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$\mathrm{The} 2.5 \mathrm{kilogram} \mathrm{brick} \mathrm{of} \mathrm{figure} \mathrm{is} \mathrm{being} \mathrm{pulled} \mathrm{by} \mathrm{a} \mathrm{cord} \mathrm{that} \mathrm{makes} \mathrm{an} \mathrm{angle} \mathrm{of} 20° \mathrm{with} \mathrm{the} \mathrm{horizontal} \mathrm{and} \mathrm{has} 7.0 \mathrm{N} \mathrm{of} \mathrm{tension} \mathrm{in} \mathrm{it}.$
$\mathrm{Find} \mathrm{the} \mathrm{following}:$
                                         
$\left(\mathrm{a}\right) \mathrm{the} \mathrm{force} \mathrm{of} \mathrm{friction}$
$\left(\mathrm{b}\right) \mathrm{the} \mathrm{elastic} \mathrm{recoil} \mathrm{of} \mathrm{the} \mathrm{table} \mathrm{top}.$

A block of weight 5N is placed on a horizontal table. A person push the block from the top by exerting a downward force of 3N on it. Find the force exerted by the table on the block.
                                                   

A ball of mass 500g is thrown with a velocity of 72 km/hr. What is it's initial momentum?

A 650 kg rocket is to be speeded up from 440 meters per second to 520 meters per second in outer space. If the thrust of the engine is 1200N, for how long must the engine be fired?

A 0.01 kg ball is dropped onto a tabletop. The speeds of the ball right before hitting the tabletop and right after hitting the tabletop are 5.0 m/s, and 4.0 m/s, respectively. If the collision between the ball and the tabletop lasts 0.15s, what is the average force exerted on the ball by the tabletop.

$\mathrm{a} \mathrm{boy} \mathrm{of} \mathrm{mass} 58 \mathrm{kg} \mathrm{jumps} \mathrm{with} \mathrm{a} \mathrm{horizontal} \mathrm{velocity} \mathrm{of} 3 {\mathrm{ms}}^{-1} \mathrm{onto} \mathrm{a} \mathrm{stationary} \mathrm{skateboard} \mathrm{of} \mathrm{mass} 2\mathrm{kg}. \mathrm{What} \mathrm{is} \mathrm{his} \mathrm{velocity} \mathrm{as} \mathrm{he} \mathrm{moves}$
$\mathrm{off} \mathrm{on} \mathrm{the} \mathrm{skateboard}?$

A force acts for 0.1s on a body of mass 1.2 kg initially at rest. The force then ceases to act and the body moves through 2m in the next one second. Find the magnitude of the force.

A motorcar is moving with a velocity of 108 km/hr. and it takes 4s to stop after the brakes are applied. Calculate the force exerted by the brakes on the motorcar if its mass along with the passengers in 1000 kg.

A force of 20N acts on a body of mass 5kg for 5 sec. Find the following:
(i) the acceleration of the body
(ii) velocity at the end of 5 sec.
(iii) displacement at the end of 5 sec.

$$\begin{gathered} \mathrm{A} \mathrm{ball} \mathrm{of} \mathrm{mass} 10\mathrm{g} \mathrm{is} \mathrm{initally} \mathrm{moving} \mathrm{with} \mathrm{a} \mathrm{velocity} \mathrm{of} 50 {\mathrm{ms}}^{-1}. \mathrm{On} \mathrm{applying} \mathrm{a} \mathrm{constant} \mathrm{force} \mathrm{on} \mathrm{ball} \mathrm{for} 2.0\mathrm{s}, \mathrm{it} \mathrm{acquires} \mathrm{a} \mathrm{velocity} \mathrm{of} \\ 70 {\mathrm{ms}}^{-1}. \mathrm{Calculate} \mathrm{the} \mathrm{following}: \\ \left(\mathrm{i}\right) \mathrm{the} \mathrm{initial} \mathrm{momentum} \mathrm{of} \mathrm{ball} \\ \left(\mathrm{ii}\right) \mathrm{the} \mathrm{final} \mathrm{momentum} \mathrm{of} \mathrm{ball} \\ \left(\mathrm{iii}\right) \mathrm{the} \mathrm{rate} \mathrm{of} \mathrm{change} \mathrm{of} \mathrm{momentum} \\ \left(\mathrm{iv}\right) \mathrm{the} \mathrm{acceleration} \mathrm{of} \mathrm{ball} \\ \left(\mathrm{v}\right) \mathrm{the} \mathrm{magnitude} \mathrm{of} \mathrm{force} \mathrm{applied} \end{gathered}$$

