A 0.60 kg sphere rotates around a vertical shaft supported by two strings, as shown. If the tension in the upper string is 18 N. Calculate
the tension in the lower string?
the rotation rate (in rev/min) of the system?
1rad/s
To calculate the tension in the lower string, we can use the fact that the sphere is in equilibrium, meaning that the net force acting on it must be zero. In this case, the tension in both strings and the weight of the sphere contribute to the net force.
First, let's consider the forces acting on the sphere:
1. Tension in the upper string (T1): 18 N (given in the question)
2. Tension in the lower string (T2): unknown
3. Weight of the sphere (mg): When an object is in equilibrium, the weight is equal to mg, where m is the mass of the object and g is the acceleration due to gravity. In this case, m = 0.60 kg and g = 9.8 m/s^2.
Since the sphere is rotating in a circle, the net force acting on it is equal to the centripetal force:
T1 + T2 - mg = m * (v^2 / r)
where v is the linear velocity of the sphere and r is the radius of the circular path. Since we're not given those values, we cannot directly calculate the tension in the lower string.
However, we can use the fact that the sphere is in equilibrium to determine the net torque acting on it. The net torque should be zero since the sphere is not rotating faster or slower than it is at that moment.
The torque generated by the tension in the upper string is given by:
τ1 = T1 * r
where r is the distance between the shaft and the point where the upper string is attached.
Similarly, the torque generated by the tension in the lower string is:
τ2 = T2 * r
Since the sphere is in equilibrium, the net torque is zero:
τ1 + τ2 = 0
Substituting the values into the equation:
(T1 * r) + (T2 * r) = 0
From this equation, we can see that T2 must be equal in magnitude but opposite in direction to T1. This means that the tension in the lower string is also 18 N.
Next, let's calculate the rotation rate of the system. The rotation rate is typically measured in rev/min (revolutions per minute). Since the sphere is attached to the shaft, it will rotate at the same rate as the shaft.
To calculate the rotation rate, we need to know the time it takes for one full revolution. However, that information is not provided in the question. Without the time value, we cannot directly calculate the rotation rate in rev/min.