The block brake consists of a pin-connected lever and friction block at BB. The coefficient of static friction between the wheel and the lever is μsμs = 0.3, and a torque of 5 NN ⋅⋅ mm is applied to the wheel. Determine if the brake can hold the wheel stationary when the force applied to the lever is (a) PP = 30 NN, (b) PP = 70 NN.

Answer (a) 4.378 N-m

             (b) 10.21 N-m

Explanation:

(a) FB= Frictional Force

For 30N force (p=30N)

P x (400+200) +(FB X50) -(NB X 200) =0

(30 X 600) +(0.3 X NB X 50) -(NB X 200) =0

NB= 97.29N

FB = 0.3 X 97.29 = 29.187N

Frictional torque on the wheel = FB x radius

                                                   = (29.189 x 0.15) N-m

                                                  =4.378 N-m which is less than 5 N-m

Since the torque is less than 5N-m the 30N force is not enough to hold the wheel without moving.

(b) For 70N force (p=70N)

P x (400+200) +(FB X 50) - (NB X 200) =0

(70 X 600) +(0.3 X NB X 50) -(NB X 200) =0

NB= 227.02N

FB = 0.3 X 227.02N = 68.10N

Frictional torque on the wheel = FB x radius

                                                   = (68.10 x 0.15) N-m

                                                  =10.21 N-m which is greater than 5 N-m

Since the torque(10.21 N-m) is greater than 5N-m the 70N force will be enough to hold the wheel at a place without moving.

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