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Amirah and Dana want to move the piano in their living room. Amirah pushes from behind with a force of 300 N and Dana pulls from the front using a rope with a force of 200 N. The piano has a mass of 180 N and the friction force of the floor and the piano is 230 N Calculate the acceleration of the piano. Round your answer to the nearest tenth.

Sagot :

MrRoyal

The force acting on an object is the product of mass and the object's acceleration.

The acceleration of the piano is 15.0m/s^2

Given that:

[tex]F_A = 300N\\[/tex]-- Amirah

[tex]F_D =200N[/tex] -- Dana

[tex]F_f = -230N[/tex] --- the frictional force

[tex]W = 180N[/tex] --- the piano's weight

First, we calculate the net force pushing the piano

[tex]F = F_A + F_D + F_f[/tex]

So, we have:

[tex]F = 300N + 200N -230N[/tex]

[tex]F = 270N[/tex]

Next, we calculate the mass of the piano

[tex]W = mg[/tex]

Make m the subject

[tex]m = \frac Wg[/tex]

So, we have:

[tex]m = \frac{180}{10}[/tex]

[tex]m = 18[/tex]

The force acting on an object is calculated as:

[tex]F = ma[/tex]

Substitute values for F and m

[tex]270 = 18 \times a[/tex]

Divide through by 18

[tex]15 = a[/tex]

[tex]a = 15[/tex]

Hence, the acceleration of the piano is 15.0m/s^2

Read more about force and acceleration at:

https://brainly.com/question/20511022

The acceleration is a transition in an object's motion or speed over a time. It can be determined by splitting the velocity change so over total time. In brief, it is a percentage at which speed changes over time, to regard to direction and speed.

Given:

Force apply by Amirah [tex]\bold{F_A = 300\ N}[/tex]

Force apply by  Dana [tex]\bold{ F_D=200\ N}[/tex]

Frictional force [tex]\bold{ F_f=-230\ N}[/tex]

Weight of piano [tex]\bold{W=180\ N}[/tex]

Calculating all the forces:

[tex]\to \bold{F=F_A+F_D+F_f}[/tex]

         [tex]\bold{=300N+200N-230N}\\\\ \bold{=500N-230N}\\\\ \bold{=270N}[/tex]

Calculating the weight of piano:

[tex]\to \bold{W=mg} \\\\\to \bold{m=\frac{W}{g}}\\\\\to \bold{m=\frac{180}{10}=18}[/tex]

Calculating the force which is apply on the object:

[tex]\to \bold{F=ma}[/tex]

[tex]\to \bold{270=18 \times a}\\\\ \to \bold{a=\frac{270}{18}}\\\\ \to \bold{a=15 \ \frac{m}{s^2}}\\\\[/tex]

Therefore the, the acceleration of the piano is [tex]\bold{15.0\ \frac{m}{s^2}}[/tex]

Learn more:

brainly.com/question/4514563  

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