A water skier is towed by a motorboat at a constant velocity of magnitude 15 km/hr. The boat speeds up and after a short interval, the skier is towed at a new constant velocity of magnitude 20 km/hr. What is the net force on the slier when she is 
(i) moving at 15 km/hr.
(ii) moving at 20 km/hr.

$\mathrm{What} \mathrm{thrust} \mathrm{is} \mathrm{needed} \mathrm{to} \mathrm{fire} \mathrm{a} 350-\mathrm{kilogram} \mathrm{rocket} \mathrm{straight} \mathrm{up} \mathrm{with} \mathrm{an} \mathrm{acceleration} \mathrm{of} 8.0 \mathrm{m}/{\mathrm{s}}^2 ?$

A pile driver of mass 150 kg falls from a height of 5m above the pile and is brought to rest in 0.5s. Ignoring the motion of the pile, calculate the average force exerted on the pile.

$$\begin{gathered} \mathrm{A} \mathrm{force} \mathrm{of} 20 \mathrm{N} \mathrm{acting} \mathrm{on} \mathrm{a} \mathrm{mass} m_1, \mathrm{produces} \mathrm{an} \mathrm{acceleration} \mathrm{of} 4 \mathrm{m}/{\sec }^2. \mathrm{The} \mathrm{same} \mathrm{force} \mathrm{is} \mathrm{applied} \mathrm{on} \mathrm{mass} m_2 \mathrm{then} \mathrm{the} \mathrm{acceleration} \\ \mathrm{produced} \mathrm{is} 0.5 \mathrm{m}/{\sec }^2. \mathrm{What} \mathrm{acceleration} \mathrm{would} \mathrm{the} \mathrm{same} \mathrm{force} \mathrm{produce}, \mathrm{when} \mathrm{both} \mathrm{masses} \mathrm{are} \mathrm{tied} \mathrm{together}. \end{gathered}$$

Find acceleration and contact force between the two bodies mass 20 kg and 30 kg.
                             

Draw F.B.D of the system diagram.
  

A bullet of mass m is fired from a gun of mass M with a horizontal velocity of v. What is the recoil velocity of the gun?

$$\begin{gathered} \mathrm{Two} \mathrm{particles} \mathrm{of} \mathrm{mass} 200\mathrm{g} \mathrm{and} 500\mathrm{g} \mathrm{are} \mathrm{released} \mathrm{from} \mathrm{rest} \mathrm{at} \mathrm{some} \mathrm{mutual} \mathrm{separation}. \mathrm{If} \mathrm{the} \mathrm{velocity} \mathrm{of} \mathrm{the} \mathrm{smaller} \mathrm{mass} \mathrm{be} 2.5 {\mathrm{ms}}^{-1} \\ \mathrm{at} \mathrm{any} \mathrm{instant}, \mathrm{then} \mathrm{what} \mathrm{is} \mathrm{the} \mathrm{velocity} \mathrm{of} \mathrm{the} \mathrm{larger} \mathrm{mass}? \end{gathered}$$

