When a carpenter shuts off his circular saw, the 10.0-inch diameter blade slows from 4670 rpm to zero in 3.00 s.
1) What is the distance traveled by a point on the rim of the blade during the deceleration? (in ft}
2)What is the magnitude of the net displacement of a point on the rim of the blade during the deceleration? (in inch}
To find the distance traveled by a point on the rim of the blade during deceleration, we can use the formula:
Distance = (Initial Velocity + Final Velocity) * Time / 2
Given:
Initial Velocity (Vi) = 4670 rpm (revolutions per minute)
Final Velocity (Vf) = 0 rpm
Time (t) = 3.00 s
To convert the initial and final velocities from rpm to inches per second, we can use the fact that there are 60 seconds in a minute:
Initial Velocity (Vi) = 4670 rpm * (2π * 10 inches / 1 revolution) * (1 minute / 60 seconds) = 4670 * 2 * π * 10 / 60 inches per second
Final Velocity (Vf) = 0 rpm * (2π * 10 inches / 1 revolution) * (1 minute / 60 seconds) = 0 inches per second
Now, substitute the values into the formula:
Distance = (Vi + Vf) * t / 2
Distance = (4670 * 2 * π * 10 / 60 + 0) * 3.00 / 2
The resulting distance will be in inches. To convert it to feet, divide it by 12 since there are 12 inches in a foot.
To find the magnitude of the net displacement of a point on the rim of the blade during deceleration, we can use the formula:
Displacement = (Final Velocity^2 - Initial Velocity^2) / (2 * Acceleration)
Since the circular saw is decelerating from an initial velocity to a final velocity of 0 rpm, the acceleration is determined by the formula:
Acceleration = (Final Velocity - Initial Velocity) / Time
Now, we can substitute the values into the displacement formula:
Acceleration = (0 - 4670 * 2 * π * 10 / 60) / 3.00
Displacement = (0^2 - (4670 * 2 * π * 10 / 60)^2) / (2 * ((0 - 4670 * 2 * π * 10 / 60) / 3.00))
The resulting displacement will be in inches.