A uniform rectangular marble slab is 3.4m and 2.0m wide.it has a mass of 180kg.its originally lying on surface flat ground with It's 3.4m*2.0m surface facing up.How much work is needed to stand it on It's short end?(hint,think about its centre of gravity)
Work done = ∆P.E
W=(mhg)f - (mgh)i
(mgh)i =0, since it was lying down
And, h = ½(h of the marble)
h= ½(3.4)=1.7m
W= 180 kg × 9.8 m/s² × 1.7m
W= 2,998.8 J
W = 3.0 kJ
Answer is right.
Work done = Change in potential Energy. Initially it was flat. so h = 0. Now when it is standing, the centre of gravity is at height of 3.4/2
Please give me full answer
ty sa solution and formula
To find out how much work is needed to stand the rectangular marble slab on its short end, we need to consider the change in potential energy.
The potential energy of an object is given by the formula: P.E. = mgh
Where:
m = mass of the object
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height or change in height of the object
In this case, the height is the distance the slab needs to be lifted to stand on its short end.
To calculate the height, we need to determine the position of the center of gravity of the slab. The center of gravity of a uniform rectangular object is located exactly at its geometric center.
The geometric center of the slab is at half of its length and half of its width. So, the distance from the surface of the ground to the center of gravity is half of the length of the slab, which is 3.4m / 2 = 1.7m.
Now we can calculate the change in height:
The slab is originally lying flat on the ground, so its initial height is 0.
When it is standing on its short end, the height is the distance from the center of gravity to the surface, which is 1.7m.
So, the change in height (h) is 1.7m - 0m = 1.7m.
Now we can calculate the work needed using the formula for potential energy:
P.E. = mgh
P.E. = 180kg * 9.8 m/s^2 * 1.7m
So, the work needed to stand the slab on its short end is:
Work = 180kg * 9.8 m/s^2 * 1.7m