Final answer:
To calculate the centripetal force in a centrifuge, convert the mass to kilograms and the rotational speed to radians per second. Apply the formula Fc = m * r * ω². The centripetal force for a mass of 3.00 g rotating at 6.00 x 10⁴ rpm in a 10 cm radius centrifuge is approximately 118.435 Newtons.
Step-by-step explanation:
The subject of this question is Physics, and it is suitable for a high school level of understanding. The question is asking to calculate the centripetal force exerted on an object of mass 3.00 g, which is rotating at 6.00 x 104 rpm in a centrifuge with a radius of 10.0 cm.
First, we need to convert the mass from grams to kilograms and the rotational speed from rev/min to rev/s:
- Mass in kilograms = 3.00 g * (1 kg / 1000 g) = 0.003 kg
- Rotational speed in rev/s = 6.00 x 104 rpm * (1 min / 60 s) = 1000 rev/s
We then convert revolutions per second to radians per second (since 1 rev = 2π radians):
- Angular velocity in rad/s = 1000 rev/s * (2π rad / 1 rev) = 2000π rad/s
Using the formula for centripetal force Fc = m * r * ω2, where 'm' is the mass, 'r' is the radius, and 'ω' is the angular velocity, we get:
- Centripetal force = 0.003 kg * (0.1 m) * (2000π rad/s)2
- Fc = 0.003 kg * 0.1 m * (4π2 * 106) rad2/s2
- Fc ≈ 0.003 kg * 0.1 m * 39.478 x 106 rad2/s2
- Fc = 118.435 N
Therefore, the centripetal force exerted on the object is approximately 118.435 Newtons.