Question

in order to move the rectangular stones which built the pyramids the ancient egyptians used a system of cylindrical logs placed close to each other on the ground which rolled along (without slipping) as the stone on top was pulled by slaves (it also did not slip). if the radii of the logs were all 19 cm and their maximum angular velocity about their axis was 8 radians per second, what was the maximum linear speed (in m/s) of the pyramid stones.

Answer 1

The maximum linear speed of the pyramid stones, given the logs' radius of 19 cm and the angular velocity of 8 radians per second, is calculated as 1.52 m/s.

Step-by-step explanation:

The question involves finding the maximum linear speed (in m/s) of pyramid stones when they were being transported using cylindrical logs as wheels to build the pyramids. The angular velocity provided is 8 radians per second, and the radius of the cylindrical logs is 19 cm.

To convert the radius to meters, we use the conversion 1 cm = 0.01 m, yielding a radius of 0.19 m. The linear speed v of a point on the circumference of a rotating body is related to the angular velocity ω and the radius r of the rotation through the equation v = rω. Given the angular velocity ω = 8 rad/s and the radius r = 0.19 m, the maximum linear speed v is:

v = rω = 0.19 m × 8 rad/s = 1.52 m/s

Therefore, the maximum linear speed of the pyramid stones was 1.52 m/s.