Sheet no.4 Page 1 of 3

Faculty Of Engineering 1st Year Engineering Mechanics

Sheet 4 Problems on Reduction of system of forces

1. A piece of sheet metal is bent into the shape shown and is acted upon by three forces. If the forces have the same magnitude P, replace them with an equivalent wrench and determine;

a) The magnitude and the direction of the resultant force R,

b) The pitch of the wrench,

c) The axis of the wrench.

2. The forces and couples shown a re applied to two screws as a piece of sheet metal is fastened to a block of wood. Reduce the forces and the couples to an equivalent wrench and determine;

a) The resultant force R

b) The pitch of the wrench

c) The point where the axis of the wrench intersects the XZ plane.

3. Three children are standing on a 5X5 m raft. If the weights of the children at points A, B, and C are 375 N, 260N, and 400N, respectively, determine the magnitude and the point of application of the resultant of the three weights.

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4. Three workers trying to move a 3 X 3 X 4 ft crate apply to the crate the three horizontal forces shown.

a) If P= 60 lb replace the three forces with an equivalent force-couple system at A.

b) Replace the force-couple system of part a with a single force and determine where it should be applied to side AB.

c) Determine the magnitude of P so that the three forces can be replaced with a single equivalent force applied at B.

5. Three cables are attached to a bracket as shown in figure ,

a) Replace the forces exerted by the cables with an equivalent force-couple system at A

b) Find the pitch of the wrench

c) Find the axis of the wrench.

Problems on Equilibrium of Rigid bodies

6. The maximum allowable value of each of the reactions is 180 N. neglecting the weight of the beam determine the range of the distance d for which the beam is safe.

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7. A hand truck is used to move two barrels, each of mass 40 Kg. Neglecting the mass of the hand truck, determine;

a) The vertical force P which should be applied to the handle to maintain equilibrium when α =35o

b) The corresponding reaction at each of the two wheels.

8. The bracket BCD is hinged at C and attached

to a control cable at B. for the loading shown, determine;

a) The tension in the cable,

b) The reaction at C.

9. Determine the tension in each cable and the reaction at D

10. A slender rod AB of weight W is attached to blocks A and B which move freely in the guide shown. The constant of the spring is K and the spring is unstretched when = 0 a) neglecting the weight of the blocks, derive an equation in W, K, L and which must be satisfied when the rod is in equilibrium. b) determine the value of when W= 300 N, L= 0.75 m, and K= 480 N/m.