Final answer:
The magnitude of the stone's centripetal force is calculated using the formula Fc = mv²/r. Given the mass of 0.40 kg, velocity of 4 m/s, and radius of 0.80 m, the centripetal force is determined to be 6.4 Newtons.
Step-by-step explanation:
To determine the magnitude of the stone's centripetal force, we will use the formula for centripetal force, which is Fc = mv²/r, where m is the mass of the object, v is the velocity, and r is the radius of the circular path.
For the given values:
- The mass (m) of the stone is 0.40 kg.
- The constant speed (v) is 4 meters per second.
- The radius (r) of the horizontal circle is 0.80 meter.
Plugging these values into the formula, we get:
Fc = (0.40 kg)(4 m/s)² / 0.80 m
Fc = (0.40 kg)(16 m²/s²) / 0.80 m
Fc = 6.4 N
Therefore, the magnitude of the stone's centripetal force is 6.4 Newtons.