In the following diagram, the hanging mass is 3.5kg, and the box has a mass of 1.5kg. If the force of the box with the surface is 0.80N,

a) find the acceleration of the masses
b)determine the force of tension in the string

The diagram shows a box on a surface and a hanging mass (looks like a pulley system thing)

force on the weight: 3.5g

force pulling box=3.5g
forceretarding box=.8N

net force= total mass * acceleration
3.5g-.8N=(3.5+1.5)a
solve for a

Tension= 3.5(g-a)

To find the acceleration of the masses in the given system, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.

a) To find the acceleration of the masses:
First, we need to determine the net force acting on the system. In this case, the force of tension in the string is pulling the box, and the weight of the hanging mass is pushing it in the opposite direction. Since the box is not accelerating vertically, the sum of the forces in the vertical direction must be zero.

Force of tension in the string = Force of gravity on the hanging mass
Force of tension = m * g
Force of tension = 3.5 kg * 9.8 m/s^2 (acceleration due to gravity)
Force of tension = 34.3 N

The force of tension in the string is equal to the force pushing the box horizontally, which is given as 0.80 N. Therefore, we can equate the force of tension to the force pushing the box and solve for acceleration:

34.3 N = 0.80 N + (mass of the box * acceleration)

Rearranging the equation to solve for acceleration:
acceleration = (34.3 N - 0.80 N) / mass of the box
acceleration = (34.3 N - 0.80 N) / 1.5 kg
acceleration = 33.5 N / 1.5 kg
acceleration = 22.33 m/s^2

Therefore, the acceleration of the masses in the system is 22.33 m/s^2.

b) To determine the force of tension in the string:
The force of tension in the string can be found using the equation:

Force of tension = mass of the hanging mass * acceleration
Force of tension = 3.5 kg * 22.33 m/s^2
Force of tension = 77.855 N

Therefore, the force of tension in the string is 77.855 N.