Problem Solving with Vectors

Anything that involves an amount and an associated direction is a potential application of vectors. The direction and speed of a car during a collision is a good example; the direction and distance from your house to your school or office is another. Anything that you can see or imagine has application of vector theory. In this lesson, we will explore several examples from force-related problems to velocity where vectors are applied. All these examples involve vectors in quadrant 1, but the idea can be extended to any vector.

The first of three video introduces two questions involving objects at equilibrium (when the object isn’t moving). At equilibrium, the sum of all horizontal forces acting on a body is zero, the sum of all vertical forces acting on a body is zero, and the sum of all moments acting on a body is also zero. Without getting too technical, the moment of a force about some point is the product of the force F and the perpendicular distance from the force to the point’s center of gravity. In these examples, Newtons are used to measure weight or force and 1 N is equivalent to 1 kg⋅m per s² SI units.

  • Notice how in question 1, weight is given in Newtons rather than, let’s say, kilograms or pounds. Remember that there’s a difference between weight – which is what they’re asking for – and mass. Mass is a measurement of the amount of matter something contains, while weight is the measurement of the pull of gravity on an object.

It’s recommended that you get as much exposure as possible to vector-related word problems. Part 2 of this lesson can be watched below, and caters exclusively to velocity.

The last video introduces two new words used commonly in physics. The normal or normal component is the vector component that is at 90° to the object, while the tangential component is the vector component that is moving in the same direction as the force.