Question

Define work for one-dimensional motion.

a) (W = F Delta d cos(theta))

b) (W = F Delta d sin(theta))

c) (W = frac{Delta p}{Delta t})

d) (W = frac{1}{2}mv^2)

Answer 1

Work for one-dimensional motion is defined as the product of the component of the force in the direction of motion and the distance through which the force acts.

It is represented by the equation W = Fd cos(θ), where W is the work, F is the magnitude of the force, d is the magnitude of the displacement, and θ is the angle between the force and displacement vectors.

Step-by-step explanation:

Work for one-dimensional motion is defined as the product of the component of the force in the direction of motion and the distance through which the force acts. It is represented by the equation W = Fd cos(θ), where W is the work, F is the magnitude of the force, d is the magnitude of the displacement, and θ is the angle between the force and displacement vectors.

For one-way motion in one dimension, the work equation simplifies to W = Fd, as the angle θ is 0 degrees and the cosine of 0 is 1.

When analyzing motion that is not one-way or in two or three dimensions, we can divide the motion into one-way one-dimensional segments and sum up the work done over each segment.