A washing machine drum has a diameter of 46 cm and spins at 400 revolutions per minute. Find the centripetal acceleration at the drum's surface. Give your answer in m/s
To find the centripetal acceleration at the drum's surface, we need to use the following formula:
Centripetal Acceleration (aᴄ) = (angular velocity)^2 × radius
First, let's convert the revolutions per minute (rpm) to radians per second (rad/s). Since one revolution is equal to 2π radians, we can calculate the angular velocity (ω) as follows:
Angular Velocity (ω) = (400 rpm) × (2π rad/1 min) × (1 min/60 s) = 400 × 2π/60 rad/s
Next, we need to find the radius of the drum. The diameter of the drum is given as 46 cm.
Radius (r) = (diameter) / 2 = 46 cm / 2 = 23 cm = 0.23 m
Now we can substitute the values into the formula:
aᴄ = (ω)^2 × r
aᴄ = (400 × 2π/60 rad/s)^2 × 0.23 m
Calculating this expression will give us the centripetal acceleration in m/s².
aᴄ ≈ 159.15 m/s²
Therefore, the centripetal acceleration at the drum's surface is approximately 159.15 m/s².