Answered: Both girls arrive at the same time at…

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter10: Fixed-axis Rotation

Section: Chapter Questions

Problem 117AP: Two children push on opposite sides of a door during play. Both push horizontally and perpendicular...

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Question

Both girls arrive at the same time at opposite sides of a door that can swing open in both directions. Without either of them knowing that someone is on the other side, Carly pushes with a force of 1,000-N at a 60° angle 40-cm from the hinge, while Delaney pushes perpendicularly with a force of 650-N 65-cm from the hinge. In which direction does the door open? Demonstrate and explain.

Expert Solution

Step 1

The estimation of torque for each person will give the answer.

The expression for torque is,

$\begin{matrix} \vec{τ} = \vec{r} \times \vec{F} \\ | τ | = | r | | F | \sin θ \end{matrix}$

Here, $τ$ is the torque, r is the radius, F is the force and $θ$ is the angle between the radius and force.

For girl 1, the given data is,

Force, $F_{1} = 1000 N$

Radius, $r_{1} = 40 cm = 0.40 m$

Angle, $θ_{1} = 60^{0}$

For girl 2, the given data is,

Force, $F_{2} = 650 N$

Radius, $r_{2} = 65 cm = 0.65 m$

Angle, $θ_{2} = 90^{0}$

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