The magnitude of the minimum force is about 735 N
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Let's recall Moment of Force as follows:
[tex]\boxed{\tau = F d}[/tex]
where:
Ï„ = moment of force ( Nm )
F = magnitude of force ( N )
d = perpendicular distance between force and pivot ( m )
Let us now tackle the problem !
Given:
mass of child = m_c = 15 kg
distance between pivot and child = d_c = 1.5 m
distance between force and pivot = d = 0.30 m
Asked:
magnitude of force = F = ?
Solution:
Firstly , we will find clockwise moment by weight of the child:
[tex]\tau_{clockwise} = w \times d_c[/tex]
[tex]\tau_{clockwise} = mg \times d_c[/tex]
[tex]\tau_{clockwise} = ( 15 \times 9.8 ) \times 1.5[/tex]
[tex]\tau_{clockwise} = 220.5 \texttt{ Nm}[/tex]
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Next, we will find counterclockwise moment by pushing force:
[tex]\tau_{counterclockwise} = F \times d[/tex]
[tex]\tau_{counterclockwise} = F \times 0.30[/tex]
[tex]\tau_{counterclockwise} = 0.30F \texttt{ Nm}[/tex]
[tex]\texttt{ }[/tex]
Finally , we could calculate the mininum force as follows:
[tex]\texttt{clockwise moment} = \texttt{counterclockwise moment}[/tex]
[tex]220.5 = 0.30F[/tex]
[tex]F = 220.5 \div 0.30[/tex]
[tex]\boxed{F = 735 \texttt{ N}}[/tex]
[tex]\texttt{ }[/tex]
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Grade: High School
Subject: Physics
Chapter: Moment of Force
