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How much work would it take to push a # 2 kg # weight up a # 4 m # plane that is at an incline of # (5pi) / 12 #?

Answer 1

Sebastian Acosta

#75.73J#

We can use the formula #W=mgh.#

We will use #g =9.8 ms^-2# assuming we are at sea level on earth.
#m=2kg#

Working out #h# needs a bit of trigonometry, the diagram below will help us understand the situation a bit better:

As it is the opposite surface to the angle, in order to work #h# use #h = 4sin((5pi)/12)#

Now putting all these values into #W = mgh# we get:

#W = 2*9.8*4sin((5pi)/12)=75.73J#

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Answer 2

Olivia Askew

To calculate the work required to push a 2 kg weight up a 4 m plane at an incline of (5π)/12 radians, you can use the formula:

Work = Force × Distance

First, calculate the force required to overcome gravity acting on the weight along the incline:

Force = Weight × sin(θ) = m × g × sin(θ)

Where: m = mass of the weight (2 kg) g = acceleration due to gravity (approximately 9.81 m/s²) θ = angle of inclination ((5π)/12 radians)

Next, calculate the distance along the incline:

Distance = hypotenuse of the triangle formed by the incline (4 m)

Now, you can plug in the values and calculate the work.

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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.