$$\begin{gathered} \mathrm{A} \mathrm{force}, {\mathrm{F}}_1 \mathrm{acting} \mathrm{on} \mathrm{a} 2.0 \mathrm{kg} \mathrm{body} \mathrm{produces} \mathrm{an} \mathrm{acceleration} 2.5 \mathrm{m}/{\mathrm{s}}^2. \mathrm{Another} \mathrm{force} {\mathrm{F}}_2 \mathrm{acting} \mathrm{on} \mathrm{a} 5.0 \mathrm{kg} \mathrm{body} \mathrm{produces} \mathrm{an} \\ \mathrm{acceleration} \mathrm{of} 2.0 \mathrm{m}/{\mathrm{s}}^2. \mathrm{Find} \mathrm{the} \mathrm{ratio} {\mathrm{F}}_2/{\mathrm{F}}_1. \end{gathered}$$

$$\begin{gathered} \mathrm{A} \mathrm{force} \mathrm{acts} \mathrm{on} \mathrm{a} \mathrm{particle} \mathrm{of} \mathrm{mass} 200\mathrm{g}. \mathrm{The} \mathrm{velocity} \mathrm{of} \mathrm{the} \mathrm{particle} \mathrm{changes} \mathrm{from} 15 \mathrm{m}/\mathrm{s} \mathrm{in} 2.5\mathrm{s}. \mathrm{Assuming} \mathrm{the} \mathrm{force} \mathrm{to} \mathrm{be} \mathrm{constant}, \\ \mathrm{find} \mathrm{its} \mathrm{magnitude}. \end{gathered}$$

A bullet of mass 20 g moving with a speed of 120 m/s hits a thick muddy wall and penetrates into it. It takes 0.03 s to stop in the wall. Find (a) the acceleration of the bullet in the wall, (b) the force exerted by the wall on the bullet, (c) the force exerted by the bullet on the wall, and (d) the distance covered by the bullet in the wall.

Two particles A and B of masses 20 g and 30 g respectively are at rest at a certain time. Because of the forces exerted by them on each other, the particles start moving. At a given instant, particle A is found to move towards the east with a velocity of 6 cm/s. What is the velocity of particle B at this instant?

A body of mass 300g kept at rest breaks into parts due to internal forces. One part of mass 200g is found to move at a speed of 12 m/s towards the east. What will be the velocity of the other part?

A force of 12 N starts acting on a body kept at rest. Find the momentum of the body at 1 s, 2 s and 5 s after the force starts acting.

Find the acceleration of masses and tension in the string for the system shown in figure $\left(\mathrm{g} = 10 \mathrm{m}/{\mathrm{s}}^2\right)$.
                                     

Find maximum force applied on the lower mass so that the two masses move together, for the system of masses shown.
                                                    

Explain why it is easier to pull than push a box on a rough surface.

A mass of 5 kg having initial velocity of 20 m/s comes to rest after travelling a distance of 200m. Find the coefficient of friction and friction force acting on the body.

Find the acceleration and contact forces between the two masses given in the figure.
                               

$\mathrm{When} \mathrm{a} \mathrm{force} \mathrm{of} 50\mathrm{N} \mathrm{is} \mathrm{applied} \mathrm{on} \mathrm{a} \mathrm{body} \mathrm{of} \mathrm{mass} 10 \mathrm{kg} \mathrm{it} \mathrm{is} \mathrm{about} \mathrm{to} \mathrm{move} \mathrm{and} \mathrm{once} \mathrm{the} \mathrm{body} \mathrm{is} \mathrm{set} \mathrm{into} \mathrm{motion} \mathrm{the} \mathrm{same} \mathrm{force} \mathrm{of} 50\mathrm{N}$
$\mathrm{produces} \mathrm{an} \mathrm{acceleration} \mathrm{of} 0.5 \mathrm{m}/{\mathrm{s}}^2. \mathrm{Find} \mathrm{the} \mathrm{coefficient} \mathrm{of} \mathrm{static} \mathrm{and} \mathrm{kinetic} \mathrm{friction} \left(\mathrm{g} = 10 \mathrm{m}/{\mathrm{s}}^2\right)$

Which of the following has more inertia :
(a) a rubber ball and a stone of the same size?
(b) a bicycle and a train?
(c) a five-rupees coin and a one-rupee coin?

