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Chapter 9: Q4 PE (page 316)

Use the second condition for equilibrium(net τ=0)to calculateFPinExample 9.1, employing any data given or solved for in part (a) of the example.

Short Answer

Expert verified

The calculated force is FP=568N.

Step by step solution

01

Given data

  • The mass is,m1=26kg.
  • The distance from the hinge is,r1=1.60m.
  • The mass of the other is, m2=32kg.
  • The distance of the other from the hinge is,r2=1.30m.
02

Introduction of force

When the system is in equilibrium, the net force acting on a body will be equal to zero. In other words, the forces will balance each other, and the system will remain in equilibrium as long as no external disturbance is there.

03

Calculation of the force

The net torque is zero; we can write the equation as,

∑τ=0FP×r1-W2r1+r2=0Fp×r1-m2gr1+r2=0

Here g is the gravitational acceleration.

Substitute the values in the above expression, and we get,

FP×1.60=32×9.8×1.60+1.30FP=32×9.8×1.60+1.301.60FP=568N

Hence, the force isFP=568N.

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Most popular questions from this chapter

A sandwich board advertising sign is constructed as shown inFigure\({\rm{9}}{\rm{.35}}\). The sign’s mass is \({\rm{8}}{\rm{.00}}\;{\rm{kg}}\). (a) Calculate the tension in the chain assuming no friction between the legs and the sidewalk. (b) What force isexerted by each side on the hinge?

Suppose you pull a nail at a constant rate using a nail puller as shown inFigure 9.23. Is the nail puller in equilibrium? What if you pull the nail with some acceleration – is the nail puller in equilibrium then? In which case is the force applied to the nail puller larger and why?

Two children of mass \({\rm{20}}\;{\rm{kg}}\)and \({\rm{30}}\;{\rm{kg}}\) sit balanced on a seesaw with the pivot point located at the center of the seesaw. If the children are separated by a distance of \({\rm{3}}\;{\rm{m}}\), at what distance from the pivot point is the small child sitting in order to maintain the balance?

Figure \({\rm{9}}{\rm{.1}}\)

When opening a door, you push on it perpendicularly with a force of 55.0 N at a distance of 0.850 m from the hinges. What torque are you exerting relative to the hinges? (b) Does it matter if you push at the same height as the hinges?

Repeat the seesaw problem in Example 9.1 with the center of mass of the seesaw \({\rm{0}}{\rm{.160}}\;{\rm{m}}\) to the left of the pivot (on the side of the lighter child) and assuming a mass of \({\rm{12}}{\rm{.0}}\;{\rm{kg}}\) for the seesaw. The other data given in the example remain unchanged. Explicitly show how you follow the steps in the Problem-Solving Strategy for static equilibrium
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