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A piano technician slides a Steinway grand piano across a level floor at Carnegie Hall. The piano has a mass of 490 kg.
(a) Draw a free-body diagram, and calculate the normal force supporting the piano.

(b) If the coefficient of static friction between the floor and the piano is 0.35, calculate the minimum amount of force needed to get the piano to move.

(c) Once the piano is moving, a horizontal force of 1.1 x 10²N is necessary to keep it moving at a constant speed. Determine the coefficient of kinetic friction.

Respuesta :

okpalawalter8

We have that the normal force is given as [tex]F_N=4802N[/tex],while the minimum amount of force needed to get the piano to move to be [tex]F_f=1680.7N[/tex] and

Coefficient of kinetic friction as [tex]\mu_k=0.23[/tex]

A)  [tex]F_N=4802N[/tex]

B) [tex]F_f=1680.7N[/tex]

C)  [tex]\mu_k=0.23[/tex]

From the question we are told that:

Mass [tex]m=490kg[/tex]

A)

Generally, the equation for normal force  is mathematically given by

[tex]F_N=mg[/tex]

[tex]F_N=(490kg*9.81)[/tex]

[tex]F_N=4802N[/tex]

B)

From the question we are told that:

Coefficient of static friction [tex]\mu=0.35[/tex]

Generally, the equation for Frictional Force  is mathematically given by

[tex]F_f=\mu mg\\\\F_f=4802*0.35[/tex]

[tex]F_f=1680.7N[/tex]

C)

From the question we are told that:

Horizontal force [tex]F_h =1.1 * 10^2 N[/tex]

Generally, the equation for coefficient of kinetic friction  is mathematically given by

[tex]\mu_k=\frac{F_h}{mg}[/tex]

[tex]\mu_k=\frac{1.1 x 10^2}{4802}[/tex]

[tex]\mu_k=0.23[/tex]

Therefore in conclusion

the normal force is given as [tex]F_N=4802N[/tex],while the minimum amount of force needed to get the piano to move to be [tex]F_f=1680.7N[/tex] and

Coefficient of kinetic friction as [tex]\mu_k=0.23[/tex]

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