Note: The direction of the acceleration ~a of

the system is given in the figure.
Three masses (17 kg, 21 kg and 67 kg) are
connected by strings. The 67 kg mass slides
on a horizontal surface of a table top and the
17 kg and 21 kg masses hang over the edge of
the surface. The string connecting the 17 kg
and 67 kg masses runs over a massless and
frictionless pulley. The coefficient of sliding
friction, µ, between the 67 kg mass and the
table top is 0.384.
The acceleration of gravity is 9.8 m/s.

Find the magnitude of acceleration of the system.
Answer in units of m/s
2
.

plz help

To find the magnitude of acceleration of the system, we need to analyze the forces acting on the masses.

First, let's consider the 17 kg and 21 kg masses hanging over the edge of the table. These masses experience the force of gravity pulling them downward. The force of gravity can be calculated using the equation F = mg, where m is the mass and g is the acceleration due to gravity.

For the 17 kg mass:
F17 = (17 kg)(9.8 m/s^2) = 166.6 N

For the 21 kg mass:
F21 = (21 kg)(9.8 m/s^2) = 205.8 N

Now, let's consider the 67 kg mass sliding on the horizontal surface of the table. It experiences several forces. The force of gravity acting on it is:

F67 = (67 kg)(9.8 m/s^2) = 656.6 N

There is also a frictional force opposing the motion of the 67 kg mass. The frictional force can be calculated using the equation F_friction = µN, where µ is the coefficient of sliding friction and N is the normal force.

The normal force N is equal to the force of gravity acting perpendicular to the table, which is:

N = F67 = 656.6 N

So, the magnitude of the frictional force is:

F_friction = µN = (0.384)(656.6 N) = 252.3 N

Since the 67 kg mass slides to the right, the net force acting on it is given by:

F_net = F_applied - F_friction

Since we are not given any applied force in the question, we can assume that there is no applied force (F_applied = 0). Therefore, the net force is simply equal to the frictional force:

F_net = F_friction = 252.3 N

Now, let's consider the acceleration of the system. The net force acting on the 67 kg mass is related to its acceleration by the equation F_net = ma, where a is the acceleration.

Therefore, we have:

252.3 N = (67 kg) * a

Rearranging the equation to solve for the acceleration:

a = 252.3 N / (67 kg) = 3.77 m/s^2

So, the magnitude of the acceleration of the system is 3.77 m/s^2.