# A piano of mass 224kg rests on a level floor, where the coefficient of static friction is 0.35 and the coefficient of kinetic friction is 0.18. What is the minimum horizontal force needed to begin...

A piano of mass 224kg rests on a level floor, where the coefficient of static friction is 0.35 and the coefficient of kinetic friction is 0.18. What is the minimum horizontal force needed to begin sliding the piano along the floor? If this minimum force is used and the piano begins to slide, what will its initial acceleration be?

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The piano will start sliding when the applied force is equal to or greater than the force of static friction, that is the applied force is sufficient enough to overcome the friction. This means

Fmin = Fr-stat = `mu_s`N = `mu_s` mg

where m is the mass of piano, g is acceleration due to gravity and `mu_s` is the coefficient of static friction.

Substituting the values, we get Fmin = 0.35 x 224 x 9.8 = **768.32 N**

If this much force is applied, the acceleration can be determined by balancing the forces as:

Fmin - Fr-kin = Fnet = ma

where Fr-kin is the force of kinetic friction and a is the acceleration of the piano. The minimum force tends to push the piano, while the kinetic friction opposes this motion.

thus, `mu_s mg - mu_k mg = ma`

or, a = `(mu_s - mu_k)g`

or, a = (0.35- 0.18) x 9.8 = **1.666 m/s^2**.

Hope this helps.

The piano will start sliding when the applied force is equal to or greater than the force of static friction, that is the applied force is sufficient enough to overcome the friction. This means, Fmin = Fr-stat = mu_sN = mu_s mg where, m is the mass of piano, g is acceleration due to gravity and mu_s is coefficient of static friction. Substituting the values, we get, Fmin = 0.35 x 224 x 9.8 = 768.32 N If this much force is applied, the acceleration can be determined by balancing the forces as: Fmin - Fr-kin = kinetic friction and a is the acceleration of the piano. The minimum force tends to push the piano, while the kinetic friction opposes this motion. thus, mu_s mg - mu_k mg = ma or, a = (mu_s - mu_k)g or, a = (0.35- 0.18) x 9.8 = 1.666 m/s^2. Hope this helps.