

Conditions for Static Equilibrium
Worksheet 1  Questions on Static Equilibrium
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1. An object of mass, M, is suspended between a block of mass 10kg and a wall by a string which makes and angle of 30°with the vertical. The coefficient of friction between the table top and the block is 0.5. What is the maximum weight that can be suspended?

Fig 1. 

2. A leaf of mass 1 gram hangs on a rafter by a spider's thread as in fig 2b. The wind blows horizontally and the thread makes an angle of 20° with the vertical. Calculate (a) the tension on the thread and (b) the force of the wind on the leaf.

Fig 2a. 

3. A flower pot of mass 8kg is hung from two wires as show in in fig 3a. Find the tension in each wire.

Fig 3a. 

4. Several men with a combined strength of 4000N pull horizontally on a girder of mass 5000kg suspended from a crane. Assuming that the rope stays horizontal during the operation, What is the maximum angle, θ, that the bean can be shifted?

Fig 4a. 

5. A 3m ladder having a uniform density and a mass 30kg rests against a frictionless vertical wall at an angle of 30°. The lower end rests on a flat surface where the coefficient of static friction is µ = 0.40. A painter with a mass M = 60kg is at the middle of the ladder. At what point in his journey up the ladder will it begin to slip?

Fig 5.1. 
Answer 


6. The system in Fig. 6.1 is in equilibrium with the string in the center exactly horizontal.
Find (a) tension T_{L}, (b) tension T_{h}, (c) tension T_{r} and (d) angle θ.

Fig 6.1. 

7. The crane in Fig. 7.1 is in equilibrium. A ball of mass 225 kg hangs from the end of the uniform strut whose mass is 50.0 kg.
Find (a) the tension T^{c} in the cable and the (b) horizontal and (c) force exerted on the strut by the hinge.

Fig 7.1. 

8. The stepladder shown in Fig. 8.1, has sides AC and CE are each 3.0 m long with a hinge at C. The tie bar BD is 0.6m long, halfway up. An man of mass 80kg climbs 2.0m along the ladder. Assuming that the floor is frictionless and neglecting the weight of the ladder, find (a) the tension in the tie–rod and the forces exerted on the ladder by the floor at (b) A and (c) E.

Fig 8.1. 
9. A 50 kg wooden crate rests on a wooden ramp with an adjustable angle of inclination and a coefficient of friction between the block and ramp of 0.30.
(a) Draw a free body diagram of the crate.
(b) If the angle of the ramp is set to 10°, determine…
(i) the component of the crate's weight that is perpendicular to the ramp
(ii)
the component of the crate's weight that is parallel to the ramp
(iii)
the normal force between the crate and the ramp
(iv) the static friction force between the crate and the ramp
(c) At what angle will the crate just begin to slip?


10. A farmer has a uniform bar which can swing out on a hinge to secure his access road. The 5m bar has a mass of 20kg and is supported by a cable hinged to the top of the gate post and attached to the middle of the bar. A second hinge is attached to the post at its mid point of the 2m post. Calculate
(a)
the tension, T, in the cable.
(b) the force on the hinge at the end of the bar.

Fig 10.1. 
