PS-5.8 Use the formula F = ma to solve problems related to force.
In the SI system of measurement, the unit of force is the Newton. The Newton unit is derived during the calculation of force using the equation F=ma. In this equation "F" is force, "m" is mass, and "a" is acceleration. When mass is measured in kilograms and acceleration is measured in m/s2, then the force will be calculated in Kgm/s2 or Newtons. 1 Newton is equal to 1Kgm/s2. A Newton of force is the amount of applied force required to accelerate a 1kg mass at a rate of 1m/s2. The following diagram illustrates this relationship.
Look at the problems below. Determine the force, mass, or acceleration, in each.
Example #1: How much force is required to accelerate a 2000kg car at 3.0m/s2?
In this first example the Unit of force, the Newton, is derived using dimensional analysis. By multiplying "kg" times "m/s2", no units cancel. They must all appear in the answer. Remember, 1kgm/s2 is equal to a Newton force.
Example #2: A kicker applies a force of 300N to a .454kg soccer ball. What is the acceleration of the ball?
In example #2 above, the Unit of acceleration, m/s2, is derived using dimensional analysis. By dividing the Newton force unit ( Remember a Newton is actually a kgm/s2 !), by kilogram mass units, the kilogram unit cancels, leaving only acceleration units of m/s2. The unit that appears in the answer is m/s2. Remember, a Newton is actually a kgm/s2.
Example #3: What is the mass of a cart that is accelerated at 2.5m/s2 by a 30N force?
In example #3 above, the Unit of mass, the kg, is derived using dimensional analysis. By dividing the Newton force unit ( Remember a Newton is actually a kgm/s2.), by the m/s2 acceleration unit, the m/s2 unit cancels, leaving only mass units of kilograms in the answer!