Particles $A$ and $B,$ of masses $0.2 \mathrm{kg}$ and $0.45 \mathrm{kg}$ respectively, are connected by a light inextensible string of length $2.8 \mathrm{m}.$ The string passes over a small smooth pulley at the edge of a rough horizontal surface, which is $2 \mathrm{m}$ above the floor. Particle A is held in contact with the surface at a distance of $2.1 \mathrm{m}$ from the pulley and particle B hangs freely (see diagram). The coefficient of friction between A and the surface is $0.3.$ Particle A is released and the system begins to move.

Given that $B$ remains on the floor, find the speed with which $A$ reaches the pulley.

Particles $A$ and $B,$ of masses $0.3 \mathrm{kg}$ and $0.7 \mathrm{kg}$ respectively, are attached to the ends of a light inextensible string. Particle $A$ is held at rest on a rough horizontal table with the string passing over a smooth pulley fixed at the edge of the table. The coefficient of friction between $A$ and the table is $0.2.$ Particle $B$ hangs vertically below the pulley at a height of $0.5 \mathrm{m}$ above the floor (see diagram). The system is released from rest and $0.25 \mathrm{s}$ later the string breaks. $A$ does not reach the pulley in the subsequent motion. Find

the speed of $B$ immediately before it hits the floor,

Particles $A$ and $B,$ of masses $0.3 \mathrm{kg}$ and $0.7 \mathrm{kg}$ respectively, are attached to the ends of a light inextensible string. Particle $A$ is held at rest on a rough horizontal table with the string passing over a smooth pulley fixed at the edge of the table. The coefficient of friction between $A$ and the table is $0.2.$ Particle $B$ hangs vertically below the pulley at a height of $0.5 \mathrm{m}$ above the floor (see diagram). The system is released from rest and $0.25 \mathrm{s}$ later the string breaks. $A$ does not reach the pulley in the subsequent motion. Find

the total distance travelled by $A.$

A slope is inclined at $30°$ to the horizontal. A small box $A,$ of mass $2 \mathrm{kg},$ is held on the slope. Box $A$ is attached to one end of a light inextensible string. The string passes over a small smooth pulley, $P_1,$ fixed at the top of the slope and then passes under a small smooth pulley, $P_2,$ fixed near ground level. The other end of the string is attached to a small box $B,$ of mass $2 \mathrm{kg},$ at rest on the ground. The ground is horizontal and the portion of the string between pulley $P_2$ and box $B$ is horizontal (see diagram). The coefficient of friction between box $A$ and the slope is $0.2$ and the coefficient of friction between box $B$ and the ground is $\mu .$

The distance from the bottom of the slope to $A$ is $1 \mathrm{m}$ and the distance from pulley $P_2$ to $B$ is $0.6 \mathrm{m}.$ Box $A$ is released and the system begins to move. It takes $1 \mathrm{s}$ for box $B$ to reach pulley $P_2.$

Find the speed of box $B$ just before it hits the pulley.

A slope is inclined at $30°$ to the horizontal. A small box $A,$ of mass $2 \mathrm{kg},$ is held on the slope. Box $A$ is attached to one end of a light inextensible string. The string passes over a small smooth pulley, $P_1,$ fixed at the top of the slope and then passes under a small smooth pulley, $P_2,$ fixed near ground level. The other end of the string is attached to a small box $B,$ of mass $2 \mathrm{kg},$ at rest on the ground. The ground is horizontal and the portion of the string between pulley $P_2$ and box $B$ is horizontal (see diagram). The coefficient of friction between box $A$ and the slope is $0.2$ and the coefficient of friction between box $B$ and the ground is $\mu .$

The distance from the bottom of the slope to $A$ is $1 \mathrm{m}$ and the distance from pulley $P_2$ to $B$ is $0.6 \mathrm{m}.$ Box $A$ is released and the system begins to move. It takes $1 \mathrm{s}$ for box $B$ to reach pulley $P_2.$

Show that the tension in the string is $4.14 \mathrm{N},$ to $3$ significant figures.

A slope is inclined at $30°$ to the horizontal. A small box $A,$ of mass $2 \mathrm{kg},$ is held on the slope. Box $A$ is attached to one end of a light inextensible string. The string passes over a small smooth pulley, $P_1,$ fixed at the top of the slope and then passes under a small smooth pulley, $P_2,$ fixed near ground level. The other end of the string is attached to a small box $B,$ of mass $2 \mathrm{kg},$ at rest on the ground. The ground is horizontal and the portion of the string between pulley $P_2$ and box $B$ is horizontal (see diagram). The coefficient of friction between box $A$ and the slope is $0.2$ and the coefficient of friction between box $B$ and the ground is $\mu .$

The distance from the bottom of the slope to $A$ is $1 \mathrm{m}$ and the distance from pulley $P_2$ to $B$ is $0.6 \mathrm{m}.$ Box $A$ is released and the system begins to move. It takes $1 \mathrm{s}$ for box $B$ to reach pulley $P_2.$

Find the value of $\mu .$ When box $B$ hits the pulley, the string breaks.

A slope is inclined at $30°$ to the horizontal. A small box $A,$ of mass $2 \mathrm{kg},$ is held on the slope. Box $A$ is attached to one end of a light inextensible string. The string passes over a small smooth pulley, $P_1,$ fixed at the top of the slope and then passes under a small smooth pulley, $P_2,$ fixed near ground level. The other end of the string is attached to a small box $B,$ of mass $2 \mathrm{kg},$ at rest on the ground. The ground is horizontal and the portion of the string between pulley $P_2$ and box $B$ is horizontal (see diagram). The coefficient of friction between box $A$ and the slope is $0.2$ and the coefficient of friction between box $B$ and the ground is $\mu .$

The distance from the bottom of the slope to $A$ is $1 \mathrm{m}$ and the distance from pulley $P_2$ to $B$ is $0.6 \mathrm{m}.$ Box $A$ is released and the system begins to move. It takes $1 \mathrm{s}$ for box $B$ to reach pulley $P_2.$

Find the speed of box $A$ just before it reaches the bottom of the slope.