Review Session #2Motion and ForcesMINNETONKA HIGH SCHOOL | IB PHYSICS

Reminder of our Equations

Units m m s-1 m s-1 m s-2 s

𝑣 = 𝑢 + 𝑎𝑡 𝑢 𝑣 𝑎 𝑡

𝑠 = 𝑢𝑡 + 12𝑎𝑡2 𝑠 𝑢 𝑎 𝑡

𝑣2 = 𝑢2 + 2𝑎𝑠 𝑠 𝑢 𝑣 𝑎

𝑠 = 𝑣+𝑢 𝑡2

𝑠 𝑢 𝑣 𝑡

Finding the Components of a Vector

20 N

θ = 34°

What are the x and y components of a 20 N force applied 34° from horizontal?

X-Component

Y-Component

Dropping a marble

𝑠

𝑢

𝑣

𝑎

𝑡

How fast must you launch a baseball straight in the air to reach the height of the Empire State Building (380 m)?*Assuming no air resistance*

Motion Graphs Guide

d

v

a

Co

nst

ant

Dis

pla

cem

ent

Co

nst

ant

+ V

elo

city

Co

nst

ant

-V

elo

city

+ A

ccel

erat

ion

Sp

eed

ing

up

+ A

ccel

erat

ion

Sl

ow

ing

Do

wn

-A

ccel

erat

ion

Sp

eed

ing

up

-A

ccel

erat

ion

Sl

ow

ing

Do

wn

Use the graphs to tell you MORE!Sl

op

eA

rea Un

der

Cu

rve

Displacement vs Time

Velocity vs Time

Acceleration vs Time

What Happens When…

v

t

a

d

t

What happens when you throw a ball straight up in the air?

Projectile Motion

X-Y Problem Solving Steps

X Y

𝑠

𝑢

𝑣

𝑎

𝑡

1. Start with Y and pretend it’s just a freefall problem

2. The air time is the same for X and Y so make tx = ty

3. Solve for X. • Constant velocity

• (ux = vx)• ax = 0• s = vt

Horizontal Projectile

X Y

𝑢

𝑣

𝑠

𝑎

𝑡

u

15 cm

1 m

Projectile at an Angle

24°

X Y

𝑢

𝑣

𝑠

𝑎

𝑡

vx =

vy =

You hit a baseball at 24° above the horizontal as a speed of 30 m/s. How far does the ball travel before it hits the ground?

Acceleration from FBD

How fast is this 100 kg block accelerating?

600 N

200 N

400 N100 N

Calculating Acceleration w/ Friction

Step 1:Find the Force from Friction• Fg = mg• R = Fg

• Ff = μ × R

Step 2:Find Fnet

• Fnet = Fpush - Ff

Step 3:Find acceleration

Fnet = ma a = Fnet / m

FpushFf

Fg

R

Calculate Friction | Try This…

Santa’s reindeer pull his 2000 kg sleigh with a force of 4980 N. How fast does the sleigh accelerate if the coefficient of kinetic friction (µk) is 0.05?

Air Resistance

Force of gravity is always constant

Force of air resistance increases whenvelocity increases

10

m/s

30

m/s

50

m/s

Fw

Fw

Fw

Terminal VelocityD

isp

lace

men

t (m

s-1

)

Time (s)

Vel

oci

ty (

m s

-1)

Time (s)

Ramp Problem

40°

m 10 kg

Fg

F⊥

F∥

R

Ff

Fnet

a

μ = 0.15

Calculating Gravitational Force

What is the force of gravity between the earth and the moon?

m = 6 × 1024 kgm = 7.4 × 1022 kg

r = 3.8 × 108 m

𝐹 = 𝐺𝑀𝑚

𝑟2G = 6.67 × 10-11 𝑁×𝑚2

𝑘𝑔2

Gravitation Field Strength

What is the gravitational field strength of the earth at the position of the moon?

m = 6 × 1024 kgm = 7.4 × 1022 kg

r = 3.8 × 108 m

𝑔 = 𝐺𝑀

𝑟2G = 6.67 × 10-11 𝑁×𝑚2

𝑘𝑔2

Defining Circular Motion | Summary

𝑣 =2𝜋𝑟

𝑇= 𝜔𝑟𝜔 =

2𝜋

𝑇

Angular Velocity Tangential Velocity (linear speed)

r radian

Centripetal Acceleration

A 3 kg rock swings in a circle of radius 5 m. If its constant speed is 8 m s-1, what is the centripetal acceleration?

What is the tension?

m = 2 kg

Fc

Fc

m 2 kg

vt 5 m/s

r 0.5 m

Fc

Fnet

Fg

FT

m 2 kg

vt 5 m/s

r 0.5 m

Fc

Fnet

Fg

FT

Top Bottom

Calculating Work

When you push a lawn mower, you are really applying a force down the angled handle bar as shown in this picture

FHow much work do you do when you push a lawn mower 20 m with a force of 200 N directed at an angle of 30° with the ground?

30°

Work and Power

How much power is required from the engine to move at a constant 30 m s-1? The force of drag (Ff) is 500 N. How much work is done in 4 seconds?

Conservation of Energy

100 m 70 m

What is the velocity of a 1 kg marble at point A?

Conservation of Energy | w/ spring

How far up the 15° incline of a pinball table will a 0.1 kg pinball move after it is launched? The spring constant is 100 N/m and is compressed by 0.08 m.

h

Work-Energy Theorem

A 0.005 kg bullet moving at 650 m/s hits a tree trunk and penetrates to a depth of 0.04 m. What is the force of the tree?

Which impulse is larger?Fo

rce

(N)

2

4

6

8

10

2 4 6 8 101 3 5 7 9

12

1

3

5

7

9

11

13

Time (s)

Calculating with Impulse-Momentum

You launch a marshmallow out of a 11 inch paper tube. If you can provide a consistent 0.28 N of force, how fast does the 0.7 g marshmallow travel when it exits the tube if it is in the tube for 0.05 seconds?

𝐹

𝑡

𝑚

𝑢

𝑣

Conservation of Momentum

mB

vBi = 0 m/s

mA

vAi = 4 m/smA = 18 kg mB = 12 kg

BEFORE

vBf = vf

mA

vAf = vf

mA = 18 kg mB = 12 kg

mB

After

What is the final velocity of block A and B if they stick together