A box of mass 50.0 kg is connected to a second box with a mass of 54.0 kg. Both are sitting on a horizontal surface and the coefficient of kinetic friction between the surface and each box is 0.51. If the second box is pulled away from the first box with a force of 605.8 N, find the magnitude of the tension in the string between the two boxes.

To find the magnitude of tension in the string between the two boxes, we need to analyze the forces acting on each box separately.

First, let's consider the box with a mass of 50.0 kg. The only horizontal force acting on this box is the tension force in the string. According to Newton's second law, the net force on an object is equal to its mass multiplied by its acceleration:

Net force = mass * acceleration

Since the box is not accelerating horizontally (it is stationary), the net force acting on it is zero. Therefore, the tension force in the string is equal in magnitude but opposite in direction to the force of kinetic friction:

Tension force = Frictional force 1

The frictional force can be calculated using the formula:

Frictional force = coefficient of kinetic friction * normal force

where the normal force is equal to the weight of the box (mass * gravitational acceleration).

Next, let's consider the box with a mass of 54.0 kg. The net force on this box is the force applied to it minus the tension force (since the boxes are connected), which gives us:

Net force = Applied force - Tension force

Since this box is moving horizontally, the net force is equal to the product of its mass and acceleration:

Net force = mass * acceleration

By rearranging the equation, we can solve for the tension force:

Tension force = Applied force - mass * acceleration

Now, let's calculate the tension force step-by-step.

1. Calculate the frictional force on the box with a mass of 50.0 kg:
Frictional force 1 = coefficient of kinetic friction * normal force
Frictional force 1 = 0.51 * (50.0 kg * 9.8 m/s^2)

2. Calculate the tension force using the equation: Tension force = Frictional force 1
Tension force = Frictional force 1

3. Calculate the acceleration of the box with a mass of 54.0 kg:
Net force = mass * acceleration
Net force = Applied force - Tension force
mass * acceleration = Applied force - Tension force
acceleration = (Applied force - Tension force) / mass

4. Substitute the given values into the equation to find the tension force:
acceleration = (605.8 N - Tension force) / 54.0 kg
Solve for Tension force.

By following these steps, you can find the magnitude of the tension in the string between the two boxes.

To find the magnitude of tension in the string between the two boxes, we need to analyze the forces acting on the system.

Let's start by considering the first box, which has a mass of 50.0 kg. The gravitational force acting on it is given by the equation:

F_gravity = m1 * g

where m1 is the mass of the first box, and g is the acceleration due to gravity (approximately 9.8 m/s^2).

F_gravity = 50.0 kg * 9.8 m/s^2 = 490.0 N

Next, we need to consider the second box. It has a mass of 54.0 kg, so the gravitational force acting on it is:

F_gravity = m2 * g

F_gravity = 54.0 kg * 9.8 m/s^2 = 529.2 N

Now, let's analyze the forces acting horizontally on the system. The force of friction opposes the motion and is given by:

F_friction = coefficient of friction * normal force

The normal force is equal to the gravitational force:

F_friction = 0.51 * (F_gravity1 + F_gravity2)

F_friction = 0.51 * (490.0 N + 529.2 N)

F_friction = 507.09 N

Finally, the tension force in the string can be found by subtracting the force of friction from the applied force:

Tension = Applied force - Force of friction

Tension = 605.8 N - 507.09 N

Tension = 98.71 N

Therefore, the magnitude of the tension in the string between the two boxes is 98.71 N.