How much work would it take to push a # 4 kg # weight up a # 4 m # plane that is at an incline of # pi / 4 #?

Answer 1

Olivia Askew

#110.9# joules

Work is represented by the following equation:

#W=F*d*costheta#

#F# is the force in newtons

#d# is the distance moved in meters

#theta# is the angle of incline

The force here is the weight of the box, which is #4 \ "kg"*9.8 \ "m/s"^2=39.2 \ "N"#.

And so,

#W=39.2 \ "N"*4 \ "m"*cos(pi/4)#

#=(156.8sqrt(2) \ "N m")/2#

#=78.4sqrt(2) \ "J"#

#~~110.9 \ "J"#

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Answer 2

Benjamin Asiedu

The work ((W)) done in lifting the 4 kg weight up the 4 m incline can be calculated using the formula (W = m \cdot g \cdot d \cdot \sin(\theta)), where (m) is the mass (4 kg), (g) is the acceleration due to gravity (approximately 9.8 m/s²), (d) is the displacement along the incline (4 m), and (\theta) is the angle of the incline ((\pi/4) radians). Substituting these values, (W = 4 \cdot 9.8 \cdot 4 \cdot \sin(\pi/4)). Calculating this expression gives the work required to push the weight up the incline.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.