Question

A dense particle with mass 9 kg follows the path r(t)=(sin(3t),cos(8t),2t⁷/² ) with units in meters and seconds.

What force acts on the mass at t=0 ?

Answer 1

The force acting on the mass at t=0 is (0,0,0)

Step-by-step explanation:

The path of the particle is given by r(t) = (sin(3t), cos(8t), 2t⁷/²). To find the force acting on the mass at t = 0, we need to calculate the acceleration vector. The acceleration vector is the second derivative of the position vector with respect to time.

So, the acceleration vector a(t) is given by a(t) = (-9sin(3t), -64cos(8t), 7t⁵). Now to find the force, we can use Newton's second law, which states that force is equal to mass times acceleration. Since the mass of the particle is 9 kg, the force at t = 0 is F(0) = (0,0,0).