Aim: How do we explain Newton’s first two laws of motion?

DoNow: Contact Forces and Field Forces Identify examples of each type of force.

Newton’s 1st Law of Motion Law of Inertia- In the absence of force, an object at rest will stay at rest and an object in motion will stay in motion at constant velocity.

Inertial Reference Frames If no forces act on an object, any reference frame with respect to which the acceleration of the object remains zero is an inertial reference frame.

Which of the following is an inertial reference frame? A person standing on a merry go round An apple falling from a tree A spacecraft moving at constant velocity A satellite orbiting earth at constant speed

Why is this an inertial reference frame?

Thought Question 1 Is it possible to have motion in the absence of a force? Is it possible to have force in the absence of motion?

Thought Question 2 If a single force acts on an object, does the object accelerate? If an object experiences an acceleration, is a force acting on it? If an object experiences acceleration, is no force acting on it?

Inertial Mass What is inertial mass? Inertial mass is the measure of an object’s resistance to a change in motion in response to an external force. Are inertial mass and gravitational mass the same thing?

Newton’s 2nd Law ∑F = ma The net force acting on an object is the vector sum of all forces acting on an object. It is also called the resultant force. The net force acting on an object is equal to the mass of the object multiplied by the acceleration of the object.

Force as a Vector Forces are vectors so we add forces like vectors.

Newton’s 2nd Law restated The acceleration of an object is directly proportional to the net force acting on it.

Thought Question 3 If an object experiences a net force in the x- direction, does it move in the x-direction?

Units of Force What are the derived units of Force if F=ma?

Thought Question 4 In a train, the cars are connected by couplers. The couplers between the cars exert forces on the cars as the train is pulled by the locomotive in the front. Imagine that the train is speeding up in the forward direction. As you imagine moving from the locomotive to the caboose, does the force exerted by the couplers increase, decrease, or stay the same?

Ex 1 A 0.30 kg hockey puck slides on the horizontal frictionless surface of an ice rink. It is struck simultaneously by two different hockey sticks. The two constant forces that act on the puck as a result of the hockey sticks are parallel to the ice surface and are shown in the pictorial representation shown. The force F1 has a magnitude of 5.0 N and F2 has a magnitude of 8.0 N. Determine the acceleration of the puck while it is in contact with the two sticks.

Ex 1 34 m/s^2 at 30 degree angle

Ex 1 Cont Determine the components of a third force that when applied to the puck along with the two causes the puck to have zero acceleration. -8.7N=x, -5.2N=y

Ex 2 A 6.0 kg object undergoes an acceleration of 2.0 m/s2 . a) What is the magnitude of a the net force acting on the object? b) If this same force is applied to a 4.0 kg object, what acceleration does it produce? a) 12 N b) 3.0 m/s2

Ex 3 A 1.80 x 103 kg car is traveling in a straight line with a speed of 25.0 m/s. What is the magntiude of the constant horizontal force needed to bring the car to rest in a distance of 80.0m? 7.03 x 10^3 N

Ex1. A sliding ice cream carton problem A given force produces an acceleration of 5m/s2 on the standard object of m1=1kg. When an equal force is applied to a carton of ice cream of mass m2, it produces an acceleration of 11m/s2. What is the mass of the carton of ice cream? What is the magnitude of the force? a) 0.45 kg b) 5 N

Ex 1- (cont) A force of 3 N produces an acceleration of 2 m/s2 on an object of unknown mass. What is the mass of the object? If the force is increased to 4 N, what is the acceleration? a) 1.5 kg b) 2.67 m/s2

Ex2. Walk in Space You’re stranded in space away from your spaceship. Fortunately, you have a propulsion unit that provides a constant force F for 3s. After 3s you have moved 2.25 m. If your mass is 68 kg, find F 34N

Ex3. Multiple Forces A particle of mass 0.4kg is subjected simultaneously to two forces F1 = -2Ni – 4Nj and F2=-2.6Ni + 5Nj. If the particle is at the origin and starts from rest, Find its position vector at t = 1.6 s Find its velocity vector at t= 1.6s a) -14.7m i + 3.20 m j b)-18.4 m/s i + 4 m/s j

Ex 4. Link to Calculus A 3kg particle moves along the x-axis according to the position function x(t) = x3 – 2x2 + 10. At what time is the net force on the particle equal to 0? t = 2/3 s

Weight Fg = mg The weight of an object is equal to the mass of an object multiplied the acceleration due to gravity (gravitational field value) (9.81 N = 2.20 lb) Fg=weight m= mass g = 9.81m/s2 = gravitational acceleration due to gravity = 32.2 ft/s2

Thought Question 1 Suppose you are talking by interplanetary telephone to your friend who lives on the Moon. He tells you that he has just won a piece of gold weighing one newton in a contest. Excitedly, you tell him that you entered the Earth version of the same contest and also won a newton of gold! Who’s richer?

Thought Question 2 A baseball of mass m is thrown upward with some initial speed. If air resistance is ignored, what is the magnitude of the force on the ball (a) when it reaches half its maximum height and (b) when it reaches its peak?

Thought Question 3 In the absence of air friction, it is claimed that all objects fall with the same acceleration. A heavier object is pulled to the Earth with more force than a light object. Why does the heavier object not fall faster?

Ex 5. Accelerating Student The net force acting on 130 pound student is 25 pounds. What is her acceleration? 6.19 ft/s2

Ex 5. (cont) What force is needed to give an acceleration of 3ft/s2 to a 5 pound block? 0.466 pounds