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(II) A constant force $\vec { \mathbf { F } } = ( 2.0 \hat { \mathbf { i } } + 4.0 \hat { \mathbf { j } } ) \mathrm { N }$ acts on an object as it moves along a straight-line path. If the object's displacement is $\mathbf { d } = ( 1.0 \mathbf { i } + 5.0 \mathbf { j } ) \mathrm { m } ,$ calculate the work done by $\vec { \mathbf { F } }$ using these alternate ways of writing the dot product: (a) $W = F d \cos \theta ;$ (b) $W = F _ { x } d _ { x } + F _ { y } d _ { y }$

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$$22 \mathrm{J}$$

Physics 101 Mechanics

Chapter 7

Work and Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

Cornell University

University of Washington

Simon Fraser University

Lectures

04:05

In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

03:47

In physics, the kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest. The kinetic energy of a rotating object is the sum of the kinetic energies of the object's parts.

04:40

A constant force $\overrig…

01:39

(II) Assume that a force a…

02:55

Constant Force A constant …

01:05

A constant force of magnit…

01:22

A force $\vec{F}=(4.0 \mat…

00:29

A force F of strength 20 N…

02:56

As an object moves along t…

05:56

A variable force $F$ acts …

01:14

How much work is done by a…

01:45

A force $\vec{F}$ in the p…

02:00

(II) An object, moving alo…

So we have a force vector and it's this's equaling 2.0. I had plus 4.0 j Hat Newtons and then we can find the A magnitude of this vector two squared plus four squared to the 1/2 power and this is giving us to radical. Five. Nunes. We can say that data is going to be equal to tangent. Negative one of four over too. So this will be our 10 of two. We know that the distance vector or the displacement vector would be equal to 1.0. I had plus 5.0 jae ha and the unit would be meters. Finding the magnitude of this would be one squared plus five squared. So this is giving us radical 26 meters. And so, in order to solve for party party, they want us to solve it the classical or the using the angle so f d co sign a fada and this would be a radical move rather. Rather, we could say to radical five Nunes times radical 26 meters and then co sign of attendant, Our 10 of five minus our 10 of two. And so work is going to be equal to 22 jewels now for part B, they're simply asking us to find it the dot product way. So this will be path of X d of X plus half of why d of why. And this is giving us to Nunes Times one meter plus four Newtons times five meters and again, this is equal in the same answer of 22 jewels. Yeah, so you simply have to solve it both ways in order to prove that no matter how you solve it, you're of course, getting the same answer. That is the end of the solution. Thank you for watching.

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