Physics 170 - MechanicsLecture 10

Newton’s Laws

ForceKinematics vs. dynamics: what causes acceleration? Answer: force.

Force: push or pull

Force is a vector – it has magnitude and direction

The Law of Inertia You push on an object and it moves. If you stop pushing an object, does it stop moving?

Only if there is friction! In the absence of any net external force, an object will keep moving at a constant speed in a straight line, or remain at rest.

This is Newton’s 1st Law, and it is also known as the Law of Inertia.

In order to change the velocity of an object – in magnitude or in direction – a net force is required. An inertial reference frame is one in which the first law is true. Accelerating reference frames, e.g., a rotating frame, are not inertial.

Motion and Inertial Frames

Newton’s First Law of Motion

Newton’s 1st Law:In the absence of external forces, an object at rest remains at rest; an object in motion remains in motion.

Inertia If no force acts on an object, an inertial reference frame is any frame in which there is no acceleration on an the object.

In (a) the plane is flying horizontally at constant speed, and the tennis ball does not move horizontally.

In (b) the pilot suddenly opens the throttle and the plane rapidly gains speed, so that the tennis ball accelerates toward the back of the plane.

Inertia is the tendency of mass to resist acceleration, so that a force must be supplied to overcome inertia and produce acceleration.

Mass Mass is the measure of how hard it is to change an object’s velocity.

Mass can also be thought of as a measure of the quantity of matter in an object or the quantity of inertia possessed by the object.

One liter of water has a mass of 1 kg.

Calibrating Spring Force Two equal weights exert twice the force of one; this can be used for calibration of a spring:

Acceleration vs. Force Now that we have a calibrated spring, we can do more experiments. Acceleration is proportional to force:

∝

∝

Acceleration vs. MassAcceleration is inversely proportional to mass:

∝

∝

Combining these two observations gives:

Newton’s Second Law of Motion

This is the mathematical expression ofNewton’s 2nd Law of Motion.

Units: Mass has SI units of kg, and acceleration has SI units of m/s2. We define the SI unit of force as:1 newton = 1 N ≡ 1 kg m/s2.

Or, more familiarly:

Drawing Force Vectors

Example: Accelerated Mass

A net force of 3.0 N produces an acceleration of 2.0 m/s2 on an object of unknown mass.

What is the mass of the object?

m1

Newton’s Second Law

Newton’s Second Law of Motion An object may have several forces acting on it;

the acceleration is due to the net force:

Combining Forces

Forces add vectorially.

Newton’s Second Law of MotionFree-body diagrams:

A free-body diagram shows every force acting on an object. To draw a free-body diagram:

Sketch the forces

Isolate the object of interest

Choose a convenient coordinate system

Resolve the forces into components

Apply Newton’s second law to each coordinate direction

Newton’s 2nd Law:An object of a given mass m subjected to forces F1, F2, F3, … will undergo an acceleration a given by: a = Fnet /m

whereFnet = F1 + F2 + F3 + …

The mass m is positive, force and acceleration are in the same direction.

Newton’s Second Law of Motion

Example: A Sliding Ice-Cream Carton

A force exerted by a stretched rubber band produces an acceleration of 5.0 m/s2 on an ice cream carton of mass 1.0 kg. When a force exerted by an identical rubber band stretched the same amount is applied to a carton of ice cream of mass m2, it produces an acceleration of 11.0 m/s2.

(a) What is the mass of the second carton?

(b) What is the magnitude of the force applied by the rubber band?

Example: Three Forces

Moe, Larry, and Curley push on a 752 kg boat, each exerting a 80.5 N force parallel to the dock.(a) What is the acceleration of the boat if they all push in the same direction?(b) What is the acceleration if Moe pushes in the opposite direction from Larry and Curley as shown?

Example: A Space Walk You are stranded in space, away from your spaceship. Fortunately, you have a propulsion unit that provides a constant net force F for 3.0 s. You turn it on, and after 3.0 s you have moved 2.25 m.

If your mass is 68 kg, find F.

The Vector Nature of Forces:Forces in 2D

The easiest way to handle forces in two or three dimensions is to treat each dimension separately, as we did for kinematics.