A beetle whose mass is 2 g sits on a turntable at a distance of 12 cm from the center. The turntable is rotating at 33 rpm.
(a) What are its acceleration and the centripetal force on it?
a =______ m/s2
Fc=_____ N
(b) What is the interaction that provides the centripetal force? Select all that apply.
-the gravitational force
-the force of friction
-the force of the beetle on the turntable
-the concentration of the mind of the beetle
Ac = w^2 r = v^2/r
w = 33*2pi radians in 60 seconds = 3.46 radians/s
w^2 = 11.9
Ac w^2 r = 11.9 * .12 = 1.43 m/s^2
Fc = m Ac = .002 * 1.43 = .00286 N
yes
yes
yes
no
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To answer part (a) of the question, we need to calculate the acceleration and centripetal force of the beetle.
First, let's convert the beetle's mass to kilograms. Since there are 1000 grams in 1 kilogram, the mass of the beetle is 0.002 kilograms.
The formula for acceleration in uniform circular motion is given by:
a = (v^2) / r
where:
- a is the acceleration
- v is the linear velocity
- r is the radius
To find the linear velocity, we first need to convert the turntable's rotational speed from rpm (revolutions per minute) to radians per second.
1 revolution = 2π radians
33 rpm = (33 rev/min) * (2π radians/1 rev) * (1 min/60 s) ≈ 3.45 radians/s
Since the beetle's distance from the center is the radius, r = 0.12 meters.
Now we can calculate the linear velocity:
v = (r) * (ω)
where:
- v is the linear velocity
- r is the radius
- ω is the angular velocity (in radians per second)
v = (0.12 m) * (3.45 radians/s) ≈ 0.414 m/s
Next, we can calculate the acceleration:
a = (v^2) / r = (0.414 m/s)^2 / 0.12 m ≈ 1.435 m/s^2
So, the acceleration of the beetle is approximately 1.435 m/s^2.
Now let's calculate the centripetal force using the equation:
Fc = m * a
where:
- Fc is the centripetal force
- m is the mass
Fc = (0.002 kg) * (1.435 m/s^2) ≈ 0.00287 N
Therefore, the centripetal force acting on the beetle is approximately 0.00287 N.
Moving on to part (b) of the question, the centripetal force is provided by the force of friction. Since the beetle is sitting on the turntable, the frictional force between them provides the centripetal force needed to keep the beetle in circular motion. Hence, the correct options are:
- The force of friction
Neither the gravitational force, the force of the beetle on the turntable, nor the concentration of the beetle's mind provide the centripetal force in this scenario.