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

2. 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.

3. 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.

4. 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

5. Why is this an inertial reference frame?

6. Thought Question 1
If a single force acts on an object, does the object accelerate? YES
If an object experiences an acceleration, is a force acting on it? YES
If an object experiences acceleration, is no force acting on it? NO

7. 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.

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

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

10. Thought Question 2
If an object experiences a net force in the x- direction, does it move in the x-direction? Not necessarily. Consider circular motion.

11. Units of Force
What are the derived units of Force if F=ma? 1 Newton=1 kilogram meter/second2

12. Ex 1
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

13. Ex 2
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

14. Ex3. 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

15. Ex 4
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

16. Ex5. 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

17. Ex 6. Link to Calculus
A 3kg particle moves along the x-axis according to the position function x(t) = x3 – 2x At what time is the net force on the particle equal to 0?
t = 2/3 s

18. Thought Question 3
At time t=0, a single force F of constant magnitude begins to act on a rock that is moving along an x-axis through deep space. The rock continues to move along that axis.
For time t>0, which of the following is a possible function x(t) for the rock’s position
x=4t-3 ii)x=-4t2+6t-3 iii)x=4t2+6t-3
b) For which function is F directed opposite the rock’s initial direction of motion?