Find Net Force of 2.5x10^5N Training Helicopter

[xmflea]

The position of a 2.5x10^5N training helicopter under test is given by
r=(0.020m/s^3)t^3i + (2.2m/s)tj-(0.060m/s^2)t^2k , find the net force of the helicopter at t=5.0s

express F in the form Fx Fy and Fz

F=ma F=Fx+Fy+Fz


so far i plugged in t to each component to get 2.5m, 11m, and 1.5 m,
now i just need to know how to use the force that is given to find the x, y, and z components. need a little guidance.

 

[Doc Al]

The net force is not given, you have to figure it out. What does Newton's 2nd law say about net force? (That should give you a hint about what you need to do.)

 

[baba89]

I would approach this problem by first understanding the basic principles of force and motion. The net force is the overall force acting on an object, which is equal to the mass of the object multiplied by its acceleration. In this case, the net force of the helicopter can be calculated using the equation F=ma, where F is the net force, m is the mass of the helicopter, and a is the acceleration.

To find the net force at t=5.0s, we need to plug in the values for the mass and acceleration of the helicopter. The mass of the helicopter is not given in the problem, so we cannot calculate the net force directly. However, we can use the given position vector to find the acceleration of the helicopter at t=5.0s.

To do this, we can use the equation a=d^2r/dt^2, where a is the acceleration, r is the position vector, and t is time. By differentiating the position vector with respect to time twice, we can find the acceleration at t=5.0s.

Once we have the acceleration, we can plug it into the equation F=ma to find the net force of the helicopter at t=5.0s. This net force will have three components: Fx, Fy, and Fz, corresponding to the x, y, and z directions respectively.

To find these components, we can use the fact that the position vector r is given in terms of i, j, and k unit vectors. This means that the x component of the net force, Fx, will be equal to the mass of the helicopter multiplied by the x component of the acceleration. Similarly, the y and z components of the net force, Fy and Fz, will be equal to the mass of the helicopter multiplied by the y and z components of the acceleration, respectively.

In summary, to find the net force of the helicopter at t=5.0s, we need to first calculate the acceleration of the helicopter at that time using the given position vector. Then, we can use the equation F=ma to find the net force, which will have three components: Fx, Fy, and Fz. These components can be found by multiplying the mass of the helicopter by the x, y, and z components of the acceleration, respectively.