Newton Law of Motion Exercise - I

NEWTON LAW OF MOTION Exercise - I Page # 17 UNSOLVED PROBLEMS Q.1 Give the magnitude and direction of the net force acting on (a) a drop of rain falling down with a constant speed. (b) a cork of mass 10 g floating on water. (c) a kite skillfully held stationary in the sky, (d) a car moving with a constant velocity of 30 km/h on a rough road, (e) a high-speed electron in space far from all gravitating objects, and free of electric and magnetic fields. Q.2 A pebble of mass 0.05 kg is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble. (a) during its upward motion, (b) during its downward motion, (c) at the highest point where it is momentarily at rest. Do your answer change if the pebble was thrown at an angle of say 45° with the horizontal direction ? Ignore air resistance. Q.3 Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg. (a) just after it is dropped from the window of a stationary train. (b) just after it is dropped from the window of a train running at a constant velocity of 35 km/h. (c) just after it is dropped from the window of a train accelerating with 1 m s–2, (d) lying on the floor of a train which is accelerating with 1 m s–2, the stone being at rest relative to the train. Neglect air resistance throughout. Q.4 One end of a string of length l is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves i a circle with speed v the net force on the particle (directed towards the centre) is. mv 2 mv 2 (iii) T + (iv) 0   T is the tension in the string. [Choose the correct alternative]. (i) T, (ii) T – Q.5 A constant retarding force of 50 N is applied to a body of mass 20 kg moving initially with a speed of 15 m s–1. How long does the body take to stop ? Q.6 A constant force acting on a body of mass 3.0 kg changes its sped from 2.0 m s–1 to 3.5 s–1 in 25 s. The direction of the motion of the body remains unchanged. What is the magnitude and direction of the force ? Q.7 A body of mass 5 kg is acted upon by two perpendicular forces 8 N and 6 N. Give the magnitude and direction of the acceleration of the body. Q.8 The driver of a three-wheeler moving with a speed of 36 km/h sees a child standing in the middle of the road and brings his vehicle to rest in 4.0 s just in time to save the child. What is the average retarding force on the vehicle ? The mass of the three-wheeler is 400 kg and the mass of the driver is 65 kg. Q.9 A rocket with a lift-off mass 20,000 kg is blasted upwards with an initial acceleration of 5.0 m s–2. Calculate the initial thrust (force) of the blast. Q.10 A particle of mass 0.40 kg moving initially with a constant speed of 10 m s–1 to the north is subject to a constant force of 8.0 N directed towards the south for 30 s. Take the instant the force is applied to be t = 0, the position of the particle at that time to be x = 0, and predict its position at t = – 5 s, 25 s, 100 s. Q.11 A truck starts from rest and accelerates uniformly with 2.0 m s–2. At t = 10 s, a stone is dropped by a person standing on the top of the truck (6 m high from the ground). What are the (a) velocity, and (b) acceleration of the stone at t = 11 s ? (Neglect air resistance.) Q.12 A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is 1 m s–1. What is the trajectory of the bob if the string is cut when the bob is (a) at one of its extreme positions, (b) at its mean position. Q.13 A man of mass 70 kg stands on a weighing scale in a lift which is moving (a) upwards with a uniform speed of 10 m s–1, (b) downwards with a uniform acceleration of 5 m s–2, (c) upwards with a uniform acceleration of 5 m s–2 What would be the readings on the scale in each case ? NEWTON LAW OF MOTION Page # 18 (d) What would be the reading if the lift mechanism Q.21 A stone of mass 09.25 kg tied to the end of a failed and it hurtled down freely under gravity ? string is whirled round i a circle of radius 1.5 m with a Q.14 Figure shows the position-time graph of a particle of mass 4 kg. What is the (a) force on the particle for t < 0, t > 4 s, 0 < t < 4 s ? (b) impulse at t = 0 and t = 4 s ? (Consider one-dimensional motion only). x(m) speed of 40 rev./min in a horizontal plane. What is the tension in the string ? What is the maximum speed with which the stone can be whirled around if the string can withstand a maximum tension of 200 N ? Q.22 If in 5.21 the speed of the stone is increased beyond the maximum permissible value, and the string breaks suddenly, which of the following correctly 3 describes the trajectory of the stone after the string A breaks : 0 4 t(s) (A) the stone jerks radially outwards. (b) the stone flies off tangentially from the instant Q.15 A horizontal force of 600 