B M Sharma Solutions for Chapter: Newton's Laws of Motion (With Friction), Exercise 55: Exercises

In the following figure shows an accelerating conveyor belt inclined at an angle $37°$ above horizontal. The coefficient of friction between the belt and block is $1.$ Find the least time (in sec) in which block can reach the top, starting from rest at the bottom.

A block of mass $m=4 \mathrm{kg}$ is placed over a rough inclined plane as shown in the figure. The coefficient of friction between the block and the plane is $\mu =0.5.$ A force $F=10 \mathrm{N}$ is applied on the block at an angle of $30°.$ Find the contact force (in $N$) between the block and the plane.

A side view of a simplified form of the vertical latch $B$ of mass $m=0.6 \mathrm{kg}$ is as shown in the figure. The lower member $A$ can be pushed forward in its horizontal channel. The sides of the channels are smooth, but at the interfaces of $A$ and $B,$ which are at $45°$ with the horizontal, there exists a static coefficient of friction $\mu =0.4.$ What is the minimum force $F$ (in $N$) that must be applied horizontally to $A$ to start the motion of the latch $B.$

Masses $M_1, M_2$ and $M_3$ are connected by light strings which pass over pulleys $P_1$ and $P_2$ as shown. The masses move such that the string between $P_1$ and $P_2$ is parallel to incline and the string between $P_2$ and $M_3$ is horizontal, $M_2=M_3=4 \mathrm{kg}.$ The coefficient of kinetic friction between masses and the surface is $0.25.$ The angle of inclination of plane is $37°$ to the horizontal. If the mass $M_1$ moves downward with uniform velocity, find the tension in the horizontal string (in $N$). (Given $g=10 \mathrm{m}/{\mathrm{s}}^2$)

The maximum value of the mass of block $C$ (in undefined) so that neither $A$ nor $B$ moves is (Given that mass of $A$ is undefined and that of $B$ is undefined Pulleys are smooth and friction coefficients between $A$ and $B$ and between $B$ and horizontal surface is ( undefined)

In the figure shown, block $A, B$ and $C$ weigh undefined and undefined respectively. The coefficient of sliding friction between any two surfaces is undefined is held at rest by a massless rigid rod fixed to the wall while $B$ and $C$ are connected by a string passing around a frictionless pulley. Find the force needed (in $\mathrm{N}$) to drag $C$ along the horizontal surface to the left at a constant speed. Assume the arrangement shown in the figure is maintained all through.

   

Block $A$ has a mass of $30 \mathrm{kg}$ and block $B$ a mass of $15 \mathrm{kg}.$ The coefficients of friction between all surfaces of contact are ${\mu }_s=0.15$ and ${\mu }_k=0.10.$ Knowing that $\mathrm{\theta }=30°$ and that the magnitude of the force $F$ applied to block $A$ is $250 \mathrm{N},$ determine the acceleration of block $A$ (in $\mathrm{m} {\mathrm{s}}^{-2}$).

With two hands, you hold a cone motionless upside down, as shown in figure. The mass of the cone is $m=1 \mathrm{kg},$ and the coefficient of static friction between your fingers and the cone is $\mu =0.5.$ What is the minimum normal force (in $N$) you must apply with each hand in order to hold up the cone? Consider only translational equilibrium.