In the following example, try to identify the number of times the velocity of the ball changes:
"A football player kicks a football to another player of his team who kicks the football towards the goal. The goalkeeper of the opposite team collects the football and kicks it towards a player of his own team".
Also, identify the agent supplying the force in each case.

Explain why some of the leaves may get detached from a tree if we vigorously shake its branch.

Why do you fall in the forward direction when a moving bus brakes to a stop and falls backward when it accelerates from rest?

If action is always equal to the reaction, explain how a horse can pull a cart.

Explain, why it is difficult for a fireman to hold a hose, which ejects large amounts of water at a high velocity. 

$\mathrm{From} \mathrm{a} \mathrm{rifle} \mathrm{of} \mathrm{mass} 4 \mathrm{kg}, \mathrm{a} \mathrm{bullet} \mathrm{of} \mathrm{mass} 50\mathrm{g} \mathrm{is} \mathrm{fired} \mathrm{with} \mathrm{an} \mathrm{initial} \mathrm{velocity} \mathrm{of} 35 {\mathrm{ms}}^{-1}. \mathrm{Calculate} \mathrm{the} \mathrm{initial} \mathrm{recoil} \mathrm{velocity} \mathrm{of} \mathrm{the} \mathrm{rifle}.$

$$\begin{gathered} \mathrm{Two} \mathrm{objects} \mathrm{of} \mathrm{masses} 100 \mathrm{g} \mathrm{and} 200 \mathrm{g} \mathrm{are} \mathrm{moving} \mathrm{along} \mathrm{the} \mathrm{same} \mathrm{line} \mathrm{and} \mathrm{direction} \mathrm{with} \mathrm{velocities} \mathrm{of} 2 {\mathrm{ms}}^{-1} \mathrm{and} 1 {\mathrm{ms}}^{-1}, \mathrm{respectively}. \\ \mathrm{They} \mathrm{collide} \mathrm{and} \mathrm{after} \mathrm{the} \mathrm{collision}, \mathrm{the} \mathrm{first} \mathrm{object} \mathrm{moves} \mathrm{at} \mathrm{a} \mathrm{velocity} \mathrm{of} \mathrm{I} .67 {\mathrm{ms}}^{-1}. \mathrm{Detemine} \mathrm{the} \mathrm{velocity} \mathrm{of} \mathrm{the} \mathrm{second} \mathrm{object}. \end{gathered}$$

An object experiences a net zero external unbalanced force. Is it possible for the object to be traveling with a non-zero velocity? If yes, state the conditions that must be placed on the magnitude and direction of the velocity. If no, provide a reason. 

When a carpet is beaten with a stick, dust comes out . Explain why ? 

Why is it advised to tie any luggage kept on the roof of a bus with a rope?

A truck starts from rest and rolls down a hill with a constant acceleration. It travels a distance of 400 m in 20 s. Find its acceleration. Find the force acting on it if its mass is 7 metric tonnes (Hint: I metric tonne = 1000 kg.)

$\mathrm{A} \mathrm{stone} \mathrm{of} \mathrm{I} \mathrm{kg} \mathrm{is} \mathrm{thrown} \mathrm{with} \mathrm{a} \mathrm{velocity} \mathrm{of} 20 {\mathrm{ms}}^{-1} \mathrm{across} \mathrm{the} \mathrm{frozen} \mathrm{surface} \mathrm{of} \mathrm{a} \mathrm{lake} \mathrm{and} \mathrm{comes} \mathrm{to} \mathrm{rest} \mathrm{after} \mathrm{travelling} \mathrm{a} \mathrm{distance} \mathrm{of} 50 \mathrm{m}.$
$\mathrm{What} \mathrm{is} \mathrm{the} \mathrm{force} \mathrm{of} \mathrm{friction} \mathrm{between} \mathrm{the} \mathrm{stone} \mathrm{and} \mathrm{the} \mathrm{ice}?$

