces at work on the two masses.

Note that there is a force of TENSION (T) that exists along the rope. Tension acts the same as all other forces, with two important peculiarities: 1) It is an internal force, acting… 2) It cancels out…

Both masses have a Fg that pull downwards, but since they are connected by a pulley those forces work in ______________ _________________. The masses will accelerate so that the… Since they are attached by a rope the acceleration of the masses must be _____________________.

The Strategies: • When solving these problems it is easiest for us to choose

the direction …

• Remember that the acceleration on the two masses...

• It can also be easier to conceptualize this problem if we “unfold” the masses and lay them out in a line, while keeping all of our forces as they are…I know that sounds weird so, here’s an example.

Ex Two masses are suspended from a lightweight rope over a frictionless pulley as shown. What will their acceleration be once released?

kg

kg

NOTE: When calculating the acceleration we use the _____________ because the Fnet is accelerating the entire system (both masses)!

Alright that wasn’t too hard, but can you find the tension in the rope?

If we use the same force diagrams and equations as before we hit a snag. The two tension forces ______________ !!! This is because tension is an___________ ____________. In order to solve for tension we have to consider…

Strategy: To solve for tension chop your diagram in half and only consider one of the masses. Either one is fine because…

The Hanging Mass: One mass hanging, one horizontal Ex Consider the two masses shown. Find their acceleration and the tension in the rope.

8.0 kg

6.0 kg

Ex - Find the tension in the rope in the preceding example. Note: When finding the tension we are only considering half of the equation therefore we only use ___________.

Ex In the name of physics, a monkey is attached to a sleeping sheep on a ramp. Don’t ask why. As we all know, the coefficient of friction for a sleeping sheep on a ramp is precisely 0.15. Determine: a. The acceleration of the system. b. The tension in the rope.

Because one tricky concept is never enough, I give you…

Ex Two forces are attached by a rope over a frictionless pulley as shown. (Assume the incline is frictionless) Determine: a. The acceleration of the masses. b. The tension in the rope.

m2 = 6.0 kg

m1 = 4.0 kg

30o

Problem: What direction will they accelerate? In earlier pulley problems it was obvious, the bigger mass always wins. When an inclined plane is involved this is not always the case because for the mass on an incline only...

So determine the forces on each one separately and see which one is the winner. Force 1 =_________ Force 2 = _________

even adorabler

sheep 28 kg

adorable monkey

24 kg

40o Strategies: 1. Find the forces acting on the two

bodies separately to determine a winner

2. Determine the friction on the sheep. Friction can work either up or down the ramp, because it always opposes motion, so we don’t know which direction it is acting until we know the winner.

3. Based on the winner find the acceleration using mtotal

4. Choose either body and examine it separately to determine the tension in the rope