a particle is given a displacement r 20mi 50mj along a straight line during the displacement a c

Step 1:** Calculate the work done by the force using the dot product of the force and displaceme

A particle is given a displacement r 20mi 50mj along a...

A particle is given a displacement Δr = (2.0 m)i - (5.0 m)j along a straight line. During the displacement, a constant force F = (3.0 N)i + (4.0 N)j acts on the particle. (a) Find the work done by the force, and (b) the component of the force in the direction of the displacement.

Transcript

00:01 Work is a way of energy transfer and it is solved as the dot product of the force and the displacement this problem we're given with a particle that has a displacement of which it has a displacement that is defined by the vector 2 i .8 minus 5 j hat along a straight line during the displacement it is acted by a force which vector form is 3 i had plus 4 j hat we want to find for letter a the work done by the force and for letter b the component of the force in the direction of the displacement.

00:33 So let us perform the dot product of the two vectors to solve for the work.

00:40 So we have force which is 3 i .hat plus 4 j hat, that product with 2 i .hat minus 5 jhat.

00:59 To execute the dot product, we'll just multiply the component.

01:06 Components and the corresponding components of the vectors of our i -hat we have three times two and then we'll add them up so plus the product of four and negative five so in case you still have more components then you just add you just extend this sum by the product of that other component so this becomes six minus 20 or that that negative 14 and the unit is joules so work is a scalar quantity so you don't have you don't need direction to report the value for the work next is a component of the force that is in the direction of the displacement we can also express work then as equal to the product of the work or the force parallel to the displacement so f parallel like this double lines under f means the force parallel or in the direction to the displacement we can find the displacement as simply the magnitude of the position vector or the spacement vector delta r here and we do that by simply taking the square of the component so like two squared and then adding them up.

02:37 So 2 squared plus negative 5 squared...

Question

A particle is given a displacement Δr = (2.0 m)i - (5.0 m)j along a straight line. During the displacement, a constant force F = (3.0 N)i + (4.0 N)j acts on the particle. (a) Find the work done by the force, and (b) the component of the force in the direction of the displacement.

Please give Ace some feedback