An 8000 kg engine pulls a train of 5 wagons, each Of 2000 kg. along a horizontal track. If the engine exerts a force of 40000 N and the track offers a friction force of 5000 N, then calculate:
(a) the net accelerating force
(b) the acceleration of the train
(c) the force of wagon I on Wagon 2.

$$\begin{gathered} \mathrm{An} \mathrm{automobile} \mathrm{vehicle} \mathrm{has} \mathrm{a} \mathrm{mass} \mathrm{of} 1500 \mathrm{kg}. \mathrm{What} \mathrm{must} \mathrm{be} \mathrm{the} \mathrm{force} \mathrm{between} \mathrm{the} \mathrm{vehicle} \mathrm{and} \mathrm{road} \mathrm{if} \mathrm{the} \mathrm{vehicle} \mathrm{is} \mathrm{to} \mathrm{be} \mathrm{stopped} \mathrm{with} \mathrm{a} \\ \mathrm{negative} \mathrm{acceleration} \mathrm{of} 1.7 {\mathrm{ms}}^{-1}? \end{gathered}$$

Using a horizontal force of 200 N, intend to move a wooden cabinet across a floor at a constant velocity. What is the friction that Will be exerted on the cabinet? 

$$\begin{gathered} \mathrm{Two} \mathrm{objects}, \mathrm{each} \mathrm{of} \mathrm{mass} \mathrm{I} .5 \mathrm{kg}, \mathrm{are} \mathrm{moving} \mathrm{in} \mathrm{the} \mathrm{straight} \mathrm{line} \mathrm{but} \mathrm{in} \mathrm{opposite} \mathrm{directions}. \mathrm{The} \mathrm{velocity} \mathrm{Ofeach} \mathrm{object} \mathrm{is} 2.5 {\mathrm{ms}}^{-1} \\ \mathrm{before} \mathrm{the} \mathrm{collision} \mathrm{during} \mathrm{which} \mathrm{they} \mathrm{Stick} \mathrm{together}. \mathrm{What} \mathrm{will} \mathrm{be} \mathrm{the} \mathrm{velocity} \mathrm{of} \mathrm{the} \mathrm{combined} \mathrm{object} \mathrm{after} \mathrm{collision}? \end{gathered}$$
 

According to the third law of motion when we push on an object, the object pushes back on us Wilh an and opposite force. If the Object in A massive truck parked the roadside, it will probably not move. A student justified this by answering that the two opposite and equal force cancel each other. Comment on this logic and explain why the truck does not move.

$$\begin{gathered} \mathrm{A} \mathrm{hockey} \mathrm{ball} \mathrm{of} \mathrm{mass} 200\mathrm{g} \mathrm{travelling} \mathrm{a} 10 {\mathrm{ms}}^{-1} \mathrm{is} \mathrm{Struck} \mathrm{by} \mathrm{a} \mathrm{hockey} \mathrm{stick} \mathrm{so} \mathrm{as} \mathrm{to} \mathrm{return} \mathrm{it} \mathrm{along} \mathrm{its} \mathrm{original} \mathrm{path} \mathrm{with} \mathrm{a} \mathrm{velocity} \mathrm{at} 5 {\mathrm{ms}}^{-1}. \\ \mathrm{Calculate} \mathrm{the} \mathrm{change} \mathrm{of} \mathrm{momentum} \mathrm{occurred} \mathrm{in} \mathrm{the} \mathrm{motion} \mathrm{of} \mathrm{the} \mathrm{hockey} \mathrm{ball} \mathrm{by} \mathrm{the} \mathrm{force} \mathrm{applied} \mathrm{by} \mathrm{the} \mathrm{hockey} \mathrm{stick} \end{gathered}$$

A bullet of mass 10 g traveling horizontally with a velocity of 150 ${\mathrm{ms}}^{-1}$ strikes a stationary wooden block and comes to rest in 0.03 s. Calculate the distance of penetration of the bullet into the block. Also, calculate the magnitude of the force exerted by the wooden block on the bullet. 

