Question

A piano mover raises a 1000-n piano at a constant speed using a very light rope in a frictionless pulley system, as shown in the figure. with what force is the mover pulling down on the rope?

Answer 1

The magnitude of the mover's pulling force is 500 N

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Further explanation

Newton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.

$\large {\boxed {F = ma }$

F = Force ( Newton )

m = Object's Mass ( kg )

a = Acceleration ( m )

Let us now tackle the problem !

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Given:

weight of piano = w = 1000 N

acceleration of piano = a = 0 m/s² → constant speed

Asked:

magnitude of the pulling force = T = ?

Solution:

Firstly , we will draw the free body diagram as shown in the attachment.

Next , we will calculate the pulling force by using Newton's Law of Motion as follows:

$\Sigma F = ma$

$T + T - w = ma$

$2T - w = ma$

$2T = w + ma$

$T = ( w + ma ) \div 2$

$T = ( 1000 + m(0) ) \div 2$

$T = 1000 \div 2$

$T = 500 \texttt{ N}$

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Learn more

• Impacts of Gravity : brainly.com/question/5330244
• Effect of Earth’s Gravity on Objects : brainly.com/question/8844454
• The Acceleration Due To Gravity : brainly.com/question/4189441
• Newton's Law of Motion: brainly.com/question/10431582
• Example of Newton's Law: brainly.com/question/498822

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Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics

Answer 2

Here As we can see the figure that the end of the rope is pulled by some force F

Now as we can see that Piano is connected by a pulley which is passing over the pulley so effectively net force on the piano upwards will be 2F as it is connected by 2 ropes by the pulley

Now for constant velocity of the piano we will say

$2F - mg = ma$

since velocity is constant so acceleration must be ZERO

so here we have

$2F - mg = 0$

as we know here that

mg = 1000 N

so we will have

$2F - 1000 = 0$

$F = 500 N$

so here force must be 500 N