6 - Work, Energy, and Conservation of Energy Free Online FlashCards

What is the equation for work by a constant force?

Work is the energy transferred by a force through a displacement: $W=\vec F\cdot\vec d=Fd\cos\theta$.

When does a force do zero work?

A force does zero work when it is perpendicular to the displacement, because $\cos 90^\circ=0$.

What is the SI unit of work?

The SI unit of work and energy is the joule: $1\text{ J}=1\text{ N}\cdot\text{m}$.

How is variable-force work found from an $F_x$-versus-$x$ graph?

For one-dimensional motion, $W=\int_{x_A}^{x_B}F_x(x)\,dx$, so work is the signed area under the force–position graph.

What is Hooke’s law for an ideal spring?

An ideal spring exerts a restoring force described by Hooke’s law: $F_x=-kx$, where $x$ is displacement from equilibrium.

What is the formula for kinetic energy?

Kinetic energy is $K=\frac{1}{2}mv^2$. It is a nonnegative scalar that depends on mass and the square of speed.

What happens to kinetic energy when speed doubles?

Doubling an object’s speed makes its kinetic energy four times larger because $K$ is proportional to $v^2$.

What does the work–energy theorem state?

The work–energy theorem states $W_{\text{net}}=\Delta K=K_f-K_i$. Net work changes an object’s kinetic energy.

What defines a conservative force?

A conservative force does work that depends only on initial and final positions, and its work around any closed path is zero.

How is conservative-force work related to potential energy?

For a conservative force, the work is the negative change in potential energy: $W_{\text{cons}}=-\Delta U$.

What is gravitational potential energy near Earth’s surface?

Near Earth’s surface, gravitational potential energy is $U_g=mgy$, measured relative to a chosen reference height.

What is the elastic potential energy of an ideal spring?

The elastic potential energy of an ideal spring is $U_s=\frac{1}{2}kx^2$. It is positive for both stretching and compression.