Question

A particle suffers displacement from r1(1,2,3) to r2(4,3,2) due to application of force of magnitude |vector f|=20n. the force acts along a vector a=4j^+3k^. if a quantity is defined as w=vector f.âvector r, find w.

Answer 1

W equals 4 unit....

Hope it helps...

Answer 2

Answer:

Explanation:

Concept:

Definition of displacement:

The term "displacement" refers to a shift in an object's position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial location to the ending place. For instance, if an object shifts from location A to position B, its position changes.

Definition of vector:

A vector is a quantity with both magnitude and direction in physics; see image for definition. It is often represented by an arrow whose length is proportional to the magnitude of the quantity and whose direction is the same as that of the quantity. A vector does not have position, while having magnitude and direction.

Definition of force:

The push or pull that causes a massed object to change its velocity. Force is an external agent that has the power to alter a body's resting or moving position. It has a direction and a magnitude.

Definition of work:

Force applied across a distance is called work. Examples of work include dragging down a captive helium balloon, driving a car up a hill, and lifting an object against the gravitational attraction of the Earth. Energy manifests mechanically as work. The joule (J), or newton-meter, is the accepted unit of labour.

Given:

$F =$ $20n$

$a=$ $4j + 3k$

$r1 = ( 1, 2, 3)$

$r2 = ( 4, 3, 2)$

Find:

work

Solution:

$F = 20n$

$a = 4j + 3k$

$F = 20 (4j + 3k)/\sqrt(4^2 + 3^2)$

$F = 20(4j + 3k)/5$

$F = 16j + 12k$

$r = r2 - r1$

$r = ( 4i + 3j + 2k) - ( i + 2j + 3k)$

$r = 3i + j - k$

$w = F . r$

$w = ( 16j + 12k). ( j - k)$

$w = 16 - 12$

$w = 4joules$

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