Week 7 Work, Energy And Power Flashcards
Impulse
WORK OF A CONSTANT FORCE
When an applied net force moves an object resulting in displacement, the work done by that force is the product of the force and the displacement
Work = |F| ^d
If the direction of force and the direction of movement are the same, the work is positive, and if they are opposite, the work is negative.
•Work is a scalar physical quantity with the unit of Joule: J=N m.
MUSCULAR WORK
Muscles perform work when they generate force and cause displacement
• Concentric contraction – muscle shortens and force applied acts to move insertions in direction of force - muscle performs positive work
• Eccentric contraction – muscle lengthens and force applied acts while insertions move in opposite direction - muscle performs negative work
• Isometric contraction – no mechanical work as there is no displacement
EXAMPLE :
WORK OF THE GRAVITATIONAL FORCE
Gravitational force (weight) has constant magnitude and direction. Since it is directed vertically, it will perform work only on the vertical component of displacement.
Consider an object being lifted from position 1 to position 2, which is at an elevation H.
The work of gravity will equal
Work = -( m.g.) x H
Since the force is acting in the direction opposite to movement, the work is negative.
WORK OF A FORCE WITH VARYING MAGNITUDE
If the magnitude of force changes as the object is moving, the work of force as the object moves from point 1 to point 2 is equal to the area beneath the force-displacement curve.
EXAMPLE:
WORK OF FORCE IN ELASTIC SPRINGS
Elastic springs (and elastic anatomical structures such as tendons and ligaments) generate force which is proportional to displacement (deformation), defined by the spring constant (stiffness, k), which acts to oppose the displacement.
^L
Consider an elastic spring aligned with axis x being stretched by a distance DL. The force- displacement curve is a straight line, and the work is equal to the area beneath the curve,
i.e., the area of a triangle with sides DL and F=kDL. deformation, the work is negative.
WHAT HAPPENS AFTER WORK IS DONE?
Work transfers energy
• Energy is the capacity to do work
• Heat, Light, Sound, Chemical, Mechanical
4 TYPES OF MECHANICAL ENERGY
• Linear Kinetic Energy
• Rotational Kinetic Energy
• Gravitational Potential Energy
• Elastic Potential (Strain) Energy
• Total Mechanical Energy is the SUM of all components
KINETIC ENERGY
Kinetic energy of an object is defined as the product of the mass and the square of speed divided by two:
E =1/2mv2
- Rotational kinetic energy based on angular equivalents: ER = 1⁄2 I ω 2
• Kinetic energy is a scalar quantity with the unit of Joule. Energy shares the same unit as work. This is because the two quantities are closely linked as energy can be converted into work, and vice versa.
WORK-ENERGY THEOREM
The work-energy theorem states that the change in kinetic energy of an object between two points equals the net work performed by all forces acting on the object:
1/2mv (2/2) - 1/2mv (2/1)= W1,2
• The kinetic energy between points 1 and 2 will increase if the work is positive, stay the same if the work is zero, and decrease if the work is negative.
• The concepts of work and energy, and the connection between the two, can be useful for practical purposes, solving many problems in biomechanics using simple mathematics.
POTENTIAL ENERGY
• The work performed to lift an object against gravity, or to deform a spring against its elastic recoil, can be reclaimed in the form of kinetic energy. This is because the gravity or the elastic force will perform positive work if the object is released.
• The amount of work that can be transformed into kinetic energy is referred to as the “potential energy”.
• Gravitational Potential Energy is defined as:
EP =mgH
•The elastic potential or “strain” energy
for an elastic spring is defined as:
Es= 1/2 k^ L2
LAW OF CONSERVATION OF ENERGY
Energy can neither be created nor destroyed, it can only change form or be converted to work. For example, the chemical energy in the muscle cells can be converted into heat and mechanical work to contract the muscles.
•If we focus only on mechanical energy then all the energy converted into heat can be regarded as being “dissipated”.
• If the sum of kinetic and potential energies (both gravitational and elastic) of an object is constant, then its mechanical energy is conserved. In many everyday situations related to human biomechanics, this is approximately the case.
KE
+
PE
= Constant
EXAMPLE:
MAXIMAL HEIGHT IN VERTICAL JUMP
Derive the equation for the maximal height in vertical jump with takeoff speed V0 assuming that the mechanical energy of the person is conserved.
Initially the centre of mass is at zero elevation and the speed is V0. Therefore, the potential, kinetic, and net mechanical energies are: E P = 0
E K = 12 m V 0 2
E = E P + E K = 12 m V 0 2
When the maximal height is reached the speed is zero. Therefore, the potential, kinetic, and
net energies are:
Equating the net energy at the take-off and at the maximum elevation:
mgHmax =12mV02
H =V02
EP= mgHmax
EK =0
E=EP +EK =mgH
max
2g
EXAMPLE:
ENERGY “BURNED” IN STAIR CLIMBING
For every Joule of mechanical energy gained through work performed by the muscles, four Joules of chemical energy stored in the muscles are converted to heat. Calculate how many calories are “burned” if a person with a body mass of 70 kg climbs one storey to increase the elevation of their centre of mass by H=4 m. NB. 1 Cal=4,184 J.
The mechanical work performed by the muscles results in an increase in potential energy equalling:
^EP= mg^H = 70.9.81.4 = 2746.8J The energy converted to heat is:
Q=4.^EP =10987.2J The net energy invested is:
E=^EP +Q=13734J=3.3Cal
EXAMPLE: POTENTIAL, KINETIC, AND NET ENERGY IN VERTICAL JUMP
Leg muscles first absorb energy during the counter-movement, and then add energy during the active push-off. While airborne no net energy is added or absorbed, rather the energy changes form between potential and kinetic.
POWER
Power is the rate of doing work (or work per unit time). For a force acting in the direction of movement, power equals force times velocity (the rate of displacement):
P = w/t. P= Fd/t P= F.v
Power is a scalar quantity with the unit of Watt=J/s
• In a more general sense, power is the rate at which the energy is transferred or released. For example, in the isometric contraction of muscles, an “activation” energy (heat) is released at a certain rate although there is no movement (contraction).
