A mobile is constructed from a thin rod of mass 50 g and length 50 cm. Two hanging masses are positioned at each end of the rod. The mass of one of the hanging masses is 100 g. What must be the mass of the other hanging mass so that the mobile is in static equilibrium with the rod horizontal? The whole assembly hang from a ceiling support with a cord attached at the rod's center. What is the tension in the suspension cord?
To find the mass of the other hanging mass, we need to consider the condition for static equilibrium. In this case, the mobile will be in static equilibrium if the net torque acting on it is zero and the net force acting on it is also zero.
First, let's calculate the torque. Torque is calculated as the product of the force and the lever arm (the perpendicular distance from the force to the pivot point). In this case, the pivot point is the center of the rod.
The weight of the rod can be assumed to act at its center, so it will not contribute to the torque. The tension in the suspension cord will provide a clockwise torque, while the hanging masses will provide a counterclockwise torque.
Let's denote the mass of the other hanging mass as 'm.'
The torque due to the tension in the suspension cord is calculated as T * (length of the rod / 2), as it acts at the center. Here, T represents the tension.
The torque due to the hanging masses is calculated as m * g * (length of the rod / 2), as they act at the ends of the rod. Here, g represents the acceleration due to gravity.
For static equilibrium, the sum of the clockwise and counterclockwise torques must be equal.
Therefore, T * (length of the rod / 2) = m * g * (length of the rod / 2)
Canceling out the common factors and rearranging the equation, we get:
T = m * g
Now, to find the mass of the other hanging mass, we can substitute the values we know into this equation.
m * g = 0.05 kg * 9.8 m/s^2 (converting the mass to kg and using the acceleration due to gravity)
Simplifying, we find:
m ≈ 0.049 kg
Therefore, the mass of the other hanging mass should be approximately 49 g.
To calculate the tension in the suspension cord, we can use the equation we derived earlier:
T = m * g
Plugging the value of 'm' and the acceleration due to gravity into the equation:
T = 0.049 kg * 9.8 m/s^2
Simplifying, we find:
T ≈ 0.48 N
Therefore, the tension in the suspension cord is approximately 0.48 Newtons.