Calculating Maximum Force Acting on 28kg Mass: F=ma

[kopinator]

The position of a mass m = 28.0 kg is given in by x(t) = 3.0sin ((15.0)t). Calculate the magnitude of the maximum force acting on the mass.

F=ma. I tried deriving x(t) twice to get the acceleration equation so i could plug it into F=ma and then pick a random number for t. I chose t=1 but i still didn't get the right answer.

 

[rock.freak667]

Hint: the maximum value of sin(kt) or cos(kt) is 1 where k is any constant.

 

[kopinator]

So I guessed correctly with t=1. But I'm still stumped on where to go from there. Do I still take the 2nd derivative of x(t)?

 

[SteamKing]

You are confusing the maximum value of sin(kt) with the value of t.

If k = 1, is sin (1) a a maximum? Sin (x) and Cos (x) both have maximum values of 1, but the x values where this occurs are different.

 

[Nickie]

I would like to clarify that the equation F=ma is only applicable for objects moving in a straight line with constant acceleration. In this case, the position of the mass is given by a sinusoidal function, which implies that the acceleration is not constant. Therefore, we cannot use F=ma to calculate the maximum force acting on the mass.

To accurately calculate the maximum force, we need to use the equation for force in terms of position, F=-kx, where k is the spring constant and x is the displacement from the equilibrium position. In this case, the maximum force will occur at the maximum displacement of the mass from its equilibrium position, which can be calculated by setting x(t) = 3.0sin ((15.0)t) equal to its maximum value, which is 3.0.

Therefore, the maximum force acting on the 28kg mass can be calculated as F = -(k)(3.0) = -3k. To determine the value of k, we need to know the specific system in which this mass is moving (e.g. a spring system, a pendulum, etc.). Once we have the value of k, we can calculate the magnitude of the maximum force acting on the mass.

In conclusion, it is important to use the correct equations and consider the specific system in order to accurately calculate the maximum force acting on a mass. Simply using F=ma may not yield the correct answer in this case.