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Answer :
The angular acceleration of the crankshaft is approximately 179.52 rad/s^2. The crankshaft makes approximately 31.75 revolutions while reaching 3600 rpm.
To calculate the angular acceleration of the crankshaft, we can use the following formula:
Angular acceleration (α) = (Δω) / Δt
where Δω is the change in angular velocity and Δt is the time interval.
Given:
Initial angular velocity (ω_i) = 0 rad/s (since the crankshaft starts from rest)
Final angular velocity (ω_f) = 3600 rpm = (3600 rev/min) × (2π rad/rev) / (60 s/min) = 376.99 rad/s (approximately)
Δt = 2.1 s
Using the formula for angular acceleration:
α = (ω_f - ω_i) / Δt
= (376.99 rad/s - 0 rad/s) / 2.1 s
≈ 179.52 rad/s^2 (approximately)
Therefore, the angular acceleration of the crankshaft is approximately 179.52 rad/s^2.
To determine the number of revolutions the crankshaft makes while reaching 3600 rpm, we need to calculate the change in angular position (Δθ). The change in angular position is given by:
Δθ = ω_i × Δt + (1/2) × α × (Δt)^2
Since the initial angular velocity is 0 rad/s, the first term becomes 0. Thus, the equation simplifies to:
Δθ = (1/2) × α × (Δt)^2
Substituting the given values:
Δθ = (1/2) × 179.52 rad/s^2 × (2.1 s)^2
≈ 199.62 radians (approximately)
To express the number of revolutions, we divide the change in angular position by 2π:
Number of revolutions = Δθ / (2π)
= 199.62 radians / (2π)
≈ 31.75 revolutions (approximately)
Therefore, the crankshaft makes approximately 31.75 revolutions while reaching 3600 rpm.
The question should be:
The crankshaft in a race car goes from rest to 3600 rpm in 2.1 s. What is the crankshaft's angular acceleration? How many revolutions does it make while reaching 3600 rpm? Express your answer using two significant figures.
To learn more about angular acceleration visit: https://brainly.com/question/13014974
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