Calculate the force of friction that keeps a 80-kg person sitting on the edge of a horizontal rotating platform when the person sits 2.4m from the center of the platform and has a tangential speed of 3.2m/s .
Express your answer to two significant figures and include the appropriate units.
Ac = v^2/r
F = m Ac = m v^2/r
= 80 (3.2^2)/2.4
= 341 N
= 340 N to two figures
Well, well, well, if it isn't the classic "force of friction" problem. Allow me to juggle some numbers for you.
To start off, we need to find the centripetal acceleration of the person sitting on the rotating platform. The centripetal acceleration (ac) is given by the equation: ac = v^2/r, where v is the tangential speed and r is the distance from the center.
Plugging in the provided values, we have ac = (3.2 m/s)^2 / 2.4 m = 4.27 m/s^2.
Now, the force of friction (Ff) needed to keep the person in place can be found using the equation Ff = m * ac, where m is the mass of the person.
Substituting the mass of the person (80 kg) and the calculated centripetal acceleration (4.27 m/s^2), we get Ff = (80 kg) * (4.27 m/s^2) = 342 N.
So, the force of friction that keeps the 80-kg person from sliding off the rotating platform is approximately 342 Newtons (N). Don't slip away without those units!
To calculate the force of friction that keeps the person sitting on the edge of the rotating platform, we can first find the centripetal acceleration experienced by the person.
The centripetal acceleration (a) can be calculated using the formula:
a = v^2 / r
where:
v = tangential speed = 3.2 m/s
r = distance from the center of the platform = 2.4 m
Plugging in the given values:
a = (3.2 m/s)^2 / 2.4 m
a ≈ 4.27 m/s^2
Next, we can calculate the force of friction using Newton's second law, which states that the net force (F) is equal to the mass (m) multiplied by the acceleration (a).
F = m * a
where:
m = mass of the person = 80 kg
a = centripetal acceleration = 4.27 m/s^2
Plugging in the values:
F = 80 kg * 4.27 m/s^2
F ≈ 342 N
Therefore, the force of friction that keeps the person sitting on the edge of the rotating platform is approximately 342 N.
To calculate the force of friction that keeps a person sitting on the edge of a rotating platform, we can use the centripetal force acting on the person.
1. First, we need to determine the centripetal force acting on the person.
Centripetal force (Fc) = (mass * tangential speed^2) / radius
Given:
Mass (m) = 80 kg
Tangential speed (v) = 3.2 m/s
Radius (r) = 2.4 m
Plugging the values into the formula:
Fc = (80 kg * (3.2 m/s)^2) / 2.4 m
2. Calculate the centripetal force:
Fc = (80 * (3.2)^2) / 2.4
Fc ≈ 85.33 N (rounded to two significant figures)
3. The force of friction (Ff) is equal in magnitude and opposite in direction to the centripetal force. Therefore, the force of friction is also approximately 85.33 N.
Hence, the force of friction that keeps the person sitting on the edge of the rotating platform is approximately 85.33 N.