Answer:
To determine the maximum speed that the 8.3 kg mass can have without breaking the string, we need to consider the tension in the string when it reaches its maximum. At maximum speed, the tension in the string will be equal to the breaking strength of the string.
Given:
Mass (m) = 8.3 kg
Breaking strength of the string (Tension) = 1500 N
Radius of the circle (r) = 80 cm = 0.8 m
The centripetal force required to keep an object moving in a circular path is given by the formula:
F = m * v² / r
Where:
F = Centripetal force
m = Mass
v = Velocity
r = Radius
In this case, the centripetal force is provided by the tension in the string. So we have:
Tension = m * v² / r
Plugging in the values:
1500 N = (8.3 kg) * v² / 0.8 m
To find the maximum speed (v), we can rearrange the equation and solve for it:
v² = (1500 N * 0.8 m) / 8.3 kg
v² ≈ 144.58 m²/s²
v ≈ √(144.58 m²/s²)
v ≈ 12.03 m/s
Therefore, the maximum speed that the 8.3 kg mass can have without breaking the string is approximately 12.03 m/s.
Step-by-step explanation: