Chapter 4. Forces and Newton s Laws of Motion

Size: px

Start display at page:

Download "Chapter 4. Forces and Newton s Laws of Motion"

Joseph Green
5 years ago
Views:

1 Chapter 4 Forces and Newton s Laws of Motion

2 Chapter 4: Forces and Newton s Laws Force, mass and Newton s three laws of motion Newton s law of gravity Normal, friction and tension forces Apparent weight, free fall Equilibrium

3 Newton s Laws of Motion 1. Velocity is constant if a zero net force acts 2. Acceleration is proportional to the net force and inversely proportional to mass: a 0 if F 0 F a so F m ma Force and acceleration are in the same direction 3. Action and reaction forces are equal in magnitude and opposite in direction

4 Newton s First Law (law of inertia) Object of mass m Acceleration a 0 if F 0 Velocity v constant The velocity is constant if a zero net force acts on the mass. That is, if a number of forces act on the mass and their vector sum is zero: F net F... 1 F2 0 So the acceleration is zero and the mass remains at rest or has constant velocity.

5 Individual Forces Net Force 4 N 10 N 6 N 3 N 5 N 37 4 N

The object also experiences the force due to friction with molecules in the air, which is a result of a complicated interplay between air pressure, wind

6 Some Examples: Why does a falling object reach so called terminal velocity? The force due to gravity is acting down, accelerating the object toward the ground. The object also experiences the force due to friction with molecules in the air, which is a result of a complicated interplay between air pressure, wind speed and direction, and the shape as well as the speed of the object. If the object falls long enough, at some speed the frictional force will be equal and opposite to the force due to gravity. The forces exactly cancel producing a zero net force: And the velocity is constant: i.e. Terminal velocity!

7 Why do you have to keep your foot on the accelerator pedal, even if you want to go at a constant velocity? The weight of the car produces friction between the tires and the road and the car will slow down due to this friction unless you continue to accelerate.

8 Newton s First Law It was a revolutionary idea that objects continue to move if no force acts: experience shows that a force is needed to keep objects moving (friction) it was believed that some cosmic force keeps the planets moving in their orbits In the absence of friction, objects continue to move at constant velocity if net force is otherwise zero (Nothing is done to the object). If the net force, including the force due to friction, is zero, objects move at constant velocity (Something is pushing or pulling to offset the force due to friction).

9 Newton s First Law F N m A crate is at rest on the ground: v 0 and a 0 w What forces act on the crate? the weight: w mg According to Newton s first law, there must be another force so the net force acting on the crate is zero. It is the normal force of the ground acting on the crate F N w 0 F N w F N so the crate remains at rest

10 Inertial Reference Frame Can be defined anywhere: It is a coordinate system, (x, y, z) right here in your car... An inertial reference frame is one that is not accelerated (moves at constant velocity, including zero velocity). the law of inertia (first law) applies in an inertial frame objects at rest remain at rest if no net force acts on them. law of inertia does not apply in an accelerated (non-inertial) frame. Example: Driving around a corner velocity changes, force has to be applied to keep objects from moving a non-inertial frame. y x

11 Newton s Second Law Says what happens if the net force acting on a mass is not zero. The mass accelerates: Acceleration, a F net F net = net force acting on the mass proportional to Introduce the mass: a F net m or F net ma m is the inertial mass, a measure of how difficult it is to accelerate an object.

12 Newton s Second Law m = 1850 kg A free-body diagram shows only the forces acting on the car Two people push a car against an opposing force of 560 N. One exerts 275 N, the other 395 N of force on the car. What is the net force acting on the car? What is the car s acceleration?

13 Problem: A catapult on an aircraft carrier accelerates a 13,300 kg plane from 0 to 56 m/s in 80 m. Find the net force acting on the plane. F net ma (acceleration along a straight line) What is a? v 2 or 56 v ax 0 2a 80 so a 56 2 / m/s Therefore 2 Fnet ( 13, 300 kg ) ( 19. 6m/s ) 261, 000 N

14 The direction of force and acceleration vectors can be taken into account by using x and y components. F ma can be decomposed into F x ma x Fy ma y Then solve the equations separately in each direction.

15 Problem 4.11 What is the acceleration of the block in the horizontal direction? Work out the components of forces in the x-direction. 59 N No friction x 33 N

16 Problem 4.88 A 75 kg water skier is pulled by a horizontal force of 520 N and has an acceleration of 2.4 m/s 2. Assuming the resistive force from water and wind is constant, what force would be needed to pull the skier at constant velocity?

17 Problem 4.4 A special gun is used to launch objects into orbit around the earth. It accelerates a 5 kg projectile to 4x10 3 m/s by applying a force of 4.9x10 5 N. How much time is needed to accelerate the projectile?

19 Problem 4.14: A 41 kg box is thrown at 220 m/s against a barrier. It is brought to a halt in 6.5 ms. What is the average net force that acts on the box?

20 m = 1300 kg Wind Paddling Paddling: force F P of 17 N, to east Wind: force F W of 15 N, 67 o north of east Find a x, a y for the raft. The net force is:

Today s Lecture: Kinematics in Two Dimensions (continued) A little bit of chapter 4: Forces and Newton s Laws of Motion (next time)

Today s Lecture: Kinematics in Two Dimensions (continued) Relative Velocity - 2 Dimensions A little bit of chapter 4: Forces and Newton s Laws of Motion (next time) 27 September 2009 1 Relative Velocity