Abox has a mass of 400 g. what minimum force is needed to lift it? if it is raised to a height of 6.0 m, how much work was done?

We know that the mass of the box is m = 400g, then the weight of the box is equal to the gravitational acceleration times the mass, this is:

w = -9.8*0.4N = 3.92N downwards

Where i used 0.4kg instead of 400g, because the units are easily calculated in kg than in grams. This calculation is obtained by knowing that 1000g = 1kg, then 400g is equal to (400/1000)kg

Now, if you want to lift the box, you need to cancel this force, so you should use a force of at least 3.92N upwards.

And the work is defined as the movement done by a force, and can be calculated as:

W = F*d

in this case the minimal force is F = 3.92N, and the distance is d = 6.0m

And we have W = 3.92N*6.0m = 23.52 joules

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