Topic 4a: Work

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work: the physical effects of an external force applied to an object resulting in a net displacement in the direction of the force.

Scalar quantity

expressed in joules or Newton meters

the work done by a constant force acting on a body is equal to the force multiplied by the displacement that results from the force, WITH THE CONDITION that the force and displacement are in the same direction

W = F*d

Work = (force)*(displacement)

no work is done if the force is perpendicular to the displacement

if the force and displacement are at an angle other than 90 degrees or parallel to one another: W = F*d*cos θ

if F and d are parallel to one another, the angle is 0, and cosine of 0 is 1, so the equation is the same

Hooke’s law: the force required to stretch a spring to a certain displacement

the force required to stretch a spring

F = −k*x

force = -(spring constant)*(displacement of spring)

W= (1/2)*(k*x2)

work done in stretching spring= 1/2 * spring constant * displacement of spring squared

also the area of the triangle under the graph

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Mechanical advantage: Measure of the ratio of output force to input force in a system, used to analyze forces in simple machines.

Typically expressed in ideal terms, where there is no energy loss (heat, friction) between the input and output; this is known as 100% efficient systems.

W(in) = W(out)

Pulley system: devices that make work easier, reduces amount of force required to move the load

efficiency: comparison of work output to work input; Efficiency = (W out)/(W in) = (F out)*(d out)/(F in)*(d in)

mechanical advantage: the amount by which the force required is reduced; MA = (F out)/(F in), output force (force exerted by the pulley on the load)/input force (force exerted on the pulley by the person/machine)

force is applied to one end of the rope and it is pulled a certain distance (effort distance) so that the load bound by the rope on the other end is pulled to a certain distance (load distance)

force required decreases with increase in # of pulleys, however the effort distance increases

Work done by gases:

when heat is applied to a gas in a piston, the thermal energy is transferred to the kinetic energy of the gas atoms

this causes the volume of the gas to expand, which does work on the piston, resulting in displacement in the y direction

Work done by the gas on the piston= pressure*change in volume--> W= PΔV

derived from these equations:

work = force*displacement--> W = F*d = F*y

pressure = force*area--> P = F*A or F = P*A

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Work-energy theorem: the work done by all forces acting on a particle is equal to the change in the particle’s kinetic energy

It can be derived from Newton’s second law.

use this theorem first before trying kinematics while problem solving.