Work.. please help??!!?

Question

(a) How much work must one do (against gravity) to get a stone block (m=4000 KG) from the base of the pyramids to its place 30 m above that?

(b) How much Force (F) would a crane need to apply to lift the block into place (at a constant speed, so acceleration is very small)?

please show steps!!

what if,
(c) Instead of using a crane, use a ramp. how much force would workers need to apply to push the block up the ramp (at a constant speed, acceleration is very small)? is the work dont the same?

Answer 1

a) To work this out, we use the following equation:

W = m.g.h

where "W" is the work done, "m" is the mass of the object having work done on it, "g" is the gravitational acceleration at that point (assuming it is on the Earth's surface, it would be 9.8 m.s^-2), and "h" is the distance the particular object is forced against gravity (lifted).

Now, we simply integrate the values into the above equation:

W = 4000 x 9.8 x 30
so, W = 1.18x10^6 joules, to three significant figures.

b) Now to find the force:

F = W / d

where "F" is the force, "W" is the work done (calculated previously), and "d" is the distance it was done over. This can be explained as, "force is proportional to the work done, and inversely proportional to the distance over which it was applied."

so, F = 1.176x10^6 / 30
so, F = 3.92x10^4 newtons.

c) Yes, the amount of force applied is always the same, provided the distance moved against gravity in both cases is equal. This is because W = m.g.h, and F = W / d, where h and d are equal. Therefore, the work done and force are only derived from the "distance an object is pushed against gravity", so no extra work is required to push an object up a ramp, than to lift it up the same distance with a crane (provided we ignore friction and air resistance etc).

Hope that helps.

Answer 2

In all the three cases the work to be done is the same and
= 4000 x 9.8 x 30 m = 1176000 J

(b) force needed to apply is
Work to be done / distance through which we move the load.

In this case the crane moves the object through a distance of the same 30 m

Hence the force needed is 1176000 / 30 = 3920 N.

{However this can be calculated using F = mg since the force needed here is the same as the weight of the object}.

(c} As ion the case of (b) we can calculate the force.

In the case of ramp the distance through which the object moved is along the length of the plane.

If L is the length of the plane then the force needed is

Work to be done / distance through which we move the load.

F = {1176000 / L } N.
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In all the cases, in effect we apply a vertical force which is equal to the weight of the object. Since the net vertical force is zero, the object will be at rest or will be in uniform motion.
That is to say with no net acceleration.
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Answer 3

Well...... Since you didn't say anything about frictional losses, just assume that the total work done is in changing the potential enrgy of the 4000kg as it moves through 30 m against gravity.
W = delta Ep = mgh = 4000*9.8*30 = 1,176,000 Joules.

The force needed would be
F=ma = 4,000*9.8 = 39,200 N

Doug

Answer 4

(a) work = mgh = 4000 * 9.8 * 30
= 1176000 J

(b) Force applied by crane = W/ m
= 1176000/ 4000
= 294 N

I hope it helps.

Answer 5

a>> W=mgh = (4000Kg)*(9.81m/s^2)*(30m)= 1177200 Jouls
b>> F=mg = (4000Kg)*(9.81m/s^2)= 39240 N
f>> yes. surely. A mass of 4 tons need a heavy crane to be moved.