Question

A 15-kg child is sitting on a playground teeter-totter, 1.5 m from the pivot. what is the magnitude of the minimum force, applied 0.30 m on the other side of the pivot, that is needed to make the child lift off the ground?

Answer 1

In order to lift the child off the ground, the torque applied on the other side of the pivot must be equal to the torque produced by the child.

The torque of the child around the pivot is:
$\tau=(mg) d$
where m=15 kg is the mass of the child, g is the gravitational acceleration, d=1.5 m is the distance between the child and the pivot. So, we have
$\tau= (15 kg)(9.81 m/s^2)(1.5m)=220.7 Nm$

The torque on the other side of the pivot must be equal:
$\tau = 220.7 Nm$
and in this case, the force is applied at a distance of d=0.30 m from the pivot, therefore the intensity of the force must be
$F= \frac{\tau}{d}= \frac{220.7 Nm}{0.30 m}=735.7 N$

Answer 2

The magnitude of the minimum force is about 735 N

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Further explanation

Let's recall Moment of Force as follows:

$\boxed{\tau = F d}$

where:

τ = 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:

$\tau_{clockwise} = w \times d_c$

$\tau_{clockwise} = mg \times d_c$

$\tau_{clockwise} = ( 15 \times 9.8 ) \times 1.5$

$\tau_{clockwise} = 220.5 \texttt{ Nm}$

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Next, we will find counterclockwise moment by pushing force:

$\tau_{counterclockwise} = F \times d$

$\tau_{counterclockwise} = F \times 0.30$

$\tau_{counterclockwise} = 0.30F \texttt{ Nm}$

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Finally , we could calculate the mininum force as follows:

$\texttt{clockwise moment} = \texttt{counterclockwise moment}$

$220.5 = 0.30F$

$F = 220.5 \div 0.30$

$\boxed{F = 735 \texttt{ N}}$

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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: Moment of Force