If the coefficient of kinetic friction is 0.24, how much work do you do when you slide a 55 kg box at constant speed across a 5.4 m -wide room?
work=mg*mu*distance=...
To find out how much work you do when sliding the box, we need to calculate the force exerted and the distance it travels.
First, let's determine the force of friction. The formula for the force of friction is given by:
Frictional Force (Ff) = coefficient of kinetic friction (μ) * normal force (N)
The normal force (N) is the force exerted by a surface to support the weight of an object resting on it. In this case, it is equal to the weight of the box since it is on a horizontal surface. The formula for the weight of an object is given by:
Weight (W) = mass (m) * acceleration due to gravity (g)
Using the given mass of the box (m = 55 kg) and the acceleration due to gravity (g = 9.8 m/s^2), we can calculate the weight:
Weight (W) = 55 kg * 9.8 m/s^2 = 539 N
Since the box is moving at a constant speed, the force of kinetic friction is equal to the force needed to counterbalance it. Therefore, the force of friction (Ff) can be calculated by:
Ff = μ * N
Plugging the given coefficient of kinetic friction (μ = 0.24) and the weight (N) into the equation, we get:
Ff = 0.24 * 539 N = 129.36 N
Now, let's calculate the work done. The formula for work is given by:
Work (W) = force (F) * distance (d) * cos(θ)
Since the box is being moved horizontally, the angle (θ) between the force and the displacement is 0 degrees (cos(0) = 1). Therefore, the equation can be simplified to:
Work (W) = force (F) * distance (d)
Plugging in the calculated force of friction (F) and the given distance (d = 5.4 m), we can calculate the work:
Work (W) = 129.36 N * 5.4 m = 698.78 J
Therefore, when sliding the 55 kg box at a constant speed across the 5.4 m-wide room, the amount of work done is approximately 698.78 Joules.