Question

A particle is acted upon by only two forces, one conservative and one nonconservative and neither being a force of friction, as it moves from point A to point B. The kinetic energies of the particle at points A and B are equal if

a. the sum of the works of the two forces is zero.
b. the work of the conservative force is equal to the work of the nonconservative force.
c. the work of the conservative force is zero.
d. the work of the nonconservative force is zero.
e. None of the above.

Answer 1

a. the sum of the works of the two forces is zero.

Step-by-step explanation:

The problem at hand involves understanding how the kinetic energy of a particle changes under the influence of conservative and nonconservative forces when it moves from point A to point B. To solve this, we'll analyze the effects of these forces on the particle's kinetic energy and use the work-energy principle to determine the correct option.

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Understanding the Concepts:

• The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. Mathematically, this is represented as:

`\boxed{\left\begin{array}{ccc}\text{\underline{Work-Kinetic Energy Theorem:}}\\\\W_{\text{net}}=\Delta K\\\\\text{Where:}\\ \text{$\bullet$ $W$ is the work done}\\\text{$\bullet$ $\Delta K$ is the change in kinetic energy}\end{array}\right}`

• Conservative Forces: These are forces where the work done is independent of the path taken. Examples include gravitational and electrostatic forces. The work done by conservative forces can be associated with changes in potential energy.

• Nonconservative Forces: These forces, such as friction or air resistance (not applicable in this case), depend on the path and typically lead to energy dissipation.

It is given that the kinetic energy at points A and B are equal. Thus, the change in kinetic energy is zero (ΔK = 0). Since this is the case the sum of the work done by the two forces will be zero.

`\Longrightarrow W_(net)=\Delta K \\\\\\\\\therefore W_(c)+W_(nc)=0 \ \Big[\because \Delta K = 0\Big]`

Thus, a. is correct.