**Newton's Laws of Motion**

- This video gives the introduction of the phenomenon which causes the motion i.e force.
- This video explains the force as the sole factor for causing change in velocity of an object i.e bringing acceleration. It also familiarizes us with the famous Newton’s first laws of motion and concept of inertia.
- This video explains the underlying concept of net external force and acceleration of a body of Newton’s 2nd law of motion in detail.
- A body is acted by three forces as shown in the figure. If the body is at rest, find the force F?
- If the velocity of an object at given instance is 0, it means that Fnet on that body is zero. (a) True (b) False
- Figure shows the displacement of a particle going along the x axis as a function of time. In which region, the force acting on the particle is zero?
- This video explains the interdependence of force, mass and acceleration in accordance with the Newton’s 2nd law of motion.
- Given figure shows four situations in which an object is pulled by several force along x and y axes. Find out the direction of acceleration for each case. Also, in which situations does the object's acceleration have an x component or a y component?
- This video gives the detailed description of Newton’s 3rd law of motion. It also explains the concept of free body diagram (fbd) in detail.
- This video explains the force of attraction between objects owing to their mass called gravitational force. It also describes the concept of mass and weight.
- It gives a detailed description of normal contact force or normal reaction which always acts perpendicular to the surface of contact. It also explains the method to determine the direction of normal reaction and action-reaction pair.
- It explains the Tension of a string as a pulling force. It also describes the definition of an ideal string and pulley.
- For the given system as shown in the figure, find as many action-reaction pairs of forces.
- For the given system as shown in figure, find normal reaction on the sphere.
- A solid sphere of known mass is placed over two smooth inclined planes as shown in figure. Normal reaction on the sphere from the surfaces will be...?
- A sphere of mass m is held between two smooth inclined walls. Find the normal reaction of the wall (2).
- For the system as shown In figure, the value of W is given. Find the tensions in rope A and B.
- For the system as shown in figure, the weight W1 is given. Find T1, T2, T3 and W2.
- A mass of 10 kg is suspended from two ideal springs as shown in the figure. If the first spring stretches by 2cms and second by 5cms, find the spring constant of both the springs.
- All surfaces shown in the figure are smooth. System is released with the spring un-stretched. In equilibrium, what will be the compression in the spring?
- Find the tension in the spring for each case as shown in figures. Consider springs, cords and pulleys to be ideal.
- Two blocks A and B of known masses are held at rest such that the spring is in natural length. Find out the acceleration of both the blocks just after release.
- This video discusses the validity of Newton’s 1st and 2nd law in an accelerating frame of reference through an example.
- This video describes the Inertial and non-inertial frame of references and their relation with the Newton’s 1st and 2nd law.
- This video explains the concept of Pseudo force as a means to make Newton’s law valid in a non-inertial frame.
- Frame A and B are accelerating with respect to a point P1 and P2 respectively. Frame C and D are moving with constant velocity with respect to Frame A and D respectively. If the reference frame of P1 or P2 is not known whether it is inertial, answer the following.

(a) Which of the reference frames A, B, C, D are inertial.

(b) If Newton's first law is found to be valid in B. Which frames are inertial?

(c) If Newton's first law is found to be valid in both Frame A and Frame B, what can we say about their relative velocity? - A particle is observed from two frames S1 and S2. The frame S2 moves with respect to S1 with an acceleration ‘a’. Let F1 and F2 be the pseudo forces on the particle when seen from S1 and S2 respectively. Which of the following are not possible? (a) F1= 0, F2 = 0 (b) F1= 0, F2 = 0 (c) F1= 0, F2 = 0 (d) F1= 0, F2 = 0
- Statement 1: Newton's first law is merely a special case (a = 0) of the second law. Statement 2: Newton's first law define the frame from where Newton's second law; F = ma, F representing the net real force acting on a body; is applicable.
- Find out the correct and incorrect statement and whether statement 2 is correct explanation of statement 1.
- A particle is found to be at rest when seen from a frame S1 and moving with a constant velocity when seen from another frame S2. Which frame out of S1 and S2 is inertial and non-inertial?
- Statement 1: A particle is found to be at rest when seen from a frame S1 and moving with a constant velocity when seen from another frame S2. We can say both the frames are inertial.

