Question

Calculate the mass of an object if it took 20 N to rotate it in

a circle with a radius of 2 meters with a velocity of 4 m/s?

Answer 1

To find the mass of the object using the given force, velocity, and radius, one can apply the centripetal force formula, resulting in a calculated mass of 2.5 kg.

Step-by-step explanation:

To calculate the mass of an object based on the force needed to rotate it in a circle, we can use the formula for centripetal force, which is F = m × v^2 / r. In this formula, F is the centripetal force, m is the mass of the object, v is the tangential velocity, and r is the radius of the circle. Given that the force (F) is 20 N, the velocity (v) is 4 m/s, and the radius (r) is 2 meters, rearranging the formula to solve for mass (m) gives us m = F × r / v^2.

Substituting the given values, we have:
m = 20 N × 2 m / (4 m/s)^2
m = 40 N×m / 16 m^2/s^2
m = 2.5 kg

Therefore, the mass of the object is 2.5 kg.

Answer 2

The mass of the object being rotated in a circle with a given force, velocity, and radius is calculated using the centripetal force formula. The centripetal acceleration is found first, and then the mass is deduced from the force and acceleration, resulting in a mass of 2.5 kg.

Step-by-step explanation:

To calculate the mass of the object that is being rotated in a circle, we can use the formula for centripetal force, which is F = m × ac, where F is the force, m is the mass, and ac is the centripetal acceleration. The centripetal acceleration can be calculated using the formula ac = v² / r, where v is the velocity and r is the radius of the circular path.

In this case, the force F is 20 N, the velocity v is 4 m/s, and the radius r is 2 meters.

First, calculate the centripetal acceleration: ac = (4 m/s)² / 2 m = 16 m²/s² / 2 m = 8 m/s². Next, use the centripetal force formula to find the mass: 20 N = m × 8 m/s². Solving for m, we find m = 20 N / 8 m/s² = 2.5 kg.

Therefore, the mass of the object is 2.5 kg.