How mush work is done in lifting a 40 kilogram weight to a height of 1.5 meters?

Question

Isaiah Allen · Accepted Answer

The answer is #588J#. Always start with the definition: #W=int_a^b F(x)dx# Sometimes, the simple problems are the hardest because it looks too easy so we tend to add unnecessary things.  Since this is a vertical lift, we are dealing with gravity which is 9.8 #m/s^2#.  So, #F(x)=9.8m/(s^2)*40kg=392N# Remember that work is force times distance.  We have force which is just a constant function.  And we have distance which is #dx#.  The tendency is to add an #x# into #F(x)=392N#, but that would be incorrect.  Now, let's put it together: #a=0#
#b=1.5#
#W=int_0^(1.5) 392 dx#
#=392x|_0^(1.5)#
#=588J#

Elijah Abram · Answer

undefined The work done in lifting a 40-kilogram weight to a height of 1.5 meters can be calculated using the formula for work:

$$ \text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta) $$

Where:
- Force is the force exerted to lift the weight, which is equal to the weight of the object in this case.
- Distance is the height through which the object is lifted.
- θ is the angle between the force vector and the direction of motion. Since the force and the direction of motion are in the same line, θ = 0 and cos(θ) = 1.

Given:
- Mass (m) = 40 kilograms
- Height (h) = 1.5 meters
- Acceleration due to gravity (g) ≈ 9.8 m/s² (assuming Earth's surface)

We can calculate the force exerted to lift the weight using Newton's second law:

$$ \text{Force} = \text{Mass} \times \text{Acceleration due to gravity} $$

$$ \text{Force} = 40 \times 9.8 $$

Now, calculate the work done:

$$ \text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta) $$

$$ \text{Work} = (40 \times 9.8) \times 1.5 \times 1 $$

$$ \text{Work} = 588 \text{ joules} $$

Therefore, the work done in lifting a 40-kilogram weight to a height of 1.5 meters is 588 joules.