A disc revolve with a speed of 33.5 revolution per minute and has a radius of 15 cm .two coin are placed at 4 cm and 14 cm away from the center of disc. Coefficient of friction between coin and disc is 0.5 cm .which of the coin will revolve with the disc?
force friction on coin=mg*mu
centripetla force= m w^2 r
set them equal. Examle, the inner coin
so to stay, the mu can be found..
mg*mu=m w^2 r
mu=(33.5*2pi/60)^2*.04
mu=12.3*.04= .49 but the actual coefficient is greater than this, so that xoin stays on the disk.
Now do this for the outer coin.
Give the answer completely i don't understand it
To determine which coin will revolve with the disc, we can compare the forces acting on each coin.
First, let's calculate the linear speed of the disc:
Linear speed = (2π × radius × rotational speed) / 60
Plugging in the given values:
Linear speed = (2 × π × 15 cm × 33.5 rev/min) / 60
Linear speed ≈ 52.91 cm/min
Now, let's calculate the centripetal force acting on each coin.
The centripetal force is given by the equation:
Centripetal force = mass × (linear speed)^2 / radius
For the first coin at 4 cm from the center:
Centripetal force1 = m × (52.91 cm/min)^2 / 4 cm
For the second coin at 14 cm from the center:
Centripetal force2 = m × (52.91 cm/min)^2 / 14 cm
Now, let's calculate the frictional force between the coins and the disc.
Frictional force = coefficient of friction × normal force
The normal force is given by:
Normal force = mass × gravity
Substituting the values, the frictional force for each coin becomes:
Frictional force1 = (0.5 × m × g)
Frictional force2 = (0.5 × m × g)
Since the normal force (mass × gravity) is the same for both coins, the frictional forces will also be equal.
Now, let's compare the centripetal forces to the frictional forces for each coin.
For the first coin at 4 cm: Centripetal force1 vs. Frictional force1
For the second coin at 14 cm: Centripetal force2 vs. Frictional force2
If the centripetal force is greater than the frictional force, the coin will revolve with the disc. If the centripetal force is smaller than the frictional force, the coin will slip off.
Compare Centripetal force1 with Frictional force1 and Centripetal force2 with Frictional force2 to determine which coin will revolve with the disc.