An object of mass I kg traveling in a straight line with a velocity of 10 ${\mathrm{ms}}^{-1}$ collides with and sticks to, a stationary wooden block of mass 5 kg. Then they both move off together in the same straight line. Calculate the total momentum just before the impact and just after the impact. Also, calculate the velocity of the combined object.

An object of mass 100 kg is accelerated uniformly from a velocity of $5 {\mathrm{ms}}^{-1} \mathrm{and} 8 {\mathrm{ms}}^{-1}$ in 6 s. Calculate the initial and final momentum of the object. Also, find the magnitude of the force exerted on the Object.

Akhtar Kiran and Rahul were riding in a motorcar that was moving with a high velocity on an expressway When an insect hit the windshield and got stuck on the windscreen. Akhtar and Kiran started pondering over the situation. Kiran suggested that the insect suffered a greater change in momentum as compared to the change in momentum of the motorcar (because the change in the velocity of the insect was much more than that of the motorcar). Akhtar said that since the motorcar was moving with larger velocity, it exerted a larger force on the insect. And as a result, the insect died. Rahul while putting an entirely new explanation said that both the motorcar and the insect experienced the same force and a change in their momentum. Comment on these suggestions. 

Two balls of the same size but of different materials, rubber and iron are kept on the smooth floor of a moving train. The brakes are applied suddenly to stop the train. Will the ball start rolling? If so, in which direction? Will they move at the same speed? Give reasons for your answer.

Two identical bullets are fired-one by a light rifle and another by a heavy rifle with the same force. Which rifle will hurt the shoulder more and why? 

Suppose a ball of mass m is thrown vertically upward with an initial speed v, its speed decreases continuously till it becomes zero. Thereafter, the ball begins to fall downward and attains the speed v again before striking the ground. It implies that the magnitude of the initial and final momentums of the ball are the same. Yet, it is not an example of conservation of momentum. Explain why? 

Velocity versus time graph of a ball of mass 50g rolling on a concrete floor is shown in Fig. Calculate the acceleration and frictional force of the floor on the ball.
                                    

Two friends on roller-skates are standing 5 m apart facing each other. One of them throws a ball of 2 kg towards the other, who catches it. How will this activity affect the position of the two? Explain your answer.

Using the second law of motion, derive the relation between force and acceleration. A bullet of mass 10 g strikes a sand-bag at a speed of ${10}^3$ ${\mathrm{ms}}^{-1}$ and gets embedded after traveling 5 cm. Calculate
(i) the resistive force exerted by the sand on the bullet
(ii) the time is taken by the bullet to come to rest.

On which of these hills does the ball roll down with increaseing speed and decreasing acceleration along? (Vse this example if you wish to explain to solitons difference between speed and acceleration.)
                                 

$$\begin{gathered} \mathrm{If} \mathrm{you} \mathrm{drop} \mathrm{an} \mathrm{object}, \mathrm{its} \mathrm{acceleration} \mathrm{towards} \mathrm{the} \mathrm{ground} \mathrm{is} 10 \mathrm{m}/{\mathrm{s}}^2. \mathrm{If} \mathrm{you} \mathrm{throw} \mathrm{it} \mathrm{down} \mathrm{instead}, \mathrm{would} \mathrm{its} \mathrm{acceleration} \mathrm{after} \mathrm{throwing} \\ \mathrm{be} \mathrm{greater} \mathrm{than} 10 \mathrm{m}/{\mathrm{s}}^{2 } ? \mathrm{Why} \mathrm{or} \mathrm{why} \mathrm{not}? \end{gathered}$$
 

When your hand turns the handle of a faucet, water comes out. Do you push on the handle and the water coming out comprise an action-reaction pair? Defend your answer.

A stone is shown at rest on the ground.
                                                    
(a) The vector shows the weight of the stone. Complete the vector diagram showing another vector that results in zero net force on the
      stone.
(b) What is the conventional name of the vector you have drawn?

What the net force on "tone in Ilie when it at the top of? Whal in velocity? acceleration?