How do I solve this?
The blade of a windshield wiper moves through an angle of 90.0° in 0.453 s. The tip of the blade moves on the arc of a circle that has a radius of 0.775 m. What is the magnitude of the centripetal acceleration of the tip of the blade?
To solve this problem, we need to calculate the magnitude of the centripetal acceleration of the tip of the blade. Centripetal acceleration can be calculated using the formula:
a = (v^2) / r
where
a = centripetal acceleration
v = linear velocity
r = radius of the circle
First, let's find the linear velocity. We can use the formula:
v = (Δθ / Δt) * r
where
Δθ = angle through which the blade moves (in radians)
Δt = time taken to move through the angle (in seconds)
r = radius of the circle
Given:
Δθ = 90° = 90 * (π/180) radians (Convert degrees to radians)
Δt = 0.453 s
r = 0.775 m
Substituting the given values, we have:
v = (90 * (π/180) / 0.453) * 0.775
Simplifying this equation, we get:
v = 2.516 m/s (rounded to three decimal places)
Now, we can substitute the value of v into the centripetal acceleration formula:
a = (v^2) / r
Substituting the given values, we have:
a = (2.516^2) / 0.775
Simplifying this equation, we get:
a = 8.18 m/s^2 (rounded to two decimal places)
Therefore, the magnitude of the centripetal acceleration of the tip of the blade is 8.18 m/s^2.