Final answer:
The acceleration of the system is -6.37 m/s²for mass of 8 kg is resting on a orizontal table with a coefficient of kinetic friction of 0.35. the mass ls connected to a cable that passes over a pulley of mass 3.5 kg and radius 21 cm.
Step-by-step explanation:
To find the acceleration of the system, we need to consider the forces acting on each object in the system.
For the 8 kg mass resting on the table, the gravitational force acting downward is given by Fg = m1 * g, where m1 is the mass and g is the acceleration due to gravity. The normal force, N, exerted by the table on the mass is equal in magnitude and opposite in direction to Fg.
The frictional force, Ff, is given by Ff = μk * N, where μk is the coefficient of kinetic friction.
The net force on the 8 kg mass is given by Fnet = Ff - Fg.
For the hanging mass of 15 kg, the gravitational force acting downward is given by Fg = m2 * g, where m2 is the mass and g is the acceleration due to gravity.
The tension in the cable, T, is the force that pulls the hanging mass upward and is equal in magnitude and opposite in direction to Fg.
The net force on the hanging mass is given by Fnet = T - Fg.
Since the two masses are connected by the same cable, they have the same acceleration, a.
Using Newton's second law, F = m * a, we can set up the following equations:
For the 8 kg mass: Fnet = m1 * a = Ff - Fg
For the hanging mass: Fnet = m2 * a = T - Fg
Substituting the expressions for Ff and T, we have:
m1 * a = μk * N - m1 * g
m2 * a = m2 * g - m2 * g
Simplifying the equations, we have:
m1 * a = μk * N - m1 * g
m2 * a = m2 * g - m2 * g
Since N = m1 * g, we can substitute N with m1 * g in the first equation to get:
m1 * a = μk * m1 * g - m1 * g
Simplifying further, we have:
a = (μk - 1) * g
Substituting the values, a = (0.35 - 1) * 9.8 m/s2
a = -0.65 * 9.8 m/s2
a = -6.37 m/s2
Therefore, the acceleration of the system is -6.37 m/s2.