Work and Energy Test. 1

The horsepower is a unit of power, commonly used in the imperial system, and is equivalent to about 746 Watts.

Work is a scalar quantity calculated by the dot product of the force and displacement vectors (W = F ⋅ d), as it only has magnitude.

Gravitational force is a conservative force, meaning the work done by it (and thus the change in potential energy) depends only on the initial and final positions, not the path taken.

For both constant and variable forces, the work done is represented by the area under the force-displacement graph.

Using the formula KE = ½mv², the kinetic energy is ½ * 4 kg * (3 m/s)² = 2 * 9 = 18 J.

In physics, work is done only when a force causes displacement. Since there is no displacement while waiting, no work is done on the bag.

Since P = W/t = (F⋅d)/t and v = d/t, power can be calculated as the dot product P = F⋅v.

The elastic potential energy stored in a spring is given by the formula PE_s = ½kx², where 'k' is the spring constant and 'x' is the displacement from equilibrium.

The work-energy principle (W_net = ΔKE) provides a direct relationship between the work done by all forces on an object and the change in its kinetic energy.

Work is the dot product: W = F ⋅ d = (3)(3) + (4)(4) = 9 + 16 = 25 J.

Kinetic energy (KE = ½mv²) is proportional to the square of the velocity. If velocity is doubled, KE becomes 4 times larger.

The loss in potential energy is calculated as ΔPE = mgh = 2 kg * 9.8 m/s² * 5 m = 98 J.

Air resistance is a non-conservative (or dissipative) force because the work it does depends on the path taken and it converts mechanical energy into heat.

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In an isolated system, the total amount is constant.

Work (W = Fd cosθ) is negative when cosθ is negative, which occurs for angles between 90° and 180°. This typically happens when the force opposes the motion, like work done by friction.

In the British Engineering system, force is measured in pounds (lb) and distance in feet (ft), so the unit of work is the foot-pound (ft-lb).

Power is defined as the work done per unit time (P = W/t). Its SI unit is the Watt (J/s).

Escape velocity is the speed at which an object's kinetic energy is equal to the magnitude of its gravitational potential energy, allowing it to escape the gravitational field completely.

The escape velocity from Earth is about 11.2 kilometers per second (or 40,270 km/h).

An electron-volt is the amount of kinetic energy gained by a single electron when it accelerates through a potential difference of one volt. It is a very small unit of energy.