Problems for Practice

PROBLEMS FOR PRACTICE

On Block Brakes

1. The diameter of a block brake is 250 mm. The L-shaped lever has its longer arm horizontal. The vertical distance of the pivot (of the lever) from the centre of the drum is 75 mm. The horizontal distance of the pivot from the centre of the drum is 200 mm. An effort of 700 N (vertical) is applied to a horizontal distance of 400 mm from the pivot. The contact angle is 90 degrees. The coefficient of friction is 0.35. Determine the braking torque. 

[Ans. 62.94 N.m]

2. A bicycle and rider of mass 90 kg are travelling at the rate of 15 km/hr on a level road. A brake is applied to the rear wheel which is 0.9 m in diameter and this is the only resistance acting. How far will the bicycle travel and how many turns will it make before it comes to rest? The pressure applied on the brake is 100 N and μ = 0.06.

[Ans. 130.2 m; 60 turns]

3. A double shoe brake, as shown in Fig.9.20, is capable of absorbing a torque of 1400 N.m. The diameter of the brake drum is 350 mm and the angle of contact for each shoe is 100°. If μ = 0.4, find:

(i) the spring force necessary to set brake; and

(ii) the width of shoes if bearing pressure on lining material is not to exceed 0.3 N/mm2.

[Ans. (i) 3596 N; (ii) 162 mm]

On Band Brakes

4. The simple band brake system, as shown in Fig.9.21, is applied to a shaft carrying a flywheel of mass 400 kg. The radius of gyration of the flywheel is 450 mm and runs at 300 rpm. The coefficient of friction is 0.2 and the brake drum diameter is 240 mm. The angle of lap of the band on the drum is 150°. Determine:

(i) the torque applied due to a hand load of 100 N,

(ii) the torque applied due to a hand load of 100 N, the number of turns of the wheel before it is brought to rest, and

(iii) the time required to bring to rest, from the moment of the application of the brake. 

[Ans. (i) 32.4 N.m; (ii) 197 turns; (iii) 39.3 s]

On Band and Block Brakes

5. A differential band brake has a drum with a diameter of 800 mm. The two ends of the band are fixed to the pins on the opposite sides of the fulcrum of the lever at a distances of 40 mm and 200 mm from the fulcrum. The angle of contact is 270° and the coefficient of friction is 0.2. Determine the brake torque when a force of 600 N is applied to the lever at a distance of 800 mm from the fulcrum.

 [Ans. 636 N.m]

6. A band and block brake having 12 blocks, each of which subtends an angle of 16° at the centre, is applied to a rotating drum of 600 mm diameter. The blocks are 75 mm thick. The two ends of the band are attached to pins on opposite sides of the fulcrum at distances of 40 mm and 150 mm. Determine the maximum braking torque, if a force of 250 N is applied to the lever at a distance of 900 mm from the fulcrum. Take μ = 0.3.

[Ans.  3.7 kN.m]

7. A band and block brake having 14 blocks, each of which subtends an angle of 15° at the centre is applied to a drum of 1 m effective diameter. The drum and the flywheel mounted on the same shaft of mass 2000 kg and a combined radius of gyration of 500 mm. The two ends of a the band are attached to pins on opposite sides of the brake lever at distance of 30 mm and 120 mm, from the fulcrum. If a force of 200 N is applied at a distance of 750 mm from the fulcrum, find (a) maximum braking torque; (b) angular retardation of the drum; and (c) time taken by the system to come to rest from the rated speed of 360 rpm. Take μ = 0.25. 

[Ans.  (a) 2540 N.m; (b) 5.08 rad/s2; 7.42 s]

On Braking of a Vehicle

8. A car moving on a level road at a speed 60 km/hr has a wheel base 3 metres, distance of C.G. from ground level 600 mm, and the distance of C.G from rear wheels 1.2 metres. Find the distance travelled by the car before coming to rest when brakes are applied,

 (i) to the rear wheels only, (ii) to the front wheels only and (iii) to all the four wheels. The coefficient of friction between the tyres and the road may be taken as 0.6.

[Ans. (i) 44 m; (ii) 51.87 m; (iii) 16.4 m]

9. A vehicle moving on a rough plane inclined at 10° with the horizontal at a speed of 36 km/hr has a wheel base 1.8 metres. The centre of gravity of the vehicle is 0.8 m from the rear wheels and 0.9 m above the inclined plane. Find the distance travelled by the vehicle before coming to rest and the time taken to do so when (i) The vehicle moves up the plane, and (ii) The vehicle moves down the plane. Take μ = 0.5.

[Ans. (i) 7.657 m; 1.53 s; (ii) 16 m; 3.2 s]

10. The wheel base of a car is 3 metres and its centre of gravity is 1.2 metres ahead the rear axle and 0.75 m above the ground level. Determine the maximum deceleration of the car when it moves on a level road, if the braking force on all the wheels is the same and no wheel slip occurs. Take μ = 0.5. 

[Ans. 4.66 m/s2]