Concept explainers
Children playing pirates have suspended a uniform wooden plank with mass 15.0 kg and length 2.50 m as shown in Figure P14.27. What is the tension in each of the three ropes when Sophia, with a mass of 23.0 kg, is made to “walk the plank” and is 1.50 m from reaching the end of the plank?
FIGURE P14.27
The tension in each of the three ropes when S with mass of
Answer to Problem 27PQ
The tension in rope1 is
Explanation of Solution
The free body diagram is given below.
Here,
At equilibrium, the sum of forces and sum of torques must be zero.
Consider torque about an axis perpendicular to the page and through the left end of the plank.
Write the equilibrium condition for the torque about an axis perpendicular to the page and through the left end of the plank.
Here,
Since forces
Write the expression for the torque due to a force.
Here,
The forces
Write expression for the net torque about an axis perpendicular to the page and through the left end of the plank.
Here,
Write the expression for
Here,
Write the expression for
Here,
Substitute equation (III) and (IV) in (II) to get
Substitute above equation in equation (I) to get expression for
Write the equilibrium condition of the force along
Here,
Write expression for net force along
Here,
Substitute (VII) in (VI) to get
Write the equilibrium condition of the forces along
Here,
Write net forces along
Here,
Substitute (III) and (IV)in (X) to get
Substitute (XI) in (IX) to get
Conclusion:
Substitute
Substitute
Substitute
Therefore, the tension in rope1 is
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