A girl pushes a wooden box across a floor and exerts 140 N to keep the box moving at constant velocity. If the kinetic coefficient of friction is 0.55, find the mass of the box.

.55 m g = 140

m = 140 /[ .55*9.81 ]

To solve this problem, we can use the equation for the force of friction:

\(F_{friction} = \mu \times F_{normal}\)

where \(F_{friction}\) is the force of friction, \(\mu\) is the kinetic coefficient of friction, and \(F_{normal}\) is the normal force.

In this case, the force of friction is equal to the force applied by the girl, which is 140 N. The normal force is equal to the weight of the box, which we can calculate using Newton's second law:

\(F_{gravity} = m \times g\)

where \(F_{gravity}\) is the weight of the box, \(m\) is the mass, and \(g\) is the acceleration due to gravity (approximately 9.8 m/s^2).

Since the box is moving at constant velocity, the net force on the box is zero. Therefore, we can write the equation:

\(F_{applied} - F_{friction} = 0\)

Substituting the values we know:

\(140 - \mu \times F_{normal} = 0\)

Now, we can substitute \(F_{normal} = F_{gravity}\) into the equation:

\(140 - \mu \times m \times g = 0\)

Finally, we can solve for the mass (\(m\)):

\(m = \frac{140}{\mu \times g}\)

Substituting \(\mu = 0.55\) and \(g = 9.8\ m/s^2\):

\(m = \frac{140}{0.55 \times 9.8}\)

To find the mass of the box, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = ma). Since the box is moving at constant velocity, the acceleration is zero. However, to maintain this constant velocity, the girl needs to exert a force equal to the force of friction.

First, let's find the force of friction. The force of friction can be calculated using the equation:

force of friction = kinetic coefficient of friction * normal force

Here, the normal force is the force exerted by the floor on the box, which is equal to the weight of the box. The weight can be calculated using the equation:

weight = mass * gravity

The value of gravity is approximately 9.8 m/s^2.

Now we can set up the equation:

force of friction = kinetic coefficient of friction * weight

Since the girl needs to exert a force of 140 N to counteract the force of friction, we have:

140 N = kinetic coefficient of friction * weight

Substituting the value of weight, we get:

140 N = kinetic coefficient of friction * (mass * gravity)

Now we can rearrange the equation to solve for the mass:

mass = 140 N / (kinetic coefficient of friction * gravity)

Substituting the given value of the kinetic coefficient of friction (0.55) and gravity (9.8 m/s^2) into the equation, we can calculate the mass:

mass = 140 N / (0.55 * 9.8 m/s^2)

mass ≈ 26.735 kg (rounded to three decimal places)

Therefore, the mass of the box is approximately 26.735 kg.