The builders of the pyramids used a long ramp to lift 21000-kg (21-ton) blocks. If a block rose 1.1 m in height while traveling 20 m along the ramp’s surface, how much uphill force was needed to push it up the ramp at constant velocity?
To find the uphill force needed to push the block up the ramp at constant velocity, we can use the concept of mechanical advantage.
The mechanical advantage of an inclined plane (ramp) is given by the ratio of the length of the ramp to the height it rises: MA = length of ramp / height of ramp.
In this case, the length of the ramp is given as 20 meters, and the height it rises is given as 1.1 meters. Therefore, the mechanical advantage is calculated as:
MA = 20 m / 1.1 m ≈ 18.18
This means that the ramp provides a mechanical advantage of approximately 18.18.
Now, to calculate the uphill force needed to push the block up the ramp, we can use the formula:
Uphill force = Weight of the block / Mechanical advantage
The weight of the block is given as 21,000 kg. So, substituting in the values, we have:
Uphill force = 21,000 kg / 18.18 ≈ 1,154.21 kg
Therefore, a force of approximately 1,154.21 kg (or 11,332 N) would be needed to push the block up the ramp at constant velocity.