How Do You Calculate the Average Force of Air Resistance on a Projectile?

In summary, a projectile with a mass of 0.656 kg and an initial speed of 25.4 m/s is shot straight up, reaching a maximum height of 7.64 m. The difference in potential energy between this and the case with no air resistance is 49.116032. By using the equation W = Fcos(90)s, we can determine that the force due to air resistance is approximately 21.3 N.
  • #1
neoncrazy101
22
0

Homework Statement


A projectile of mass 0.656 kg is shot straight up with an initial speed of 25.4 m/s. (a) How high would it go if there were no air resistance? (b) If the projectile rises to a maximum height of only 7.64 m, determine the magnitude of the average force due to air resistance.

Homework Equations


1/2mvf^2 + mghf = 1/2mvo^2 + mgho

Work = KE+ PE
W = Fcos(90)s

The Attempt at a Solution



Ok, I am able to get the answer for A: (32.9m) but with B, I cannot get it. What should I do to get the answer for B? Whenever I put the equation into W = Fcos(90)s I come up with zero which is not the answer. So I don't know what I'm doing wrong.
 
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  • #2
Well, cos(90) = 0 (some sort of trig identity I suppose), so your equation for the work done by the air resistance is wrong. Looking at the problem, the projectile is shot straight up, and the air resistance acts to retard this motion. The reduction in trajectory height would be similar to using the same effort to launch a heavier projectile upward.
 
  • #3
neoncrazy101 said:
Ok, I am able to get the answer for A: (32.9m) but with B, I cannot get it. What should I do to get the answer for B? Whenever I put the equation into W = Fcos(90)s I come up with zero which is not the answer. So I don't know what I'm doing wrong.
What is the work done by air resistance? (hint: what is the difference in maximum potential energy between A and B?).

Now if that work is done by a constant force over the distance that the projectile moves, what is that force?

AM
 
  • #4
The difference in PE between A and B is 49.116032.

I'm probably very very confused (most likely, brain is fried plus headache) but if I take that 49.116032 and multiply it by the 7.64m then I come with up 375.2 which is really large.

EDIT: I figured it out! W=162.50248 (roughly) and then F = W/D thus 162.50248/7.64 = 21.3ish.
 
Last edited:
  • #5
neoncrazy101 said:
The difference in PE between A and B is 49.116032.

I'm probably very very confused (most likely, brain is fried plus headache) but if I take that 49.116032 and multiply it by the 7.64m then I come with up 375.2 which is really large.

EDIT: I figured it out! W=162.50248 (roughly) and then F = W/D thus 162.50248/7.64 = 21.3ish.
How did you get this value for W? (you should show your work). What are the units of force?

AM
 

Related to How Do You Calculate the Average Force of Air Resistance on a Projectile?

1. What is the definition of magnitude of average force?

The magnitude of average force is the measure of the strength or intensity of a force acting on an object over a period of time. It is calculated by dividing the total force by the time interval over which the force is applied.

2. How is magnitude of average force different from instantaneous force?

The magnitude of average force is the average strength of a force over a period of time, while instantaneous force is the strength of a force at a specific moment in time. Instantaneous force can vary significantly, while average force provides a more consistent measure.

3. What is the unit of measurement for magnitude of average force?

The unit of measurement for magnitude of average force is Newtons (N), which is equivalent to kg*m/s^2.

4. How is magnitude of average force related to Newton's Second Law of Motion?

Magnitude of average force is directly related to Newton's Second Law of Motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In other words, the greater the magnitude of average force, the greater the acceleration of the object.

5. How can magnitude of average force be calculated experimentally?

Magnitude of average force can be calculated experimentally by using a force sensor or by measuring the change in velocity of an object over a known distance and time. The resulting value can then be used to calculate the average force using the formula F=ma, where F is force, m is mass, and a is acceleration.

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