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A horizontal force of 40N is needed to pull a 60kg box across the horizontal floor at which coefficient of friction between floor and box? Determine it to three significant figures even through that's quite unrealistic. How much work is done in overcoming friction between the object and floor if the box slides 8m along horizontally on the floor?

Sagot :

Answer:

Coefficient of friction is [tex]0.068[/tex].

Work done is [tex]320~J[/tex].

Explanation:

Given:

Mass of the box ([tex]m[/tex]): [tex]60[/tex] kg

Force needed ([tex]F[/tex]): [tex]40[/tex] N

The formula to calculate the coefficient of friction between the floor and the box is given by

[tex]F=\mu mg...................(1)[/tex]

Here, [tex]\mu[/tex] is the coefficient of friction and [tex]g[/tex] is the acceleration due to gravity.

Substitute [tex]40[/tex] N for [tex]F[/tex], [tex]60[/tex] kg for [tex]m[/tex] and [tex]9.80[/tex] m/s² for [tex]g[/tex] into equation (1) and solve to calculate the value of the coefficient of friction.

[tex]40 N=\mu\times60 kg\times9.80 m/s^{2} \\~~~~~\mu=\frac{40 N}{60 kg\times9.80 m/s^{2}}\\~~~~~~~=0.068[/tex]

The formula to calculate the work done in overcoming the friction is given by

[tex]W=Fd..........................(2)[/tex]

Here, [tex]W[/tex] is the work done and [tex]d[/tex] is the distance travelled.

Substitute  [tex]40[/tex] N for [tex]F[/tex] and [tex]8 m[/tex] for [tex]d[/tex] into equation (2) to calculate the work done.

[tex]W=40~N\times8~m\\~~~~= 320~J[/tex]

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