Scalars don't have direction but they do have + or - signs!Calpalned said:Homework Statement
Fact: Being the dot product of force and distance, work is a scalar. Fragment from my textbook: The work done on the spring is ##\frac{1}{2}kx^2##, and so the work done by the spring is ##-\frac{1}{2}kx^2##.
Homework Equations
##W = f \cdot d ##
The Attempt at a Solution
I thought scalars don't have directions. Why is the "work done on" positive, while the "work done by" is negative?
rude man said:Scalars don't have direction but they do have + or - signs!
rude man said:Scalars don't have direction but they do have + or - signs!
It's the "aka" part of your statement that's erroneous.Calpalned said:I thought that scalars are magnitudes (aka absolute values)...
Not so. Temperature in Celsius for example is a scalar. It can be + or -, right? Or altitude - can be above or below sea level. Etc.Calpalned said:I thought that scalars are magnitudes (aka absolute values)...
When you stretch a spring, you're doing work on the spring. According to Newton's third law, the spring exerts a force on you and therefore does work on you. The action and reaction forces point in opposite directions, but the displacement is the same in either case, so the work done on the spring by you and the work done by the spring on you are always negatives of each other.Calpalned said:Homework Statement
Fact: Being the dot product of force and distance, work is a scalar. Fragment from my textbook: The work done on the spring is ##\frac{1}{2}kx^2##, and so the work done by the spring is ##-\frac{1}{2}kx^2##.
Homework Equations
##W = f \cdot d ##
The Attempt at a Solution
I thought scalars don't have directions. Why is the "work done on" positive, while the "work done by" is negative?
Work is a scalar quantity, meaning it has magnitude but no direction. This is because work is defined as the product of force and displacement, both of which are vector quantities, but their product results in a scalar value.
Yes, work can be negative. This occurs when the force and displacement are in opposite directions, resulting in a negative value for work. This is often the case when an object is being pulled in the opposite direction of its motion.
Work is the transfer of energy from one object to another, whereas energy is the ability to do work. In other words, work is a process that results in a change in energy, but energy itself is not work.
The SI unit of measurement for work is the joule (J). This is equivalent to a force of one newton (N) applied over a distance of one meter (m). Other common units for work include the calorie (cal) and the foot-pound (ft-lb).
Work and power are closely related, as power is defined as the rate at which work is done. In other words, power is the amount of work done per unit time. The SI unit of measurement for power is the watt (W), which is equal to one joule per second (J/s).