The builders of the Great Pyramids of Egypt are thought to have used ramps to move the large 20,000 kg (22 ton) stone blocks into place at the construction site. To reduce friction, the Egyptians are assumed to have used rollers between the ramp and each block, enabling the block to be more easily pushed up the ramp. (For this problem, assume they were successful at eliminating friction, and therefore the block experiences no friction as it moves up the ramp). How much force is required to push one of these blocks up a ramp, where the block rises in height 1 m and travels 20 m along the ramp’s surface? Assume the block travels at constant velocity
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To determine the force required to push the block up the ramp, we need to consider the work done against gravity. The force required can be calculated using the formula:
Force = Weight × Distance/Height
Here, the weight of the block can be calculated using the formula:
Weight = mass × acceleration due to gravity
Given that the mass of the block is 20,000 kg and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the weight of the block:
Weight = 20,000 kg × 9.8 m/s²
Weight = 196,000 Newtons (N)
The distance the block travels along the ramp's surface is 20 m, and the height it rises is 1 m. Substituting these values into the formula, we can calculate the force required:
Force = 196,000 N × 20 m / 1 m
Force = 3,920,000 N
Therefore, approximately 3,920,000 Newtons of force would be required to push one of these blocks up the ramp at a constant velocity, assuming no friction.