Two boxes with different masses are tied together on a frictionless ramp surface. what is the tension in each of the cords?

When we look at the forces acting on the boxes, all forces acting verticaly are irrelevant.

Horizantal forces acting on the body are T and mgx

However tension cannot be found with the above information included.

This question involves the concepts of the law of conservation of energy and the equations of motion.

The work done by the friction on the block as it slides down the ramp is "0.51 J".

First, we will find the time taken for the motion using the second equation of motion in the vertical direction:

where,

h = vertical distance covered by the block = 40 mm = 0.04 m

vi = initial speed in vertical direction = 0 m/s

t = time taken = ?

g = acceleration due to gravity = 9.81 m/s^2

Therefore,

Now, we will consider the horizontal motion. Since horizontal motion is uniform due to no friction. Therefore,

where,

s = horizontal distance covered by the block = 30 mm = 0.03 m

v = final horizontal speed = ?

Therefore,

v = 0.333 m/s

Now, we apply the law of conservation of energy to this scenario:

here,

W = work done by friction = ?

h = height of slide = 23 mm = 0.023 m

m = mass of block = 3 kg

Therefore,

W = 0.677 J - 0.167 J

W = 0.51 J = 510 mJ

Learn more about the law of conservation of energy here:

link

The attached picture explains the law of conservation of energy.