A force of magnitude 7.50 N pushes three boxes with masses m_1 = 1.30 kg,m_2 = 3.20 kg, and m_3 = 4.90 kg .The mass is side by side.

1-Find the magnitude of the contact force between boxes 1 and 2, and
2-Find the magnitude of the contact force between boxes 2 and 3.

without knowing where the boxes are, it is not possible.

the position is like this:-

7.50N-> |m1|m2|m3|

To find the magnitude of the contact forces between the boxes, we first need to determine the net force acting on each box.

Let's analyze each box individually:

Box 1:
The force of magnitude 7.50 N is the net force acting on box 1 because no other forces are mentioned. Therefore, the magnitude of the contact force between box 1 and box 2 is also 7.50 N. This is because objects in contact with each other exert equal and opposite forces on each other (Newton's third law).

Box 2:
For box 2, there are two forces acting on it - the force from box 1 and the force from box 3. The net force acting on box 2 is the vector sum of these two forces.

The force from box 1 (F₁→) is 7.50 N, acting to the right.

To calculate the force from box 3 (F₃→), we need to consider that boxes 2 and 3 are side by side. Since no information is given about any external forces acting on the system, the two boxes must be in equilibrium.

By applying Newton's second law, we can write the equation for box 3 in the horizontal direction:

F₃→ - F₂→ = 0

Since the two boxes are side by side, the contact force between them (F₂→) must be equal in magnitude but opposite in direction to the force from box 3 (F₃→). Therefore, F₂→ = -F₃→.

So, to find the magnitude of F₃→, we can consider the magnitude of the force exerted by box 3 (m₃ * g) and multiply it by the ratio of the masses:

F₃→ = (m₂ / m₃) * (m₃ * g)

Given m₂ = 3.20 kg and m₃ = 4.90 kg, and assuming g (acceleration due to gravity) is approximately 9.8 m/s², we can calculate F₃→:

F₃→ = (3.20 kg / 4.90 kg) * (4.90 kg * 9.8 m/s²)

Simplify this expression to find the magnitude of the contact force between box 2 and box 3.

Once we have the value of F₃→, we can determine the magnitude of F₂→ by taking its absolute value.

I will now calculate the values.