Chapter 4

Forces and the Laws of Motion

Newton’s First Law

An object at rest remains at rest, and an object in motion continues in motion with constant velocity (that

is, constant speed in a straight line) unless the object experiences a net external force.

“Equilibrium”

∑ �⃗�=0

• Is the object in equilibrium?

• Describe the motion of the object.

Newton’s Second Law

The acceleration of an object is directly proportional to the net force acting on the object and inversely

proportional to the object’s mass.

1

net force = mass x acceleration

ExampleThe net force on a golf cart is 390 N north. If the cart has a total mass of 270 kg, what are the magnitude and direction of the cart’s acceleration?

PracticeTwo students reach for a jar of mustard at the same time. One student pulls to the left with a force of 13.2 N, while the other students pulls to the right with a force of 12.9 N. If the jar has a net acceleration of 0.44 m/s2 to the left, what is the mass of the jar?

13.2 N 12.9 N

PracticeA 2.0-kg fish pulled upward by a fisherman rises 1.9 m in 2.4 s, starting from rest. Assuming the acceleration is constant, find the magnitude and direction of the net force acting on the fish during this interval.

upwards

upwards

Practice

FT,1 = 23.2 NFT,2 = 23.2 N

Practice

* Note: force of gravity = 25,000 N

(a) Fnet = 1830 N at 41.0° below the horizontal(b) anet = 0.718 m/s2 (c) ∆x = 51.5 m

ExampleA Goliath beetle with a mass of 0.080 kg is placed on a slope that makes an angle of 37.0° with the horizontal. If the force of gravity is 0.784 N, find the acceleration of the beetle along the slope (a) if there is no friction, (b) if there is a force of friction applied upward along the slope equal to 1.4 N.

37.0°

y

x

(a) no friction

down the incline down the incline

(b) with friction?

up the incline37.0°

0.784 N

Practice

* Note: force of gravity = 4008 N

(a) Fnet = 76 N at 30.0° above the horizontal(b) anet = 0.186 m/s2 at 30.0° above the horizontal(c) ∆t = 8.03 seconds

Newton’s Third Law

If two objects interact, the magnitude of the force exerted on object 1 by object 2 is equal to the magnitude of the

force simultaneously exerted on object 2 by object 1, and these two forces are opposite in direction.

“For every action, there is an equal and opposite reaction.”

These two forces are called an “action-reaction pair”

�⃗� 1on2=− �⃗� 2on1

Action-reaction pair

Action-reaction pair

Action-reaction pair: Force of Gravity

𝐹 𝑔=𝐺𝑚1𝑚2

𝑟2𝐺=6.673×10−11 N m

2

k g2

�⃗� 1on2�⃗� 2on1

Which force is bigger?

Weight

The weight of an object is the force of gravity acting on the object.

On earth,

𝑊=𝑚�⃗�

Mass vs. Weight

• Which is greater: your mass on Earth or your mass on the moon?

• Which is greater: your weight on Earth or your weight on the moon?

Normal Force

The normal force acts on a surface in the direction perpendicular to the surface

�⃗� 𝑔

�⃗� 𝑛

�⃗� 𝑔

�⃗� 𝑛

𝐹 𝑔=𝐹𝑛?

ExampleA student attaches a rope to a 20.0 kg box of books. He pulls with a force of 90.0 N at an angle of 30.0° from the horizontal. Find the magnitude of the normal force and the net acceleration of the box.

90.0 N

forward30.0°

�⃗� 𝑔

�⃗� 𝑛

Force of Friction

Force of Friction

• Friction opposes the applied force

Static friction: resists the initiation of sliding motion between two surfaces that are in contact and at rest

Kinetic friction: opposes the movement of two surfaces that are in contact and sliding over each other

Force of Friction

• The force of friction depends on – the normal force– the materials in contact

• Coefficient of friction (µ): the ratio of the force of friction to the normal force

𝐹 𝑓=𝜇𝐹 𝑛

Force of Friction