10 Questions
What are the two necessary components for work to be done in physics?
A force and a displacement
What are the three methods of finding work done by a force?
Work done by a constant force, work done by a variable force, and work done by the area under force and displacement graph
What is the formula for work done by a constant force?
W = F Δr cos θ
What happens to the work done by a force if the displacement is zero?
The work done is zero
Why is the work done by a force on a moving object zero when the force is perpendicular to the displacement?
Because cos θ = 0 when the force is perpendicular to the displacement
What is the SI unit of work?
The newton·meter (N·m) or joule (J)
What is the nature of work in physics?
Work is a scalar
Why is it important to consider the vector nature of forces when analyzing work?
Because the direction of the force and displacement affects the calculation of work
What is the difference between work done by a constant force and work done by a variable force?
The force is constant in one case and varies in the other
What is the purpose of the angle θ in the formula for work done by a constant force?
To account for the direction of the force and displacement vectors
Study Notes
Work and Kinetic Energy
- Work is associated with a force and a displacement in physics.
- For work to be done, the force must act through a distance.
- Three methods to find work done by a force:
- Work done by a constant force
- Work done by a variable force
- Work done by the area under force and displacement graph
Work Done by a Constant Force
- Work done on a system by a constant force is the product of the magnitude F of the force, the magnitude r of the displacement of the point of application of the force, and cos θ, where θ is the angle between the force and displacement vectors: W = F∆r cos θ
- A force does no work on an object if the force does not move through a displacement.
- Work is a scalar, even though it is defined in terms of two vectors, a force and a displacement.
- SI unit of work is the newton·meter (N·m or kg·m2/s2).
Work Done by a Varying Force
- If the force varies with position, the x component Fx of the force is approximately constant over a small interval.
- The work done can be calculated by integrating Fx with respect to x over the path taken by the particle: W = ∫Fxdx
Work Done by a Spring
- The force exerted by a spring on a block varies with the block's position x relative to the equilibrium position x = 0.
- The work done by the spring can be calculated by integrating the force with respect to x: W = ∫Fdx.
Work Done by Area Under F-x Graph
- This method is used when force and displacement are either parallel or antiparallel.
- The area of the graph gives the magnitude of the work done.
- If force and displacement have the same sign, work done is positive; if they have opposite signs, work done is negative.
Examples and Applications
- Examples of calculating work done by a constant force, variable force, and spring force.
- Example of finding the total work done by a force over a certain distance.
Solve problems involving net force, motion, and tension in a system. Calculate the work done by a string on blocks of different masses. Apply physics concepts to real-world scenarios.
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