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(II) Assume that a force acting on an object is given by $\vec { \mathbf { F } } = a x \hat { \mathbf { i } } + b y \hat { \mathbf { j } }$ . where the constants $a = 3.0 \mathrm { N } \cdot \mathrm { m } ^ { - 1 }$ and $b = 4.0 \mathrm { N } \cdot \mathrm { m } ^ { - 1 } .$ Determine the work done on the object by this force as it moves in a straight line from the origin to $\vec { \mathbf { r } } = ( 10.0 \hat { \mathbf { i } } + 20.0 \hat { \mathbf { j } } ) \mathrm { m }$

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$$W=950 \mathrm{J}$$

Physics 101 Mechanics

Chapter 7

Work and Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

Cornell University

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University of Sheffield

McMaster 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.

02:34

A force is dependent on po…

02:50

(II) A constant force $\ve…

01:35

A constant force F = 4.00N…

02:56

As an object moves along t…

04:40

A constant force $\overrig…

04:32

A force with magnitude giv…

12:10

An object has several forc…

0:00

A variable force of $5 x^{…

02:43

A force $\vec{F}$ acts in …

01:14

How much work is done by a…

So here we have a four Specter. This is going to be 3.0 Newtons per meter Tex High hat plus 4.0 newtons per meter. Why? J hat. And we have a displacement vector equaling 10.0 meters. I had plus 20.0 meters j. So to find the total work done, the work done would be equal to X initial integrating from ex initial tow X final of f of x dx Oh r f sub x d x plus the wine Eshel too. Why final of of y do y and so we can solve. So the work is going to be equal from is going to be equal to the integral from 0 to 10 of three x d x plus the integral from 0 to 20 of four. Why d y So this is equal three x squared over two integrating from 3 2 0 to 10 plus two y squared integrating from 0 to 20. So the work is going to be equal to three times 10 squared divided by two plus two times 20 squared and we're getting 950 jewels of work being done. That is our final answer that is thie End of the solution. Thank you for watching

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