Do Now

Dynamics warm-up: do now
Think about it

When is the acceleration negative? positive?

Skateboard A, B, C
Marvin getting smarter

What would happen if this bottle were dropped?

Newton's Masterpiece!

Newton's Principia, first edition

Sir Isaac Newton's own first edition copy of his Philosophiae Naturalis Principia Mathematica with his handwritten corrections for the second edition.

The first edition was published under the imprint of Samuel Pepys who was president of the Royal Society. By the time of the second edition, Newton himself had become president of the Royal Society, as noted in his corrections.

The book can be seen in the Wren Library of Trinity College, Cambridge.

Photograph © Andrew Dunn, 5 November 2004. www.andrewdunnphoto.com/

4. Standard Equation

Fnet = ma

(N)  =  (Kg)(m/s2)

Newton — force needed to give a 1 kg of mass an acceleration of 1 m/s2

Derived unit — A unit that comes from the combination of other units

N = Kg·m/s2

Fundamental unit (opposite) — m, s, Kg

Force Questions

Ex 1

What is the net force necessary to give a 3.0 kg mass, initially at rest, an acceleration of 5.0 m/s2?

Football player practice toss

F = ma

(3.0 kg)(5.0 m/s2)

= 15 N

or 15 kg·m/s2

Ex 2

A net force of 30. nt accelerates an object by 15. m/s2. Find the object's mass.

F = ma

30. N = m(15. m/s2)

m = 2.0 kg

Ex 3

An unbalanced force of 100. nt acts on a 50. kg mass for 5.0 seconds. Find the acceleration of the mass.

Fnet = ma

100. N = (50. kg)a

a = 2.0 m/s2

Ex 4

A 10. kg cart moving with a velocity of 2.0 m/s is brought to a stop in 2.0 sec. Find the magnitude of the average force used to stop the cart.

Given

m = 10. kg     t = 2.0 sec

Vi = 2.0 m/s     Vf = 0 m/s (stop)

a = (Vf − Vi) / t = (0 − 2.0 m/s) / (2.0 sec)

a = −1.0 m/s2

Fnet = ma = (10. kg)(−1.0 m/s2)

Fnet = −10. N

or −10. kg·m/s2

Ex 5

The object below has a mass of 5 kg. Find its acceleration.

20 N and 60 N forces on an object

Fnet = ma

40 N East = (5 kg)a

a = 8 m/s2 East

Ex 6 Force diagram for the block

The block above has an acceleration of 22. m/s2. What is the mass of the block?

5 N2 + 10 N2 = R2

Fnet = ma

Fnet = 11 N = m(22 m/s2)

m = .50 kg

Woman kicking a bag

Ex 7 Force diagram for the block

If the magnitude of the block's acceleration is 2.0 m/s2, what is the mass of the block?

Fnet = ma

10 N Left = m(2 m/s2)

m = 5 kg

Balloon in the Car

Geek question

What will the balloon do when the cart is pushed to the left?

(Click on image)

Balloon in car - click to play video

Rutgers U

Balloon_in_car

The air in the container tends to remain at rest. When the cart is pushed to the left, air pressure builds up on the right side of the container.

Try this at home!

Ranking Task

Rank the accelerations

From least to greatest.

Rank the accelerations from least to greatest
Rank the accelerations

From least to greatest.

Force, mass, acceleration diagram 1 Force, mass, acceleration diagram 2