Newton’s Second Law (The Mathematical Calculation of Force)

Newton’s Second Law of Motion Newton’s Second Law States: The acceleration of an object is related to the net force acting on it and the mass of the object Reminder about Force

Newton’s Second Law of Motion Newton’s Second Law States: The acceleration of an object is related to the net force acting on it and the mass of the object The mathematical relationship looks like this: Reminder about Force F Force = equals m mass X times a acceleration

Forces A force is a push or a pull that one object exerts upon another

Units Remember – ALL of our numbers are measurements and thus MUST HAVE UNITS Force is measured in a units called: Newtons (N) Named after . . . . . . . 1 N = 1 kg m/s2 (kg is the unit for mass and m/s2 is the unit for acceleration) 1 N is the amount of force required to accelerate one kg of mass 1 meter per second every second Isaac Newton

Solving Force Problems Solving force problems can be especially difficult because: Sometimes you will have to calculate acceleration first before you can find force. You may also have to go the other way and find velocity, acceleration, distance, time, or mass using force problems. Because there are so many variables involved in the mathematic equations for force, acceleration, and velocity (speed), it is best to follow proper steps when problem solving.

Problem-Solving Steps Read the problem and figure out what you are looking for in the final answer Write the equation(s) you need to get the final answer Ex. If trying to find acceleration, you could write either F Vf – Vi m t a = OR a = 3. Write down all of the variables that you are given and their quantities and units. If you have all of the variables needed to solve for the final answer, convert your units and solve! If you don’t have all of the variables needed to solve for the final answer. . .

Problem Solving Steps If You Don’t Have All of the Necessary Variables Write down the equation(s) you need to solve for the missing variables in your final equation. Convert your units and solve for the missing variables. Plug in those missing variables in your final equation and solve (remember to check your units!!!)

Things to Remember When Solving Force Problems -Your mass MUST be in kg, if it’s in grams, you must use your metric stairs to convert. Your acceleration must be in m/s2, if it’s not, you must use your metric stairs to convert. - Your final answer for force must be in Newtons (N) - You might have to decide, based on your variables given, which of two different acceleration equations you have to use (you may end up using both). - Just go step-by-step and you’ll be okay. Practice Problems

Practice Problems (they get more difficult as they go on. . .) A 52-kg water skier is being pulled by a speedboat. The force causes her to accelerate at 2 m/s2. Calculate the net force that causes this acceleration. What net force is needed to accelerate a 55-kg cart at 15 m/s2? m = 52 kg a = 2 m/s2 F = ? F = m x a F = 52 kg x 2 m/s2 F = 104 kg m/s2 Click For the Answer F = 104 N m = 55 kg a = 15 m/s2 F = ? F = m x a F = 55 kg x 15 m/s2 F = 825 kg m/s2 Click For the Answer F = 825 N

3. A remote control car has a mass of 24 kg and an acceleration of 120 cm/s2. What is the force of this car when it crashes into a brick wall? A 5-gram pencil is dropped out of an airplane where it accelerates toward Earth at 9.8 m/s2. With how much force does that pencil hit the ground? m = 24 kg a = 120 cm/s2 = 1.2 m/s2 F = ? F = m x a F = 24 kg x 1.2 m/s2 F = 28.8 kg m/s2 Click For the Answer F = 28.8 N m = 5 g = .005 kg a = 9.8 m/s2 F = ? F = m x a F = .005 kg x 9.8 m/s2 F = .049 kg m/s2 Click For the Answer F = .049 N

5. A 1,500 kg car is stopped at a red light 5. A 1,500 kg car is stopped at a red light. The light turns green and the car accelerates for 7 seconds until it reaches a velocity of 42 m/s, at which points it smashes into a car waiting to turn. With how much force did the 1,500 kg car hit the car waiting to turn? m = 1500 kg vi = 0 m/s vf = 42 m/s t = 7 s F = ? F = m x a a = (vf – vi)/t a = (42 m/s – 0 m/s) / 7 s a = (42 m/s) / 7 s a = 6 m/s2 F = 1500 kg x 6 m/s2 F = 9000 kg m/s2 Click For the Answer F = 9000 N

6. A 3,000-kg car is stopped at a red light 6. A 3,000-kg car is stopped at a red light. The car accelerates for 9 seconds when it smashes into a car waiting to turn. How fast was the car going at the time of the accident if it smashed into the car waiting to turn with a force of 36,000 N? m = 3000 kg vi = 0 m/s vf = ? t = 9 s F = 36000 N vf = vi + at F = m x a a = F / m a = 36000 N / 3000 kg a = 12 m/s2 vf = 0 m/s + (12 m/s2 x 9 s) vf = 108 m/s Click For the Answer vf = 108 m/s

Final Questions What causes objects to accelerate? What is a ‘Force’? If the same force acts on two objects with different masses, what will you notice about the more massive object? A net force Answer A push or pull one object exerts on another Answer The more massive object will accelerate less Answer