Force and acceleration F=ma When an object changes speed (accelerates or decelerates),its shape or direction of motion, a force is acting on it. The formula for force is given below. F=mass(kg) X acceleration(m/s/s) The unit of force is called the newton. A 100 kg person standing on wooden floor boards exerts a force of 1000 newtons on the floor. Example. A 300g cart reaches a speed of 50m/s in 20 seconds from a standing start. What is the magnitude of the force acting on it? Step 1 Change all units of mass into Kg . => 300g = 0.3Kg. Step 2 Calculate the acceleration of the cart. => Acceleration = (final speed - initial speed)/time taken = (50 - 0)/20 =2.5m/s/s Step 3 Calculate the force => F =ma = 0.3 X 2.5 = 0.75 newtons. Exercises(F =ma) We can manipulate the formula (F =ma) to work out the mass or the acceleration of the cart. a = f/m or m = f/a Example. What is the acceleration of a 2kg brick thrown with a force of 4 newtons? Step 1 Make sure all measurements are in correct units. (In this case they are) Step 2 Calculate the acceleration using the formula a = f/m => a = 4/2 = 2m/s/s Exercises(a =f/m) Example. Jonathon has an engine that can provide a force of 5.6 newtons. He wants to place the engine on a cart so it accelerates at 3.5m/s/s. What should the combined mass of the cart and engine be to achieve this acceleration? Step 1 Make sure all measurements are in correct units. (In this case they are) Step 2 Calculate the mass of the vehicle using the formula m = f/a => m = 5.6/3.5 = 1.6Kg Exercises(m =f/a) Continue