Newton’s law can be represented by the equation Fnet = m x a, where Fnet is the total force acting on the object, m is the object’s mass, and a is the acceleration of the object. When using this equation, keep your units in the metric system. Use kilograms (kg) for mass, newtons (N) for force, and meters per second squared (m/s2) for acceleration.
For this equation, you will want to convert the mass into kilograms. If the mass you have is in grams simply divide that mass by 1000 to convert to kilograms.
For example: Let’s say you and your big brother are playing tug-of-war. You pull the rope to the left with a force of 5 newtons while your brother pulls the rope in the opposite direction with a force of 7 newtons. The net force on the rope is 2 newtons to the right, in the direction of your brother. In order to properly understand the units, know that 1 newton (N) is equal to 1 kilogram X meter/second squared (kg X m/s2). [5] X Research source
Force is directly proportional to the acceleration, meaning that a greater force will lead to a greater acceleration. Mass is inversely proportional to acceleration, meaning that with a greater mass, the acceleration will decrease.
For example: A 10 Newton force acts uniformly on a mass of 2 kilograms. What is the object’s acceleration? a = F/m = 10/2 = 5 m/s2
The unit for acceleration is meters per second per second or m/s2. [8] X Expert Source Sean Alexander, MSAcademic Tutor Expert Interview. 14 May 2020. Acceleration is a vector quantity, meaning it has both a magnitude and a direction. [9] X Research source The magnitude is the total amount of acceleration whereas the direction is the way in which the object is moving. If it is slowing down the acceleration will be negative.
The unit for acceleration is meters per second per second or m/s2. [8] X Expert Source Sean Alexander, MSAcademic Tutor Expert Interview. 14 May 2020. Acceleration is a vector quantity, meaning it has both a magnitude and a direction. [9] X Research source The magnitude is the total amount of acceleration whereas the direction is the way in which the object is moving. If it is slowing down the acceleration will be negative.
Because acceleration has a direction, it is important to always subtract the initial velocity from the final velocity. If you reverse them, the direction of your acceleration will be incorrect. Unless otherwise stated in the problem, the starting time is usually 0 seconds.
If the final velocity is less than the initial velocity, acceleration will turn out to be a negative quantity or the rate at which an object slows down. Example 1: A race car accelerates uniformly from 18. 5 m/s to 46. 1 m/s in 2. 47 seconds. What is its average acceleration? Write the equation: a = Δv / Δt = (vf - vi)/(tf - ti) Define the variables: vf = 46. 1 m/s, vi = 18. 5 m/s, tf = 2. 47 s, ti = 0 s. Solve: a = (46. 1 – 18. 5)/2. 47 = 11. 17 meters/second2. Example 2: A biker traveling at 22. 4 m/s comes to halt in 2. 55 s after applying brakes. Find his deceleration. Write the equation: a = Δv / Δt = (vf - vi)/(tf - ti) Define the variables: vf = 0 m/s, vi = 22. 4 m/s, tf = 2. 55 s, ti = 0 s. Solve: a = (0 – 22. 4)/2. 55 = -8. 78 meters/second2.
Behavior of a Car How is Velocity Changing? Direction of Acceleration Driver moving right (+) hits gas pedal + → ++ (more positive) positive Driver moving right (+) hits brakes ++ → + (less positive) negative Driver moving left (-) hits gas pedal - → – (more negative) negative Driver moving left (-) hits brakes – → - (less negative) positive Driver moves at constant velocity remains the same acceleration is zero
Example Problem: A toy boat with mass 10kg is accelerating north at 2 m/s2. A wind blowing due west exerts a force of 100 Newtons on the boat. What is the boat’s new northward acceleration? Solution: Because the force is perpendicular to the direction of motion, it does not have an effect on motion in that direction. The boat continues to accelerate north at 2 m/s2.
Example Problem: April is pulling a 400 kg container right with a force of 150 newtons. Bob stand on the left of the container and pushes with a force of 200 newtons. A wind blowing left exerts a force of 10 newtons. What is the acceleration of the container? Solution: This problem uses tricky language to try and catch you. Draw a diagram and you’ll see the forces are 150 newtons right, 200 newtons right, and 10 newtons left. If “right” is the positive direction, the net force is 150 + 200 - 10 = 340 newtons. Acceleration = F / m = 340 newtons / 400 kg = 0. 85 m/s2.
