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How to Calculate Force for a Vertical Trajectory

One of the first things a student learns in physics class is that force equals mass times acceleration. This is logical and intuitive. It takes twice as much force to impart the same acceleration to a 10kg weight as it does for a 5kg weight. Using the same amount of force will accelerate the 10kg weight half as much. Suppose you want to apply enough force to an object for it to travel a certain vertical distance. A few calculations will tell you the answer.

Instructions

- 1
  Determine how far vertically you want your projectile to travel. Calculate how long the object would take to cover this distance under the Earth's gravitational acceleration, which is 9.8m/second^2. The equation for an object under constant acceleration is: x = V0 t + ½ at^2 wherein x = distance, V0 = initial velocity, a = acceleration and t = time. Suppose you want your object to travel 30 meters vertically. Initial velocity is zero. So, solving for t, we get this: t = √ (x/ ½ a). That works out to 2.47 seconds.
- 2
  Calculate the velocity the object would be traveling accelerating for the amount of time calculated in step one. V =V0 + at. If t is 2.47 seconds and acceleration is 9.8m/second^2, that works out to 24.206 meters per second. This is how fast an object would be traveling if it fell from a height of 30 meters. It's also how fast something would need to be moving to travel 30 meters up into the air.
- 3
  Calculate how much force you would need to impart to the object to accelerate it to this speed. You'll be applying this force for a specific length of time. Suppose your object is one kilogram and you want to apply the accelerating force for one second. You would need to apply a force sufficient to accelerate the object 24.206m/second^2. Since the object has a mass of one kilogram, and force = mass times acceleration, the force would be 24.206 kilogram meters/second^2. One kilogram meter / second^2 is a unit of force called a Newton. So the force necessary to send a one kilogram object 30 meters up is 24.206 Newtons, applied for one second.

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