Newton’s Second Law The Mathematical One

What is the relationship? ForceMassAcceleration Force  Constant  Mass  Constant  Acceleration  Constant  Think of a race car! Force is generated by the engine Acceleration is how fast it increases it’s speed off the line

Student Race… Let’s hit the hall!

What are the relationships? Force is proportional to acceleration ▫If F  then a  (Mass constant) Force is proportional to mass ▫If F  then m  (Acceleration constant) Acceleration is inversely proportional to mass ▫If a  then m  (Force constant)

Scenario 1: Talk to your partner about how these relationships apply to: You are late for school and your mom pulls up behind a transport truck. What would the impact be if it was: Empty? Full?

Scenario 2: Talk to your partner about how these relationships apply to: You have 2 cars that have the same mass – one car has the engine of a Ford Focus, the other has the engine of a Ford Mustang. Assume both overall masses are the same

Newton’s Second Law When a net force acts on an object, the object accelerates in the direction of the net force. F NET = ma Unit Analysis: 1N = 1 kg ۰ m/s 2

Example # 1: A student is bowling with her friends. She gives a 7.0 kg bowling ball an acceleration of 5.0 m/s 2 [forward]. Calculate the net force she exerted on the ball. ā = 5.0 m/s 2 m = 7.0 kg F net = mā = (7.0 kg)(5.0 m/s 2 [forward]) = 35 N [forward]

Example 2: A motorcycle and driver have a combined mass of 280 kg. They accelerate from 7.0 m/s [E] to 34 m/s [E] in 4.2 s. What is the net force on the motorcycle and driver?

m = 280 kg v 1 = 7.0 m/s [E] v 2 = 34 m/s [E] Δt = 4.2 s Solve for ā first ā = v 2 – v 1 Δt = 34 m/s [E] – 7.0 m/s [E] 4.2 s = 6.4 m/s 2 [E] F net =ma = (280 kg)(6.4 m/s 2 [E]) = 1.8 x 10 3 N [E]

Newton’s Second Law and Motion Day 2 – The Real Math

Equations Motion Forces BOTH!!!

Example 1: A rocket ship has engines that can produce a force of 1.8x10 5 N [up]. If the ship has a mass of 1.3x10 4 kg. a)What will the acceleration of the ship be? b)What will it’s speed be after 10s?

Example 1: A driver approaches an intersection at a velocity of 14 m/s [forward] when the light turns amber. The driver applies the brakes to get the maximum stopping force. The car has a mass of 1500 kg, and the force of friction between the tires and the road is 1.1 x 10 4 N. Ignoring the driver's reaction time calculate: a.) the maximum deceleration of the car b.) the minimum stopping time c.) the minimum stopping distance

Example 2: An elevator, including passengers, has a mass of 600 kg. When leaving the first floor, it accelerates upward at 2.0 m/s 2. What force is the cable exerting on the elevator?