Physics 170 - Mechanics Lecture 10 Newton’s Laws

Force Kinematics 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.

Motion and Inertial Frames

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.

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. Mass Acceleration is inversely proportional to mass:

∝

∝

Newton’s Second Law of Motion Combining these two observations gives: Or, more familiarly:

This is the mathematical expression of Newton’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.

Drawing Force Vectors

Example: Accelerated Mass m1

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?

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 Motion Free-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 Second Law of Motion 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 where Fnet = F1 + F2 + F3 + … The mass m is positive, force and acceleration are in the same direction.

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.