What is the work required to lift a 10 kg box off the ground to a height of
5.0 m?

490J

Explanation:

Given parameters:

Mass of box  = 10kg

Height  = 5m

Unknown:

Work done  = ?

Solution:

Work done can be derived from the product of force and distance;

   Work done = force x distance

 Force here is applied by gravity and it is the weight

 The distance is the height

  Work done  = weight x height

 Work done  = mass x acceleration due to gravity x height

 Work done  = 10 x 9.8 x 5  = 490J

Step-by-step explanation:

1/(1 - p + p²) - 1/(1 + p + p²) - 2p/(1 - p² + p⁴) =

[ (1 + p + p²)-(1 - p + p²)/(1 - p + p²)(1 + p + p²) ] - 2p/(1 - p² + p⁴) =

2p/(1 + p + p² - p - p² - p³ + p² + p³ + p⁴) - 2p/(1 - p² + p⁴) =

2p/(1 + p² + p⁴) - 2p/(1 - p² + p⁴) =

[ 2p(1 - p² + p⁴) - 2p( 1 + p² + p⁴) ]/(1 + p² + p⁴)(1 - p² + p⁴) =

(2p - 2p³ + 2p⁵ - 2p - 2p³- 2p⁵) / (1 - p² + p⁴ + p² - p⁴ + p⁶ + p⁴ - p⁶ + p⁸) =

-4p³ / (1 + p⁴ + p⁸)