Two masses are connected by a light cord over a frictionless pulley. is M1 = 8.5kg and m2 = 6.6 kg. calculate the tension in the cable (in N) . Take the coefficient of kinetic friction between M and the horizontal surface to be 0.4 and asume the acceleration to be due to gravity to be 9.81 m&s
To calculate the tension in the cable, we need to consider the forces acting on the masses.
First, let's find the acceleration of the system using Newton's second law: F = ma.
The only force acting on M1 is the tension in the cable, T. The force acting on M2 is the force of gravity acting downwards (m2 * g), minus the force of kinetic friction (μ * m2 * g), where μ is the coefficient of kinetic friction and g is the acceleration due to gravity.
Since both masses are connected by the same cord, they have the same acceleration. So we can write:
m2 * g - μ * m2 * g = (M1 + m2) * a
Now we can substitute the given values:
(6.6 kg * 9.81 m/s^2) - (0.4 * 6.6 kg * 9.81 m/s^2) = (8.5 kg + 6.6 kg) * a
Simplifying the equation:
(6.6 kg * 9.81 m/s^2) - (0.4 * 6.6 kg * 9.81 m/s^2) = 15.1 kg * a
(64.686 N) - (25.34304 N) = 15.1 kg * a
39.34296 N = 15.1 kg * a
Now we solve for acceleration, a:
a = 39.34296 N / (15.1 kg)
a ≈ 2.6096 m/s^2
Since both masses are connected by a light cord over a frictionless pulley, the tension in the cable is the same as the force of gravity acting on M1:
T = M1 * g
Substituting the given values:
T = 8.5 kg * 9.81 m/s^2
T ≈ 83.235 N
Therefore, the tension in the cable is approximately 83.235 Newtons.