write the expression for work done by a force
Answers
Answer:
work done = force × displacement
Answer:
Work is the product of force and displacement. In physics, a force is said to do work if, when acting, there is a movement of the point of application in the direction of the force.
Work
Baseball pitching motion 2004.jpg
A baseball pitcher does positive work on the ball by applying a force to it over the distance it moves while in his grip.
Common symbols
W
SI unit
joule (J)
Other units
Foot-pound, Erg
In SI base units
1 kg⋅m2⋅s−2
Derivations from
other quantities
W = F ⋅ s
W = τ θ
Dimension
M L2 T−2
For example, when a ball is held above the ground and then dropped, the work done on the ball as it falls is equal to the weight of the ball (a force) multiplied by the distance to the ground (a displacement). When the force {\displaystyle F}F is constant and the angle between the force and the displacement {\displaystyle s}s is θ, then the work done is given by W = Fs cos θ.
Units
The SI unit of work is the joule (J), which is defined as the work expended by a force of one newton through a displacement of one metre.
The dimensionally equivalent newton-metre (N⋅m) is sometimes used as the measuring unit for work, but this can be confused with the unit newton-metre, which is the measurement unit of torque. Usage of N⋅m is discouraged by the SI authority, since it can lead to confusion as to whether the quantity expressed in newton metres is a torque measurement, or a measurement of work.[4]
Non-SI units of work include the newton-metre, erg, the foot-pound, the foot-poundal, the kilowatt hour, the litre-atmosphere, and the horsepower-hour. Due to work having the same physical dimension as heat, occasionally measurement units typically reserved for heat or energy content, such as therm, BTU and Calorie, are utilized as a measuring unit.
same distance or by lifting the same weight twice the distance.
Work is closely related to energy. The work-energy principle states that an increase in the kinetic energy of a rigid body is caused by an equal amount of positive work done on the body by the resultant force acting on that body. Conversely, a decrease in kinetic energy is caused by an equal amount of negative work done by the resultant force.
From Newton's second law, it can be shown that work on a free (no fields), rigid (no internal degrees of freedom) body, is equal to the change in kinetic energy {\displaystyle KE}KE of the linear velocity and angular velocity of that body,
{\displaystyle W=\Delta KE.}W=\Delta KE.
The work of forces generated by a potential function is known as potential energy and the forces are said to be conservative. Therefore, work on an object that is merely displaced in a conservative force field, without change in velocity or rotation, is equal to minus the change of potential energy {\displaystyle PE}{\displaystyle PE} of the object,
{\displaystyle W=-\Delta PE.}W=-\Delta PE.
These formulas show that work is the energy associated with the action of a force, so work subsequently possesses the physical dimensions, and units, of energy. The work/energy principles discussed here are identical to Electric work/energy principles.
Constraint forces
Constraint forces limit the movement of components in a system, such as constraining an object to a surface (in the case of a slope plus gravity, the object is stuck to the slope, when attached to a taut string it cannot move in an outwards direction to make the string any 'tauter'). Constraint forces restrict the velocity in the direction of the constraint to zero, which means the constraint forces do not perform work on the system.
Another example is a book on a table. If external forces are applied to the book so that it slides on the table, then the force exerted by the table constrains the book from moving downwards. The force exerted by the table supports the book and is perpendicular to its movement which means that this constraint force does not perform work.
The magnetic force on a charged particle is F = qv × B, where q is the charge, v is the velocity of the particle, and B is the magnetic field. The result of a cross product is always perpendicular to both of the original vectors, so F ⊥ v. The dot product of two perpendicular vectors is always zero, so the work W = F ⋅ v = 0, and the magnetic force does not do work. It can change the direction of motion but never change the speed.
Mathematical calculation
For moving objects, the quantity of work/time (power) is integrated along the trajectory of the point of application of the force. Thus, at any instant, the rate of the work done by a force (measured in joules/second, or watts) is the scalar product of the force (a vector), and the velocity vector of the point of application.
Explanation:
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