‫Welcome back.
‫Let's now see the work for this system.
‫You have two forces here, force applied and force of gravity, so you have to compute work done by
‫both forces.
‫Let's first look at the Applied Force.
‫This is the applied force vector and the force of gravity vector is the following.
‫Its horizontal component is zero Newtons and its vertical component is minus five sine 30 degrees Newtons.
‫All right.
‫The displacement vector is the following.
‫The X component is 20 times cosine, 30 degrees, and the Y component is zero meters.
‫Right.
‫So the work done by the Applied Force is computed like this, the applied vector dart, the displacement
‫vector, which is this one times this one.
‫And then you add and I'm going to continue writing here, you add this component five sine thirty degrees
‫times, this component zero meters.
‫As a result, this term will be zero and you're left with five times 20, which is 100 times cosine,
‫30 degrees squared, and that will give you 75 joules.
‫So cosine 30 degrees squared equals zero point seventy five.
‫Now that's only work done by the Applied Force.
‫How about the work done by the force of gravity?
‫So you have the force of gravity vector times the displacement vector.
‫So you have zero times, 20 times cosine 30 degrees, which is this element times, this element here
‫plus minus five times sine thirty degrees, which is the summiteer times zero meters, which is this
‫element here.
‫And you can see that both terms are zero.
‫So work done by the force of gravity is zero joules.
‫And it makes sense because does the ball move in the direction of the force of gravity at all?
‫It doesn't.
‫It only moves horizontally.
‫But the force of gravity is vertical and work depends on the product of the force and the distance.
‫The ball must move in the direction of the force, at least a little bit in order for this force to
‫do some work.
‫If it doesn't, then there is no work.
‫And remember, the DOT product gives you a scalar and scalars are just numbers and so you can just add
‫them together, which means that the work total equals work done by the Applied Force plus work done
‫by the gravity force.
‫And since this one is zero, then you only have five joules like this.
‫And so that's why in physics you can just add energies because energies are scalar, they are not vectors,
‫energy doesn't have a direction, it's just a number, a quantity.
‫And that's why you can add them together like this.
‫So in this system, the only thing that contributes to total work is the horizontal component of the
‫applied force.
‫So that's all about the DOT product.
‫And now in the next video, we're going to start talking about the cross product.
‫Thank you very much.
‫And I'll see you there.