A jogger is running around a circular track of circumference 480 m. If the jogger has a speed of 11 km/h, what is the magnitude of the centripetal acceleration of the jogger?
2πR=480 m
R=480/2π =76.4 m
v=11 km/h =11000/3600 =3.06 m/s.
a(centr)=v²/R= 3.06²/76.4 =0.12 m/s²
To find the centripetal acceleration of the jogger, we need to use the formula:
a = v^2 / r
where:
a = centripetal acceleration
v = velocity of the jogger
r = radius of the circular track
First, let's convert the speed from km/h to m/s.
Given:
Speed of the jogger = 11 km/h
1 km = 1000 m
1 hour = 3600 seconds
Converting 11 km/h to m/s:
11 km/h * (1000 m/1 km) * (1/3600 h/1 s) = 3.06 m/s
Next, we need to find the radius of the circular track.
Given:
Circumference of the track = 480 m
Circumference of a circle = 2πr
480 m = 2πr
To find r, divide both sides of the equation by 2π:
r = 480 m / (2π)
Now, we can calculate the centripetal acceleration by substituting the values into the formula:
a = (3.06 m/s)^2 / (480 m / 2π)
a = (9.3636 m^2/s^2) / (480 m / 2π)
a ≈ 0.0383 m/s^2
Therefore, the magnitude of the centripetal acceleration of the jogger is approximately 0.0383 m/s^2.
To find the magnitude of the centripetal acceleration of the jogger, we first need to convert the speed from km/h to m/s, as the SI unit for acceleration is meters per second squared (m/s^2).
Given:
Speed of the jogger = 11 km/h
Circumference of the track = 480 m
To convert the speed from km/h to m/s, we can use the conversion factor:
1 km/h = 1,000 m / 3,600 s
Therefore, 11 km/h = (11,000 m / 3,600 s) m/s
Next, we need to find the time it takes for the jogger to complete one full round on the circular track. The time can be determined using the formula:
Time = Distance / Speed
In this case, the distance is the circumference of the track and the speed is the converted speed in m/s.
Time = 480 m / (11,000 m / 3,600 s)
Now, we can find the centripetal acceleration using the formula:
Centripetal Acceleration = (Speed^2) / Radius
Since the track is circular, the radius is equal to half of the circumference.
Radius = Circumference / 2 = 480 m / 2
Plugging in the values, we have:
Centripetal Acceleration = ((11,000 m / 3,600 s)^2) / (480 m / 2)
Now, we can simplify and calculate the magnitude of the centripetal acceleration.