The blade of a windshield wiper moves through an angle of 90.0° in 0.49 s. The tip of the blade moves on the arc of a circle that has a radius of 0.6 m.
What is the magnitude of the centripetal acceleration of the tip of the blade?
90 degrees of a circle is 1/4 the Circumference. Therefore it takes 0.49s to travel 1/4 of the way. Multiply .49 by 4 to receive the total amount of time it takes to make one revolution. To find velocity, find the circumference (2*r*pi). Divide the circumference by the time to get the velocity. The Centripetal Acceleration is (v^2/r).
To find the magnitude of the centripetal acceleration of the tip of the blade, we can use the formula:
ac = (v^2) / r
Where ac is the centripetal acceleration, v is the velocity, and r is the radius.
First, let's find the velocity of the tip of the blade. Since we know that the blade moves through an angle of 90.0° in 0.49 s, we can calculate the angular velocity using the formula:
ω = θ / t
Where ω is the angular velocity, θ is the angle, and t is the time.
In this case, we have θ = 90.0° and t = 0.49 s. So, we can calculate ω as:
ω = (90.0°) / (0.49 s)
Next, we need to convert the angular velocity to linear velocity. The linear velocity (v) of an object moving in a circle is related to the angular velocity (ω) and radius (r) by the formula:
v = ω * r
In this case, we have ω and r. So, we can calculate v as:
v = ω * r
Once we have the velocity (v), we can substitute it into the centripetal acceleration formula:
ac = (v^2) / r
Now we can plug in the values:
r = 0.6 m (radius)
θ = 90.0° (angle)
t = 0.49 s (time)
Step 1: Convert the angle from degrees to radians:
θ = (90.0°) * (π / 180) radians
Step 2: Calculate the angular velocity:
ω = θ / t
Step 3: Calculate the linear velocity:
v = ω * r
Step 4: Calculate the centripetal acceleration:
ac = (v^2) / r
By following these steps, you should be able to find the magnitude of the centripetal acceleration of the tip of the blade.