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Forces and Newton’s Laws

•  CAPA due today at 10pm – we postponed the due date, so you would have the opportunity to go to the helproom.

•  Next CAPA Assignment is available! •  Beginning Material in Chap. 5 on Forces

and Newton’s Laws

Web page: http://www.colorado.edu/physics/phys1110/phys1110_sp12/

Announcements:

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Last Wed Example Q. An object is dropped from an airplane flying at uniform velocity (constant speed in a straight line). Neglecting air resistance, the object will:

Set frequency to BA

Since the plane is traveling at uniform velocity, it is not accelerating. The object only experiences acceleration from gravity which is vertical so it will stay under the plane.

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Clicker question 1 Q. Who won the Superbowl yesterday?

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A.  Denver Broncos B.  New York Giants C.  Colorado Avalanche D.  New England Patriots E.  Who cares?

21-17 Giants over Patriots

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Force Force is a vector!

Because force is a vector the principle called superposition of forces is true.

Suppose there are a bunch of forces acting on an object. The vector sum of these forces is the net force. Applying just this net force is the same as applying all of the forces that add up to the net force.

Superposition of forces

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Analysis of force

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What forces act on the weight?

We model weight as a simple block

Gravity

Normal

Friction Rope

The rope is a force in the negative x direction Gravity is a force in the negative y direction Friction is a force in the positive x direction The normal force is the force of the ground on the weight. It is perpendicular to the surface.

This drawing is called a free body diagram which we use to show the forces acting on a body

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Analysis of force

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Assume the weight is not moving. What is the net force on the weight? 0. There is no net force.

Net force:

Often separate vectors into perpendicular components:

So in this case we have a net force of

so and

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Newton’s first law

A body acted on by no net force maintains the same velocity (can be 0)

Although we might all agree that a stationary body has no net force acting on it, this is also true for a body traveling at constant velocity (magnitude and direction are constant).

Formulations of Newton’s first law

A body moving at constant velocity has no net force acting on it

A body in motion tends to stay in motion; a body at rest tends to stay at rest

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Newton’s first law

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But how can you say there is no net force operating on the weight when it is moving at constant velocity?

It is true that the person exerts a force on the weight through the tension in the rope. But if the weight is moving at constant velocity, this force is canceled by friction so there is no net force.

If you imagine the weight on ice it would sail along once you got it started. It would require force to slow it down. The tendency to keep moving is called inertia.

Sometimes Newton’s first law is called the law of inertia.

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Clicker question 2 Set frequency to BA

Q. A sailboat is being blown across the sea at a constant velocity. What is the direction of the net force on the boat?

A.  Left ← B.  Right → C.  Net force is zero D.  Down ↓ E.  Up ↑

Boat is traveling at constant velocity so the net force is 0. There are individual forces from gravity, wind, etc. but they all add up (vectorially) to 0.

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Clicker question 3 Set frequency to BA

How large is the force of friction on Skinney's feet compared to the force of friction on Fatty's feet? A) FS > FF B) FS = FF

C) FS < FF

FRope on SF S FRope on F F F

Skinney Fatty

€

FS = FR on S , FF = FR on F ,FR on S = FR on F

FS = FF

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Inertial reference frames The person on the sailboat watching the shore go by and the person on the shore watching the sailboat go by are in two different reference frames. Neither one is preferred.

Newton’s first law implies there is no real difference between zero velocity and constant (non-zero) velocity.

Reference frames which move at constant velocity (including 0) are called inertial reference frames.

Newton’s laws work the same in all inertial reference frames

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Inertial reference frames Is the inside of a car an inertial reference frame?

When traveling at a constant speed in a straight line, everything at rest will stay at rest so yes in this case.

When the car hits the brakes causing the passenger who is not wearing a seat belt to hit his head on the dashboard, it is not an inertial reference frame. The passenger’s head is staying at rest while the car accelerates.

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A.  A car traveling at a constant 100 mph down a straight and level road.

B.  A car in the process of crashing into a concrete barricade. C.  A car traveling at a constant 20 mph around a curve. D.  More than one of the above E.  None of the above

Clicker question 4 Set frequency to BA

Q. Which of the following is an inertial reference frame?

In B and C, the car is accelerating (linear acceleration in B and centripetal acceleration in C) so they are not inertial reference frames. Objects inside the car will move relative to the car with no apparent force applied.

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What does a force do? The concept that a body will stay in motion if there is no external force applied is attributed to Galileo and stated more explicitly by Newton.

If a net force is not required to keep a body moving at constant velocity, then what does it do?

A force is required to change the velocity of a body!

Galileo Newton

What quantity deals with velocity change? Acceleration!

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Newton’s second law So, a net force causes an object to accelerate.

Does the amount of acceleration depend on the object or just the amount of force?

If you were to throw a gallon milk and a can of soda (with the same force), which would travel farther?

Longest shot put (16 lb ball): 23 m Longest baseball throw (1/3 lb ball): 136 m

Acceleration times time gives final velocity which (along with angle) determines how far a projectile travels.

Acceleration depends on force applied and mass of body. Newton’s second law:

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A.  The same: Δv=vf B.  Greater: Δv > vf C.  Less: Δv < vf D.  Depends on the

signs of v1 and v2

Clicker question 5 Set frequency to BA

Situation 1: A constant force is applied for a short time to a frictionless cart initially at rest. The cart acquires a final velocity vf. Situation 2: The same constant force is applied for the same short time interval to the same frictionless cart initially moving with velocity v1. The final velocity in this case is v2. The change of velocity Δv = v2 – v1 compared to the final speed in Situation 1 is…

Masses and forces are the same so acceleration is the same. The time interval is the same and

is the same:

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Clicker question 6 Set frequency to BA

An astronaut floating weightlessly in orbit shakes a large iron anvil rapidly back and forth. She reports back to Earth that

A: the shaking costs her no effort because the anvil has no inertial mass in space.

B: the shaking costs her some effort but considerably less than on Earth.

C: although weightless, the inertial mass of the anvil is the same as on Earth.

Just as it says! Mass is the same wherever you are. It's a measure of inertia

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Clicker question 7 Set frequency to BA

A constant force is exerted on a cart (initially at rest) on an air track. Neglect friction. The force acts for a short time and gives the cart a certain final speed. To reach the same final speed with a force that is only half as big, the force must be exerted on the cart for a time interval

A: four times as long as B: twice as long as C: equal to D: half as long as ... that for the stronger force. OR E: (Not enough information given)

Force causes acceleration = Δv/ Δt. If you want the SAME Δv, with HALF the force, it'll take TWICE the Δt.

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Clicker question 8 Set frequency to BA

F = m Δv/ Δt... If you have the same force, and the same time, but TWICE the mass, you'll get HALF the change in velocity. Since we started from rest, it means v(final) is half.

A constant force is exerted for a short time on a cart (initially at rest) on an air track. This force gives the cart a certain final speed. The same force is exerted for the same length of time on another cart, also initially at rest, that has twice the mass of the first one. The final speed of the heavier cart is: A: one-fourth B: four times C: half D:double E: the same as

….that of the lighter cart.

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A net force causes an acceleration which is inversely proportional to the mass of the object

Force review Force is a vector so superposition of forces is true (can combine all forces into one net force using vector addition).

Newton’s 1st law: A body will stay at a constant velocity unless acted upon by a net force.

We draw a free body diagram to figure out the effect of the various forces and to calculate the net force.

Newton’s 2nd law: . Can split: &