Final answer:
To find the magnitude of the balancing mass required, calculate the total mass being balanced and use the equation (mass of balancing mass) * (radius of balancing mass) = (total mass being balanced) * (radius of crank). The magnitude of the unbalanced force due to the balancing mass can be found using the equation Force = (mass of balancing mass) * (angular velocity)^2 * (radius of balancing mass). The magnitude of the unbalanced force is 0.55 N.
Step-by-step explanation:
To find the magnitude of the balancing mass required, we first need to calculate the total mass being balanced. The mass of the revolving parts is 100 kg and the mass of 2/3*r*d of the reciprocating parts is 2/3 * 150 kg = 100 kg. So the total mass being balanced is 100 kg + 100 kg = 200 kg.
The balancing mass should be placed opposite to the crank at a radius of 150 mm. To calculate the magnitude of the balancing mass, we can use the equation:
(mass of balancing mass) * (radius of balancing mass) = (total mass being balanced) * (radius of crank).
Plugging in the values, we have:
(mass of balancing mass) * (150 mm) = (200 kg) * (400 mm).
Solving for the mass of the balancing mass, we get:
mass of balancing mass = (200 kg * 400 mm) / (150 mm) = 533.33 kg.
To find the magnitude of the unbalanced force due to the balancing mass, we can use the equation:
Force = (mass of balancing mass) * (angular velocity)^2 * (radius of balancing mass).
Plugging in the values, we have:
Force = (533.33 kg) * (2π / 60)^2 * (150 mm).
Converting the radius to meters and simplifying the equation, we get:
Force = 0.55 N.