Three masses sitting on three pulleys,the masses are 5kg,9kg,8kg.the system is in equilibrium,the pulleys are frictionless & massless
Incomplete.
To determine the tensions in the strings connecting the masses, we can set up an equilibrium equation for each mass.
Let's denote T1, T2, and T3 as the tensions in the strings connected to the 5kg, 9kg, and 8kg masses, respectively.
Since the pulleys are frictionless and massless, the tensions on both sides of each pulley will be the same.
For the 5kg mass:
The only force acting on it is the tension T1, pulling upwards. Therefore, T1 = 5kg * g, where g is the acceleration due to gravity (9.8 m/s^2).
For the 9kg mass:
The forces acting on it are the tension T2 pulling downwards and the tension T1 pulling upwards. Since the system is in equilibrium, the net force on the 9kg mass is zero. Therefore, T2 - T1 = 9kg * g.
For the 8kg mass:
The forces acting on it are the tension T2 pulling downwards and the tension T3 pulling upwards. Since the system is in equilibrium, the net force on the 8kg mass is zero. Therefore, T2 - T3 = 8kg * g.
Now we have two equations with two unknowns (T2 and T3):
Equation 1: T2 - T1 = 9kg * g
Equation 2: T2 - T3 = 8kg * g
To solve these equations, we can substitute the value of T1 from the first equation into the second equation:
(9kg * g) - T1 - T3 = 8kg * g
Now we can substitute the value of T1 from the first equation (T1 = 5kg * g) into the second equation:
(9kg * g) - (5kg * g) - T3 = 8kg * g
Simplifying the equation:
4kg * g - T3 = 8kg * g
Rearranging the equation to solve for T3:
T3 = 4kg * g - 8kg * g
T3 = -4kg * g (Note: the negative sign indicates that T3 is pulling in the opposite direction as T2)
Now, substitute the known values to calculate the tension T3:
T3 = -4kg * 9.8 m/s^2
T3 = -39.2 N
Since T3 is negative, we consider it as a positive value (-39.2 N) but pulling in the opposite direction.
Finally, plug the value of T3 (considering the sign) into Equation 1 to solve for T2:
T2 - T1 = 9kg * g
T2 - (5kg * 9.8 m/s^2) = 9kg * 9.8 m/s^2
T2 - 49 N = 88.2 N
T2 = 88.2 N + 49 N
T2 = 137.2 N
Therefore, the tensions in the strings are:
T1 = 5kg * 9.8 m/s^2 = 49 N
T2 = 137.2 N
T3 = -39.2 N (acting in the opposite direction as T2)