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
[tex]2F - mg = ma[/tex]
since velocity is constant so acceleration must be ZERO
so here we have
[tex]2F - mg = 0[/tex]
as we know here that
mg = 1000 N
so we will have
[tex]2F - 1000 = 0[/tex]
[tex]F = 500 N[/tex]
so here force must be 500 N
The magnitude of the mover's pulling force is 500 N
[tex]\texttt{ }[/tex]
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.
[tex]\large {\boxed {F = ma }[/tex]
F = Force ( Newton )
m = Object's Mass ( kg )
a = Acceleration ( m )
Let us now tackle the problem !
[tex]\texttt{ }[/tex]
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:
[tex]\Sigma F = ma[/tex]
[tex]T + T - w = ma[/tex]
[tex]2T - w = ma[/tex]
[tex]2T = w + ma[/tex]
[tex]T = ( w + ma ) \div 2[/tex]
[tex]T = ( 1000 + m(0) ) \div 2[/tex]
[tex]T = 1000 \div 2[/tex]
[tex]T = 500 \texttt{ N}[/tex]
[tex]\texttt{ }[/tex]
[tex]\texttt{ }[/tex]
Grade: High School
Subject: Physics
Chapter: Dynamics
