Question

at a certain instant, a particle-like object is acted o a force f - (4.0 n)i - (2.0 x)i (9.0 n)k while the object's velocity is i - -(z.tmls)i (4.0m/s)k. what is the instantaneous rate at which the force does work on the object? (

Answer 1

The instantaneous rate at which the force does work on the object is 34.0 N*m/s.

The instantaneous rate of work done by a force on an object, or power, is the dot product of the force and velocity vectors. Multiply the X components of force and velocity, the Y components, and then sum them to determine the power delivered by the force.

Step-by-step explanation:

The instant work done by a force on an object is given by the dot product of the force and the object's velocity. To find the instantaneous rate at which the force does work on the object, we need to calculate the dot product of the force and velocity vectors.

The dot product of two vectors A = (A1, A2, A3) and B = (B1, B2, B3) is given by:

A · B = A1*B1 + A2*B2 + A3*B3

In this case, the force vector is F = (-4.0 N, -2.0 N, 9.0 N) and the velocity vector is V = (1.0 m/s, -z.tmls m/s, 4.0 m/s).

Calculating the dot product, we have:

F · V = (-4.0 N)*(1.0 m/s) + (-2.0 N)*(-z.tmls m/s) + (9.0 N)*(4.0 m/s)

Simplifying, we get:

F · V = -4.0 N*m/s + 2.0 N*m/s + 36.0 N*m/s

So the instantaneous rate at which the force does work on the object is 34.0 N*m/s.