The co-efficient of static friction \(\mu_{o}\), between block A of mass \(2kg\) and the table as shown in figure is \(0.2\). What will be the maximum mass of block B so that the two blocks do not move? The string and pulley are assumed to be smooth and massless. Given: \(g=10\frac{m}{s^{2}}\).
Ans: \(m_{B}=0.4kg\).
A block of mass \(m\) is in contact with a cart C as shown. The co-efficient of static friction between block and cart is \(\mu\). How much acceleration is given to the block so that block is preventing from falling.
Ans: \(a\geq\frac{g}{\mu}\).
A smooth block is released at rest on a \(45^{o}\) incline and then slides a distance d. If, the time taken to slide on rough incline is n times as large as that to slide on the smooth incline, find co-efficient of friction?
Ans: \(\mu=\left(1-\frac{1}{n^{2}}\right)\).
A body of mass \(3kg\) is being dragged with a uniform velocity of \(3\frac{m}{s}\) on a rough horizontal plane. The co-efficient of friction between the body and the surface is \(0.2\). calculate: the amount of heat generated per second \(g=10\frac{m}{s^{2}}\) and \(J=4.2\frac{J}{cal}\).
Ans: \(H=4.2Cal\).
The minimum force required to start pushing a body up a rough inclined plane is \(F_{1}\) while the minimum force required to prevent it from sliding down is \(F_{2}\). If, the inclined plane makes an angle \(\Theta\) with horizontal such that \(tan\theta=2\mu\) then find ratio; \(\frac{F_{1}}{F_{2}}\).
Ans: \(\frac{F_{1}}{F_{2}}=3\).
Two blocks A and B of equal mass are released from an incline plane of inclination \(\theta=45^{o}\) at time \(t=0\). Both the blocks are initially at rest. The co-efficient of kinematic friction between the block A and the inclined plane is \(0.2\) while it is \(0.3\) for block B. Initially the block is \(\sqrt{2}m\) behind the block B. When and where their front faces will come in line? Take: \(g=10\frac{m}{s^{2}}\). Ans: \(t=2s\) and \(d=8\sqrt{2}m\).
A man pulls a loaded cart of mass \(90kg\) along a horizontal surface at constant velocity as shown in figure. The co-efficient of kinematic friction \(\mu_{k}\) between the tyres of the cart and the road is 0.1 and the angle made by the rope with horizontal is \(45^{o}\). Calculate: tension in the rope.
Ans: \(T=113.38N\).
A train of \(150MT\) is drawn up a rough inclined plane of \(1in100\) at a rate of \(36\frac{km}{hr}\). If, the frictional force is \(12\frac{N}{ton}\), Calculate: power of the engine.
