Question

An object of mass 4 kg is moving in the space. The only force that acts on the object is described by the potential energy function: U=6yx²−4z²y³ Where U is in Joules and (x,y,z) are in meters. When the object is at (1, 1,1) its velocity is v(1,1,−2)m/s. A) Calculate the mechanical energy of the object at (1,1,1).

Answer 1

The mechanical energy of the object at (1,1,1) is 2 Joules.

Step-by-step explanation:

To calculate the mechanical energy of the object at (1,1,1), we need to find the kinetic energy and potential energy at this point. The potential energy function provided is U=6yx²−4z²y³. Using the given coordinates, we have (x,y,z) = (1,1,1).

Substituting these values into the potential energy function gives: U(1,1,1) = 6(1)(1)² − 4(1)²(1)³ = 6 − 4 = 2 Joules.

The mechanical energy is the sum of the kinetic energy and potential energy. Since the question does not provide the object's velocity, we are unable to calculate the kinetic energy. Therefore, the mechanical energy at (1,1,1) is 2 Joules.