How much work must one do (against gravity) to get a stone block (m4000 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!!
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 figuresb) 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 overThis can be explained as, force is proportional to the work done, and inversely proportional to the distance over which it was appliedso, F 1.176x10^6 / 30 so, F 3.92x10^4 newtonsc) Yes, the amount of force applied is always the same, provided the distance moved against gravity in both cases is equalThis is because W m.g.h, and F W / d, where h and d are equalTherefore, 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.
