Q30 of 42 Page 34

A block of mass M is held against a rough vertical wall by pressing it with a finger. If the coefficient of friction between the block and the wall is μ and the acceleration due to gravity is g, calculate the minimum force required to be applied by the finger to hold the block against the wall?


Here, the force by the finger is given by “F”, the normal force is “N”, the frictional force is “f” and the weight of the body is acting downwards given by “Mg”.

We first balance the horizontal forces:



Now we balance the horizontal forces. Here, we have to stop the block from falling. So the acceleration should be zero.
 —————(1)


The frictional force is given by:


—————(2)


Substituting (2) in (1)





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Two masses of 5 kg and 3 kg are suspended with help of massless inextensible strings as shown in Fig. 5.6. Calculate T1 and T2 when whole system is going upwards with acceleration = 2 m s2 (use g = 9.8 m s-2).


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Block A of weight 100 N rests on a frictionless inclined plane of slope angle 30° (Fig. 5.7). A flexible cord attached to A passes over a frictionless pulley and is connected to block B of weight W. Find the weight W for which the system is in equilibrium.


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A 100 kg gun fires a ball of 1kg horizontally from a cliff of height 500m. It falls on the ground at a distance of 400m from the bottom of the cliff. Find the recoil velocity of the gun. (acceleration due to gravity = 10 m s-2)

 32

Figure 5.8 shows (x, t), (y, t ) diagram of a particle moving in 2-dimensions.


If the particle has a mass of 500 g, find the force (direction and magnitude) acting on the particle.