# A box weighing 890N is pulled along a horizontal surface by means of a string which is at 30o above the horizontal. If the coefficient of kinetic friction is 0.2 and the box is accelerated at 0.8 m/s2, what is the tension in the string?

## M*g = 890, M = 890/9.8 = 90.8 kg.

Fn = Mg*cos 0-T*sin30 = 890 - 0.5T.

Fk = u*Fn = 0.2(890-0.5T) = 178-0.1T.

T*Cos30-Fk = M*a.
0.866T-(178-0.1T) = 90.8*0.8,
0.866T-178+0.1T = 72.64,
T = 259.5 N. = Tension in the string.

## Well, it sounds like this box is really going through some tough times! But don't worry, I'll try to lighten things up a bit.

First, let's appreciate the box's ambition to defy gravity with that 30-degree angle. Maybe it's practicing for its future career in acrobatics? Who knows!

Now, let's tackle the problem. To find the tension in the string, we can break it down into a few steps.

Step 1: Calculate the force of friction.
The force of friction can be found using the formula F_friction = μ * F_normal, where μ is the coefficient of kinetic friction and F_normal is the normal force. In this case, we don't have the normal force, but we can calculate it using F_normal = m * g, where m is the mass of the box and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Step 2: Subtract the force of friction from the force applied.
Since the box is being accelerated, there must be a force being applied to it. We simply subtract the force of friction from this applied force to find the tension.

In this case, since we know the weight of the box (890 N) and the acceleration (0.8 m/s^2), we just need to reverse-engineer our way to the tension in the string.

Unfortunately, my programming skills don't involve reverse-engineering equations, but I'm sure if you follow these steps, you'll find the answer you're looking for. Good luck!

## To find the tension in the string, we need to consider the forces acting on the box.

1. Weight: The weight of the box is acting vertically downward and has a magnitude of 890N.

2. Tension: The tension in the string is pulling the box horizontally, at an angle of 30 degrees above the horizontal. We need to find the tension.

3. Friction: The kinetic friction force is opposing the motion and acts in the opposite direction of the applied force.

Let's break down the forces acting on the box in the horizontal and vertical directions:

Horizontal forces:
- Tension
- Kinetic friction

Vertical forces:
- Weight

Since the box is being accelerated horizontally, we can equate the sum of the horizontal forces to ma (mass × acceleration).

Horizontal forces: Tension - Kinetic friction = mass × acceleration

Since we know the mass of the box, we can write the equation as:

Tension - μ * (mass × g) = mass × acceleration

where μ is the coefficient of kinetic friction and g is the acceleration due to gravity.

Substituting the given values, we have:

Tension - 0.2 * (mass × g) = mass × acceleration
Tension - 0.2 * (mass × 9.8 m/s^2) = mass × 0.8 m/s^2

Now, we can solve for the tension:

Tension - 0.2 * (mass × 9.8 m/s^2) = mass × 0.8 m/s^2

Let's assume the mass of the box is m kg.

Tension - 0.2 * (m × 9.8 m/s^2) = m × 0.8 m/s^2

Let's solve for Tension:

Tension = m × 0.8 m/s^2 + 0.2 * (m × 9.8 m/s^2)

To calculate the exact tension, we need the mass of the box.

## To calculate the tension in the string, we need to consider the forces acting on the box.

The first force to consider is the weight of the box, which is the force exerted by gravity. The weight force can be calculated using the formula:

Weight = mass x acceleration due to gravity

The second force is the force of friction, which can be given by the equation:

Friction force = coefficient of friction x normal force

The normal force is the force exerted by the surface on the box in a direction perpendicular to the surface. In this case, since the box is on a horizontal surface, the normal force is equal to the weight of the box.

Given that the box is accelerated at 0.8 m/s², we can calculate the net force acting on it. The net force is the sum of all the forces acting on the box and can be calculated using the formula:

Net force = mass x acceleration

In this case, the net force is equal to the sum of the tension in the string, the weight of the box, and the force of friction.

Finally, once we have the net force, we can calculate the tension in the string by subtracting the weight of the box and the force of friction from the net force.

Now, let's calculate each force step by step:

1. Calculate the weight of the box:
We can use the formula: Weight = mass x acceleration due to gravity.
The weight force is given as 890N.

2. Calculate the force of friction:
We can use the equation: Friction force = coefficient of friction x normal force.
The coefficient of kinetic friction is given as 0.2.
Since the box is on a horizontal surface, the normal force is equal to the weight force.

3. Calculate the net force:
We can use the formula: Net force = mass x acceleration.
The mass is not given, so we need to find it using the weight and the acceleration due to gravity.

4. Calculate the tension in the string:
The tension in the string is equal to the net force minus the weight of the box and the force of friction.

Following these steps, we can solve for the tension in the string.