Application of Newton's Law of Motion

A monkey of mass $20 \mathrm{kg}$ is holding a vertical rope. The rope will not break when a mass of $25 \mathrm{kg}$ is suspended from it but will break if the mass exceeds $25 \mathrm{kg}$. What is the maximum acceleration with which the monkey can climb up along the rope? $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

A circular disc with a groove along its diameter is placed horizontally on a rough surface. A block of mass $1 \mathrm{kg}$ is placed as shown. The co-efficient of friction between the block and all surfaces of groove and horizontal surface in contact is $\mu =\frac{2}{5}.$ The disc has an acceleration of $25 {\mathrm{ms}}^{-2}$ towards left. Find the acceleration of the block with respect to disc. Given, $\cos \theta =\frac{4}{5}, \sin \theta =\frac{3}{5}$

Two blocks of mass $m_1=10 \mathrm{kg}$ and $m_2=5 \mathrm{kg}$, connected to each other by a massless inextensible string of length $0.3 \mathrm{m}$ are placed along a diameter of a turn table. The coefficient of friction between the table and $m_1$ is $0.5$ while there is no friction between $m_2$ and the table. The table is rotating with an angular velocity of $10 {\mathrm{rads}}^{-1}$ about a vertical axis passing through its centre $O$. The masses are placed along the diameter of the table on either side of the centre $O$ such that the mass $m_1$ is at a distance of $0.124 \mathrm{m}$ from $O$. The masses are observed to be at rest with respect to an observer on the turn table. Calculate the frictional force on $m_1$.

Block $A$ of mass $m$ and block $B$ of mass $2m$ are placed on a fixed triangular wedge by means of a massless inextensible string and a frictionless pulley as shown in figure. The wedge is inclined at $45°$ to the horizontal on both sides. The coefficient of friction between block $A$ and the wedge is $\frac{2}{3}$ and that between block $B$ and the wedge is $\frac{1}{3}$. If the system of $A$ and $B$ is released from rest, find the magnitude and direction of the force of friction acting on $A.$

Two blocks of mass $2.9 \mathrm{kg}$ and $1.9 \mathrm{kg}$ are suspended from a rigid support $S$ by two inextensible wires each of length $1 \mathrm{m}$ see figure. The upper wire has negligible mass and the lower wire has a uniform mass of $0.2 \mathrm{kg}{\mathrm{m}}^{-1}$ . The whole system of blocks, wires and support has an upward acceleration of $0.2 \mathrm{m}{\mathrm{s}}^{-2}$ . Acceleration due to gravity is $9.8 \mathrm{m}{\mathrm{s}}^{-2}$ .

(i) Find the tension $T$ at the mid-point of the lower wire.

(ii) Find the tension  $T^{\text{'}}$  at the mid-point of the upper wire.

The bob of a $0.2 \mathrm{m}$ long pendulum describes an arc of circle in a vertical plane. If the tension in cord is $\sqrt{3}$ times the weight of the bob when cord makes an angle of $30°$ to the vertical, then acceleration of bob in that position is

What is meant by a free body diagram ?  What is its use ?

"A man standing in a lift going downward with uniform velocity experiences a loss of weight at the start, but not when the lift is in uniform motion". Why ?

Why does the horse has to apply more force to star a cart ?

The horse is able to pull the cart because_____.

A horse pulls a $250 \mathrm{kg}$ cart with a force of $250 \mathrm{N}$ at an angle of ${30}^{°}$ If the cart moves with constant velocity, find the friction force, the applied force in both the horizontal and vertical directions, the object's weight, and the normal force.

A boy stands on a weighing machine in a lift. The machine reads his weight as $\mathrm{W}$.The lift starts moving upwards with a constant speed.

The reading on the machine will be:

A body of mass $30 \mathrm{kg}$ is stands on a weighing machine lying on the floor of a lift. What will be the weight of the body when (i) the lift moves upwards with an acceleration $2.2 m{s}^{-2}$and (ii)the lift moves downwards with  an acceleration $2.2 {\mathrm{ms}}^{-2}$ and (iii) the lift falls freely.

Explain why pull is easier than push.

Deduce an expression for the acceleration of the cart when a horse is pulling it.

When a horse pulls a cart the cart also pulls the horse,Then which force helps the horse to move forward? The force exerted by: