How much work must be done to roll a metal safe, mass 116 kg, a distance of 15.0 m across a level floor? The coeffecient of friction is 0.050.

Work = Force * distance = m g mu X

Just multiply your three numbers together, along with g = 9.8 m/s^2. The answer will be in Joules.
"mu" is the coefficient of friction (0.05). It should be the Greek lower case letter, but I can't type it here.

852.6J

To calculate the work required to roll a metal safe across a level floor, we need to consider two components: the work done against gravity and the work done against friction.

First, let's determine the work done against gravity. We will assume that the safe is being rolled horizontally, so there is no vertical displacement. The work done against gravity is given by the formula:

Work_gravity = m * g * h

where m is the mass of the safe (116 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the vertical displacement (which is zero in this case).

Since there is no vertical displacement in this scenario, the work done against gravity is zero.

Next, let's calculate the work done against friction. The formula for work done against friction is:

Work_friction = μ * m * g * d

where μ is the coefficient of friction (0.050), m is the mass of the safe (116 kg), g is the acceleration due to gravity (9.8 m/s^2), and d is the horizontal distance (15.0 m).

Substituting the given values into the formula, we have:

Work_friction = 0.050 * 116 kg * 9.8 m/s^2 * 15.0 m

Simplifying this equation gives us:

Work_friction = 84.84 J (rounded to two decimal places)

Therefore, the work required to roll the metal safe a distance of 15.0 m across a level floor is approximately 84.84 Joules.