A 0.104 kg rock is attached to a 1.92 m long string and swung in a horizontal circle at a speed of 29.7 m/s. Find the tension in the string. Neglect the effect of gravity.
To find the tension in the string, we need to consider the centripetal force acting on the rock. The centripetal force is the force directed towards the center of the circular motion that keeps the rock moving in a circular path.
The centripetal force is given by the formula:
F = (m * v^2) / r
Where:
F is the centripetal force
m is the mass of the rock (0.104 kg in this case)
v is the velocity of the rock (29.7 m/s in this case)
r is the radius of the circular motion (1.92 m in this case)
Let's plug in the given values into the formula and calculate the tension:
F = (0.104 kg * (29.7 m/s)^2) / 1.92 m
F = (0.104 kg * 882.09 m^2/s^2) / 1.92 m
F ≈ 478.636 N
Therefore, the tension in the string is approximately 478.636 N.