Question

A dense particle with mass 5 kg follows the path

r(t) = (sin(6t), cos(6t), 2t¹¹/²) with units in meters and seconds.

What force acts on the mass at t = 0?

Answer 1

To determine the force on a mass at a specific time, we calculate the acceleration through the derivative of the velocity, which is the derivative of the position function, and then apply Newton's second law.

Step-by-step explanation:

The student is asking about the force acting on a mass following a specific path given by the position function r(t). To find the force acting on the mass at a particular time, one must calculate the acceleration at that time, and then use Newton's second law, F = ma, where F is the force, m is the mass, and a is the acceleration.

To find the acceleration a(t), we first need to determine the velocity v(t) by taking the derivative of the position function r(t), and then find the acceleration by taking the derivative of the velocity.

At t = 0, the velocity v(t) will be the derivative of r(t) at t = 0, and similarly, the acceleration a(t) will be the derivative of v(t) at t = 0. Once the acceleration is known, the force can be calculated using the mass provided (5 kg).