Mira and Tobias push one moving box. Mira pushes with 30 N and Tobias pushes with 40 N. Together, is that 70 N of push? That depends on something neither number mentions: direction.
A force is more than a number of newtons.
Aim a 30 N push forward, and a shopping cart rolls down the aisle. Aim the same 30 N push sideways, and the cart veers into the shelf.
Same size of push, different direction, different result. A force's description is not complete until both are given. So a force has a magnitude, measured in newtons, and a direction.
Which two pieces of information make a force's description complete?
You have already met quantities like that: displacement and velocity. A quantity with both magnitude and direction is a vector, and force is one too.
On a diagram, a force is drawn as an arrow: the length shows the magnitude, and the arrowhead shows the direction.
Which force description is complete?
And forces combine the way vectors combine, never as plain numbers: a 3 N force to the left and a 4 N force straight up do not simply add to 7 N.
Plain adding is right only when the forces point the same way. Point them differently, and the combined effect must be found the vector way, tip to tail.
Back to Mira and Tobias's box: their 30 N and 40 N act like 70 N only if the two pushes point the same way.
Lena says: 'To predict what a push does to a cart, you need the push's direction as well as its size.' Is Lena correct?
A gardener drags a hose with a 40 N pull aimed north. Give the force's full description.
A force's full description gives its magnitude and its direction.
40 N, pointing north.
Two ropes pull on one ring: 3 N to the left and 4 N straight up. A student writes 'total: 7 N'. What went wrong?
Forces combine as vectors, never as plain numbers.
These two forces point at a right angle to each other, so tip to tail they act like a single 5 N force aimed up and to the left.
The two forces do not simply add to 7 N. Combined the vector way, they act like one 5 N force.
A 3 N force and a 4 N force act on one cart. A student writes: 'combined push: 7 N, whatever the directions.' What is wrong with the claim?
Which of these quantities is a vector?
On a force diagram, one arrow is drawn twice as long as another. What does the longer arrow show?