A race car travels with a constant tangential speed of 80.0 m/s around a
circular track of radius 750 m. Find the magnitude of the car’s total
acceleration
Tangential speed is constant, so only the centripetal acceleration counts.
(centripetal acceleration) = (velocity^2)/radius
so...
(c.a.) = (80^2)/750
= 6400/750 = 8.53333... m/s^2
Answer = 8.53 m/s^2
From what height should a car be dropped to gain the same kinetic energy it would have if it were moving horizontally at 95 km/hr?
Well, well, well, looks like the race car wants to go for a spin, huh? Alrighty then, let's calculate that acceleration!
To find the magnitude of the car's total acceleration, we need to break it down into two components: the centripetal acceleration and the tangential acceleration.
The centripetal acceleration is given by the formula: ac = v²/r, where v is the tangential speed and r is the radius of the circular track. Plugging in the values, we get ac = (80.0 m/s)² / 750 m.
Now for the tangential acceleration. Since the tangential speed is constant, there is no change in speed, meaning the tangential acceleration is zero. Yep, nada, zip, zilch.
So, adding the centripetal acceleration and the tangential acceleration (zero), we find the magnitude of the car's total acceleration is equal to the centripetal acceleration alone.
Now, it's time to crunch the numbers and let the answer take the wheel!
To find the magnitude of the car's total acceleration, we need to understand that the car's total acceleration consists of two components: tangential acceleration and centripetal acceleration.
Given:
Tangential speed (v) = 80.0 m/s
Radius (r) = 750 m
1. Tangential acceleration can be calculated using the formula:
Tangential acceleration (at) = (change in velocity) / (change in time)
As the car travels with a constant tangential speed, the change in velocity is 0, and thus the tangential acceleration is also 0.
2. Centripetal acceleration can be calculated using the formula:
Centripetal acceleration (ac) = (tangential speed)^2 / radius
Substituting the given values:
Centripetal acceleration (ac) = (80.0 m/s)^2 / 750 m
ac = 6400 m^2/s^2 / 750 m
ac ≈ 8.533 m/s^2
Therefore, the magnitude of the car's total acceleration is approximately 8.533 m/s^2.
To find the magnitude of the car's total acceleration, we need to consider two components of acceleration: tangential acceleration and centripetal acceleration.
1. Tangential acceleration:
The tangential acceleration is the component of acceleration that changes the car's speed. Since the car travels with a constant tangential speed of 80.0 m/s, the tangential acceleration is zero. This is because the car is not undergoing any change in speed.
2. Centripetal acceleration:
The centripetal acceleration is the component of acceleration responsible for the car's change in direction as it moves in a circular path. The formula for calculating centripetal acceleration is given by:
ac = (v^2) / r
Where:
ac = centripetal acceleration
v = tangential speed
r = radius of the circular track
Plugging in the given values:
v = 80.0 m/s
r = 750 m
ac = (80.0^2) / 750
Simplifying the equation, we get:
ac = 6400 / 750
Evaluating the expression, we find:
ac ≈ 8.53 m/s^2
Therefore, the magnitude of the car's total acceleration is approximately 8.53 m/s^2.