Variable Force
Variable Force - Related Videos
01:10
Work and Energy for Variable Forces
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2025
When an object is acted upon by a variable force, the amount of work done and the change in energy of the object can be more complex to calculate compared to when a constant force is applied. Work is the product of force and displacement, while energy is the capacity of a system to do work. When a constant force is applied to an object, the work done can be calculated as the product of the force and the distance moved in the direction of the force. However, when a variable force is applied, the...
01:27
Variables and Equations of State
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2026
The physical state of a pure substance can be defined by certain state variables such as volume (V), pressure (p), temperature (T), and amount of substance (n). When two gases are separated by a movable wall, the gas with the higher pressure naturally compresses the gas with the lower pressure. This causes the high-pressure gas to expand and the low-pressure gas to compress until both gases achieve mechanical equilibrium. At this point, their pressures equalize, and the movement of the wall...
01:31
Functions of Three or More Variables
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2026
A function of three variables assigns a single real number to each point in three-dimensional space. Every point is identified by its Cartesian coordinates, x, y, and z, and the function maps this ordered triple to a scalar value. Such functions are commonly used to describe physical quantities that vary throughout space.A representative example is the electric potential generated by a point charge. In this case, the potential at a given location depends only on the distance from the charge. If...
01:21
Variable Costs
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2026
Variable costs are business costs that change directly with the level of production or output.Unlike fixed costs, such as rent, which remain constant regardless of production volume, variable costs increase or decrease with changes in production volume.Examples of variable costs include raw materials, packaging, and overtime labor, all of which vary according to the quantity of goods or services produced.When production increases, total variable costs rise because more resources and labor are...
06:19
The Mouse Forced Swim Test
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Cited by 541 •
2012
The forced swim test is validated as an experimental approach to assess potential antidepressant efficacy in rodents. Experimental animals are placed in a tank of water and escape-related mobility behavior is quantified. The common procedures for the mouse version of this test are described.
FAQs
Work is found by integrating the force along the object's path, rather than multiplying one constant force by displacement. On a force-displacement graph, this integral corresponds to the area under the curve. The method therefore captures how changing magnitude or direction alters energy transfer throughout the motion, providing a basis for calculating the object's resulting velocity.
Newton's second law must be applied to the force acting at each instant because the acceleration changes as the force changes. A single average force can hide important variations in the motion. Tracking the instantaneous acceleration helps describe realistic trajectories and supports calculations of velocity when the force depends on time or position.
A constant-force model assigns one unchanged force throughout the motion, whereas a variable-force analysis accounts for changes in magnitude, direction, or both. Its work is obtained from the full force-displacement relationship, and acceleration is updated continuously. This distinction matters when idealized constant-force equations cannot represent springs, changing fields, or speed-dependent friction.
The mechanical outcome depends on how the force acts along the path and how its value changes with position or time. Integrating that action determines energy transfer, while evaluating the force and resulting acceleration identifies motion or equilibrium conditions. These calculations connect the force profile to observable quantities such as velocity and the persistence of balanced motion.
First, express or determine how the force varies with position or time. Next, evaluate its mechanical effect by integrating along the path, using the area under a force-displacement curve when appropriate. Then apply Newton's second law at each instant and use the resulting energy or acceleration information to calculate velocity, motion, or equilibrium.
Numerical analysis becomes useful when the force variation does not produce a simple analytic solution. A researcher or student can represent the changing force, evaluate its effect over successive portions of the motion, and estimate the resulting behavior. This approach extends calculations of energy transfer, velocity, and equilibrium to realistic systems whose force relationships are difficult to integrate directly.
The framework applies to springs, gravitational fields that change, friction dependent on speed, and powered motion. Each example requires the force variation to be incorporated into the mechanical analysis rather than treated as fixed. In physics, these applications show how position, speed, or external input can alter energy transfer and acceleration during a system's motion.