Equilibrium & Newton’s 2nd Law of Motion

Review: Law Of Inertia Newton's 1st Law - If there is no net force acting on a body, then it will continue in it's state of constant velocity (which may be zero). Mathematically.

Add all the forces acting on a body. R = 0 - constant velocity or zero Add all the forces acting on a body. R = 0 - constant velocity or zero. It is at equilibrium – acceleration = 0

6 N, up 4 N, right The net force acting on an object is the vector sum of all the forces acting on it. Find the net force on each – it is helpful to treat horizontal (x) & vertical (Y) separately. 10 N 3 N 6 N, up 3 N 7 N 3 N 4 N, right 4 N

What is the motion of each box? 6 N, up 3 N 7 N 4 N, right 3 N 4 N Accl right Accl up

Objects not in Equilibrium will accelerate in the direction of the net force. But how much?

“Law of Acceleration”

a = Fnet m m - mass in kg a - m/s2. F - Newtons (N): 1 N = 1kg m s2 Fnet means sum the forces in one direction. A constant net force causes constant/uniform acceleration!

One Newton = the amount of force needed to accelerate a 1 kg mass to at a rate of 1 m/s2.

More massive objects require more force to accelerate!!

Finding acceleration Sketch a free body diagram show all forces on one object. Calculate magnitude & direction of Fnet. Use a = Fnet/m to find a in any direction where Fnet ≠ 0.

1. A 2000-kg car’s engine exerts a westward force of 12500-N 1. A 2000-kg car’s engine exerts a westward force of 12500-N. Friction between the tires and the road is 500-N. Sketch the free body diagram. Calculate Fnet Calculate the acceleration.

2. An 80-kg man who weighs 800-N fell out of an airplane 2. An 80-kg man who weighs 800-N fell out of an airplane. As he falls air resistance pushes him up with a force of 150-N. Sketch the free body diagram. Calculate his acceleration as he falls to Earth. Why is his actual acceleration different than g?

3. Find the acceleration of the box below. Assume the box has mass 2 3. Find the acceleration of the box below. Assume the box has mass 2.5 kg. 3 N 8 N 4 N 7 N 3 N

Vertically, we have +3N(up) and –3N (down), so they add to zero. X & Y forces separately. Vertically, we have +3N(up) and –3N (down), so they add to zero. Vertically, a = 0. Horizontally, +8N +4N (right), -7N (left), so Fnet is +12 – 7 = +5 N. a = F/m +5N / 2.5 kg = 2 m/s2. Acceleration to the right.

example prb’s

The forces on the man in the elevator are balanced The forces on the man in the elevator are balanced. Which of the following are possible? He could be: 1. Moving down. 2. At rest 3. Moving up 4. In freefall.

Graphs of Newton’s 2nd Law Equation: a = Fnet/m. Slope = 1/mass

Graphs of Newton’s 2nd Law Equation: a = Fnet/m. Slope = mass.

Increasing Mass vs. Acceleration Hold Fnet constant a = Fnet/ m How to find Fnet?

Because a requires a Fnet, you feel acceleration Because a requires a Fnet, you feel acceleration!! If there is a net force on you, you feel pushed or pulled. If you are moving at a constant velocity, you feel normal.

Weight & Mass What is mass? The amount of matter / stuff.

Review. Newton 1 Newton 2 Weight Friction. Normal force.

Prac Set

What is weight? The force of gravity acting on mass. Mass in kg, weight in Newtons (N).

Weight (W or Fg) Fg = mg. g = Fg/m m = Fg/g m in kg g = 9.81 m/s2 Since F = ma, then near Earth’s surface: Fg = mg. g = Fg/m m = Fg/g m in kg g = 9.81 m/s2 Fg = W in N.

4. What is the weight of a 100-kg person on Earth? Fg = mg =(100 kg)(9.81 m/s2) = 981 N.

Ex 5: What is the weight of a 500-g ball on earth? 500g x 1 kg/103 g = 0.5 kg. 0.5 kg x 9.81 m/s2 = 4.9 N.

Ex 6. A 600-N student weighs 100-N on Planet Jordan Ex 6. A 600-N student weighs 100-N on Planet Jordan. What is the acceleration of gravity on Planet Jordan? Find the mass on Earth. m = Fg/g 600N/9.81 m/s2 61 kg. Find g on Jordan, g = Fg/m = 100 N/ 61 kg g = 1.6 m/s2.

If you are not accelerating toward the Earth, then some force is balancing your weight!

You feel acceleration!! If there is a net force on you, you feel pushed or pulled. If you are moving at a constant velocity, you feel normal.

Or Weight with spring scale. Newton’s 3 Laws 4.5 minutes. http://www.youtube.com/watch?v=iH48Lc7wq0U Newton 2 6 minutes. http://www.youtube.com/watch?v=WzvhuQ5RWJE&feature=relmfu Or Weight with spring scale.

152 #20,21, 25-27 Weight Packet.

Weight with spring scale.

Constant Fnet = uniform a

Equilibrium When all forces are balanced they are in equilibrium. How can we determine 3 force could be in equilibrium? See Starreview pg 83.

Ted Elevator Forces http://ed.ted.com/lessons/would-you-weigh-less-in-an-elevator-carol-hedden