During the spin cycle of a washing machine, the clothes stick to the outer wall of the barrel as it spins at a rate as high as 1800 revolutions per minute. The radius of the barrel is 26 cm.
a. Determine the speed of the clothes (in m/s) which are located on the wall of the spin barrel.
b. Determine the acceleration of the clothes.
Audio Guided Solution
v=ω•R=2π•n•R =2π•(1800/60) •0.26=…
a(centripetal) = v²/R=…
54.25
Solution of the above questions
I want the Solution of the above questions
To find the speed of the clothes (v) on the wall of the spin barrel, we can use the formula:
v = ω * r
where ω is the angular velocity in radians per second and r is the radius of the barrel.
Step 1: Convert the given speed from revolutions per minute to radians per second.
To do this, we need to know that 1 revolution is equal to 2π radians.
Using the conversion factor:
1 revolution * (2π radians / 1 revolution) * (1 minute / 60 seconds) = (2π/60) radians/second
So, the angular velocity (ω) is (2π/60) radians/second.
Step 2: Now, plug in the values into the formula:
v = (2π/60) * 26 cm
Step 3: Convert the speed from centimeters per second to meters per second.
Since the SI unit of speed is meters per second, we need to convert centimeters to meters by dividing by 100.
v = (2π/60) * 26 cm / 100 cm/m
v ≈ 0.272 m/s
Therefore, the speed of the clothes on the wall of the spin barrel is approximately 0.272 m/s.
Moving on to part b, to find the acceleration of the clothes, we need to remember that acceleration is the rate of change of velocity (v) with respect to time (t), and it is the same as the centripetal acceleration (ac) in circular motion.
The formula for centripetal acceleration is:
ac = (v^2) / r
where ac is the acceleration, v is the velocity, and r is the radius.
Step 1: Plug in the values into the formula:
ac = (0.272 m/s)^2 / 0.26 m
Step 2: Calculate the acceleration:
ac ≈ 0.285 m/s^2
Therefore, the acceleration of the clothes on the wall of the spin barrel is approximately 0.285 m/s^2.