Statement 2: All frames moving uniformly with respect to an inertial frame are themselves inertial. - Find out the correct and incorrect statement and whether statement 2 is correct explanation of statement 1.
- A block of mass m is lying on a frictionless surface. It is acted upon by a force F towards right. Find acceleration of the block.
- Two blocks connected through a mass-less inelastic string are pulled by a force F towards right on a frictionless surface. Find the tension in the string.
- A train of four blocks is being pulled across a frictionless floor by force F as given in the figure. What total mass is accelerated to the right by external force F, cord 3 and cord 1. Also, rank the blocks according to their acceleration and the cords according to their tension in decreasing order.
- A constant horizontal force F of is applied to a block A of mass m1, which pushes against a bigger block B of mass m2. The blocks slide over a frictionless surface, along an x axis(a)What is the acceleration of the blocks? (b) What is the force exerted by A on B?
- A force ‘F’ is applied to the system as shown in the figure. Resulting acceleration 'a' of the rope and blocks across the frictionless surface is constant. Mass of both the block and mass of the rope is given. Find the force ‘F’, tension on both blocks and tension at the centre of the rope.
- Figure shows a block m1 lying on a frictionless horizontal surface. The block is connected by a mass-less cord that wraps over a frictionless and mass-less pulley to a second block m2. When system is released from rest; (a) Find the acceleration of m1 and m2. (b) Find the tension in the cord.
- Three boxes A,B and C with given mass are connected by cords, one of which warps over a mass-less and frictionless pulley as shown. When the assembly is released from rest, what is the tension in the cord connecting B and C.
- A monkey of mass m is climbing on a mass-less rope passing over a light frictionless and mass-less pulley. The opposite end of the rope is tied to a weight of mass M lying on a smooth horizontal plane. Find the acceleration of both bodies (relative to the plane) and the tension in the rope, given that the monkey moves upward with an acceleration b relative to the rope.
- When two objects are attached by an ideal string passing over an ideal pulley, the arrangement is called an Atwood machine. Determine the magnitude of the acceleration of the blocks and tension in the string.
- A monkey with known mass climbs up a mass-less rope that runs over a frictionless tree limb and back down to a package of given mass on the ground. What is the magnitude of least acceleration, the monkey must have if it is to lift the package off the ground? If after lifting the package, the monkey stops its climb and holds onto the rope, what will be the magnitude and direction of monkey’s acceleration and tension in the rope.
- Figure shows a man sitting in a chair having combined mass of M that dangles from a mass- less rope, which runs over a mass-less, frictionless pulley and back down to the man's hand. With what force must the man pull on the rope if he is to rise (a) with constant velocity and (b) with an upward acceleration of required magnitude.
- Three blocks A, B and C with known mass are attached by cords that loop over frictionless pulleys. Block B lies on a frictionless table while A and C hang beside the table. When the blocks are released, what is tension in the cord connecting B and C?
- A cord pulls on a box of given mass up along a frictionless plane inclined at an angle; with a certain force. What is the box's acceleration component 'a' along the inclined plane?
- A box of mass is pushed at constant speed up a frictionless inclined ramp by a horizontal force F. What are the magnitudes of the force F and the force on the box from the ramp?
- A sphere of mass m1 and a block of m2 are attached by a lightweight cord that passes over an ideal pulley. The block lies on a frictionless surface inclined at an angle as shown in figure. Find the acceleration of the two objects.
- In Figure; a force F is being applied to a mass m2, parallel to the inclined plane over which the mass is kept. m2 is connected by a cord to mass m1 on the floor. The floor, plane, and pulley are frictionless, and the masses of the pulley and cord are negligible. What will be the tension in the cord for different values of F.
- A block 'A' of mass m is tied to a fixed point C on a horizontal table through a string passing round a mass less smooth pulley B. A force F is applied by the experimenter to the pulley. Show that if the pulley is displaced x, the block will be displaced by 2x. Also find the acceleration of the block and the pulley.
- Consider the situations shown in figure. Both the pulleys and the string are light and all the surfaces are frictionless. a) Find the acceleration of the mass m1. b) Find the tension in the string connected to m2.
- There are two objects 1 and 2 placed on smooth horizontal surface and connected by an inextensible thread in the way as shown in figure. When the objects 1 and 2 move towards right along x- axis after applying a force towards right, find the relation between acceleration of object 1 and 2?
- In the figure shown, a force F is applied to mass 1 towards right. Assuming Pulleys and String are mass-less and frictionless, find the tension in the string?
- Figure shows Atwood's machine, in which two containers of known initial mass are connected by a mass-less cord passing over a mass-less and frictionless pulley. If at t=0; container 1 starts losing mass (through a leak) at a given constant rate , at what rate will the magnitude of container’s acceleration change at (a) t = 0 and t = 3.00 s? (b) When does the acceleration reach its maximum value?
- A ball of mass m is hanging through a string inside a car. The car is moving with an acceleration ‘a’ towards right. a) Find the angle with the vertical and tension 'T' in the string?
- A bob is hanging over a pulley inside a car through a string. The second end of the string is in the hand of person standing in the car. The car is moving with constant acceleration ‘a’ directed horizontally in the right. Other end of the string is pulled with constant acceleration ‘a’ vertically. Find the tension of the string?
- Find the mass M of the hanging block in figure, which will prevent the smaller block from slipping over the triangular block? All the surfaces are frictionless and the strings and the pulleys are light.
- All the surface shown in Figure are assumed to be frictionless. The block of mass m slides on the prism which in turn slides backward on the horizontal surface. Find the acceleration of the smaller block with respect to the prism.
- Three blocks of masses m1, m2 and m3 are connected as shown in figure. All the surfaces are frictionless and the string and the pulleys are light. Find the acceleration of m1.
- What horizontal force must be applied to the cart shown in figure so that the blocks remain stationary relative to the cart? Assume all surfaces and pulleys are frictionless.