What weight could be supported by a rotating object if it had a mass of 98 grams and if it were revolving in a horizontal circle, 50 cm diameter, and making 240 rev/min?

To determine the weight that could be supported by the rotating object, we need to understand the concept of centripetal force generated due to its circular motion.

The formula to calculate centripetal force is given by:

F = (m * v^2) / r

where:
F is the centripetal force,
m is the mass of the object,
v is the velocity of the object,
r is the radius of the circular path.

In this case, the mass of the object is given as 98 grams, which needs to be converted to kilograms by dividing it by 1000 since there are 1000 grams in 1 kilogram.

m = 98 grams / 1000 = 0.098 kilograms

The radius (r) of the circular path is given as half of the diameter, which is 50 cm. But it needs to be converted to meters since the formula requires that all values be in SI units. There are 100 centimeters in 1 meter.

r = 50 cm / 100 = 0.5 meters

Now, we need to find the velocity (v) of the object. The velocity of an object moving in a circle can be calculated by finding the circumference of the circle and dividing it by the time it takes to complete one revolution. In this case, we are given that the object makes 240 revolutions per minute.

First, we need to convert the time to seconds since the formula requires SI units. There are 60 seconds in 1 minute.

240 rev/min * (1 min / 60 sec) = 4 revolutions per second

Next, we need to find the circumference of the circle. The formula for the circumference of a circle is given by:

C = 2πr

where Pi (π) is a mathematical constant approximately equal to 3.14159.

C = 2 * 3.14159 * 0.5 meters = 3.14159 meters

Finally, we can calculate the velocity (v) by dividing the circumference by the time:

v = C / t

v = 3.14159 meters / 4 seconds = 0.7854 meters/second

Now, we have all the values needed to calculate the centripetal force (F):

F = (m * v^2) / r

F = (0.098 kg * (0.7854 m/s)^2) / 0.5 meters

F = 0.06166 kg * m/s^2

To convert the centripetal force (F) to weight, we need to multiply it by the acceleration due to gravity (g). On Earth, the acceleration due to gravity is approximately 9.8 m/s^2.

Weight = F * g

Weight = 0.06166 kg * m/s^2 * 9.8 m/s^2

Weight = 0.604 kg * m/s^2

Therefore, the weight that could be supported by the rotating object is approximately 0.604 kg * m/s^2.