yank hardy pulls the cord on his power mower. in order for the engine to start, the pulley must turn at 180 revolutions per minute. the pulley has a radius of 0.2 ft. how many radians per second must the pulley turn?
How fast must yank pull the cord to start the mower? when yank pulls this hard, what is the angular velocity of the center of the puller?
CORRECTION:
c. Va = 18.84rad/s. = Angular velocity.
Freda Pulliam and Yank Hardy are on opposite sides of a canal, pulling a barge with tow ropes. Freda exerts a force of 50 pounds at 20 degrees to the canal, and Yank pulls at an angle of 15 degrees with just enough force so that the resultant force vector is directly along the canal. Find the number of pounds with which Yank must pull and the magnitude of the resultant vector.
To find the angular velocity of the pulley in radians per second, we can use the formula:
Angular velocity (ω) = (2π * n) / t,
where ω is the angular velocity in radians per second, n is the number of revolutions, and t is the time taken to complete those revolutions.
Given that the pulley must turn at 180 revolutions per minute, we have n = 180 revolutions and t = 1 minute = 60 seconds.
Substituting these values into the formula, we get:
ω = (2π * 180) / 60
= 6π radians per second
= 18.85 radians per second (rounded)
Therefore, the pulley must turn at approximately 18.85 radians per second.
To calculate how fast Yank must pull the cord to start the mower, we need to relate the linear velocity of the cord to the angular velocity of the pulley. The linear velocity (v) of a point on the rim of the pulley is given by the formula:
v = ω * r,
where v is the linear velocity, ω is the angular velocity, and r is the radius of the pulley.
Given that the pulley has a radius of 0.2 ft and the required angular velocity is 18.85 radians per second, we can calculate the linear velocity:
v = 18.85 * 0.2
= 3.77 ft/s (rounded)
Therefore, Yank must pull the cord at a speed of approximately 3.77 feet per second to start the mower.
The angular velocity of the center of the pulley is the same as the angular velocity of the entire pulley, which we found to be 18.85 radians per second.
a. V=180rev/min * 6.28rad/rev *1min/60s
= 18.84 rad/s.
c. Va = 18.84 m/s = Angular velocity.