Work done by a variable force refers to the work calculated when the force acting on an object changes in magnitude or direction over the distance the object moves. Unlike a constant force, where work can be easily computed using the formula 𝑊 = 𝐹.𝑑cos (𝜃), where 𝐹 is the force,𝑑 is the displacement, and 𝜃 is the angle between the force and displacement, variable forces require integration to determine the total work done. This approach allows for the calculation of work in scenarios such as spring forces, gravitational forces varying with height, or any situation where the force is not constant throughout the displacement.
What is the definition of work done by a variable force?
Work done by a variable force is the total energy transferred by the force when it acts on an object over a distance, where the magnitude or direction of the force changes during the motion.
What is the significance of the integral in calculating work done by a variable force?
The integral allows for the summation of infinitesimally small amounts of work done over each infinitesimal displacement, accounting for the changes in force throughout the motion.
Can you give an example of a variable force?
A common example of a variable force is the spring force, which follows Hooke's Law and is given by F=−kx, where k is the spring constant and x is the displacement from the equilibrium position.
How does the work done by a variable force differ from that done by a constant force?
Work done by a constant force can be calculated using the simple formula W=Fdcos(θ), while work done by a variable force requires integration to account for the changing nature of the force over the distance.
What happens to the work done if the force is applied in the opposite direction to the displacement?
If the force is applied in the opposite direction to the displacement, the work done is negative, indicating that energy is being taken from the system.
What is the formula for work done by a variable force?
a) W=Fd
b) W=∫F(x)dx
c) W=F⋅v
d) W=F⋅d sin(0o)
Answer: b) W=∫F(x)dx
If a force varies linearly with displacement, how can the work done be calculated?
a) By using the average force
b) By using the maximum force
c) By using the minimum force
d) By using the constant force formula
a) By using the average force
Answer:
In the context of work done, what does a negative value indicate?
a) Work is done on the system
b) Work is done by the system
c) Energy is being added to the system
d) Energy is being removed from the system
Answer: d) Energy is being removed from the system
What does the area under the force vs. displacement graph represent?
a) The force applied
b) The distance traveled
c) The work done
d) The energy stored
Answer: c) The work done
Which of the following is an example of a variable force?
a) Gravitational force near the Earth's surface
b) Frictional force
c) Spring force
d) Tension in a rope
Answer: c) Spring force