N pulls two masses 10 the string breaks, kg and 20 kg (lying on a frictionless table) connected (c) the stone flies off at an angle with the tangent whose by a light string. What is the tension in the string ? magnitude depends on the speed of the particle ? Does the answer depend on which mass end the pull is applied ? Q.23 For ordinary terrestrial experiments, which of the observers below are inertial and which non-inertial Q.16 Two masses 8 kg and 12 kg are connected at (a) a child revolving in a " giant wheel". the two ends of a light inextensible string that goes (b) a driver in a sports car moving with a constant over a frictionless pulley. Find the acceleration of the high speed of 200 km/h on a straight road, masses, and the tension in the string when the masses are released. (c) the pilot of an aeroplane which is taking off, (d) the pilot of an aeroplane which is taking off, (d) a cyclist negotiating a sharp turn. Q.17 A nucleus is at rest i the laboratory frame of (e) the guard of a train which is slowing down to stop reference. Show that if it disintegrates into two smaller at a station ? nuclei the products must be emitted in opposite Q.24 One often comes across the following type of directions. statement concerning circular motion : 'A particle moving uniformly along a circle experiences a force Q.18 Two billiard balls each of mass 0.05 kg moving directed towards the centre (centripetal force) and in opposite directions with speed 6 m s–1 collide and an equal and opposite force directed away from the rebound with the same speed. What is the impulse centre (centrifugal force). The two forces together imparted to each ball due to the other ? keep the particle in equilibrium'. Explain what is wrong Q.19 A shell of mass 0.020 kg is fired by a gun of with this statement. mass 100 kg. If the muzzle speed of the shell is Q.25 Explain why 80 m s–1, what is the recoil speed of the gun ? (a) a horse cannot pull a cart and run in empty space, Q.20 a batsman deflects a ball by an angle of 45° without changing its initial speed which is equal to 54 km/h. What is the impulse imparted to the ball ? (Mass of the ball is 0.15 kg.) (b) passengers are thrown forward from their seats when a speeding bus stops suddenly. (c) it is easier to pull a lawn mower than to push it, (d) a cricketer moves his hands backwards while holding a catch. NEWTON LAW OF MOTION Page # 19 Q.26 Figure shows the position-time graph of a particle Q.29 A helicopter of mass 1000 kg rises with a vertical of mass 0.04 kg. Suggest a suitable physical context acceleration of 15 m s–2. The crew and the passengers for this motion. What is the time between two weigh 300 kg. give the magnitude and direction of the consecutive impulses received by the particle ? What (a) force on the floor by the crew and passengers, is the magnitude of each impulse ? (b) action of the rotor of the helicopter on the surrounding air, (c) force on the helicopter due to the surrounding air. x(cm) Q.30 A steam of water flowing horizontally with a 2 0 2 4 6 8 t(s) speed of 15 m s–1 gushes out of a tube of cross- sectional area 10 m2, and hits at a vertical wall –2 nearby. What is the force exerted on the wall by the impact of water, assuming it does not rebound ? Q.27 figure shows a man standing stationary with respect to a horizontal conveyor belt that is Q.31 Ten one-rupee coins are put on top of each accelerating with 1 m s . What is the net force on other on a table. Each coin has a mass m kg. give the the man ? If the coefficient of static friction between magnitude and direction of the mans shoes and the belt is 0.2, up to what (a) the force on the 7th coin (counted from the bottom) acceleration of the belt can the man continue to be due to all the coins on its top. stationary relative to the belt ? (b) the force on the 7th coin by the eighth coin, (Mass of the man = 65 kg.) (c) the reaction of the 7th coin on the 7th coin. –2 Q.32 a aircraft executes a horizontal loop at a speed of 720 km/h with its wings banked at 15°. What is the radius of the loop ? Q.33 A train rounds an unbanked circular bend of Q.28 A stone of mass m tied to the emf of a string is radius 30 m at a speed of 54 km/h. The mass of the revolved in a vertical circle of radius R. The net forces train is 106 kg. What provides the centripetal force at the lowest and highest points of the circle directed required for this purpose ? The engine or the rails ? vertically downwards are : [Choose the correct What is the angle of banking required to prevent alternative]. wearing out of the rail ? Lowest Point Highest Point (a) mg – T1 mg + T2 (b) mg + T1 mg – T2 (c) mg + T1 – (mv12)/R mg – T2 +(mv12)/R (d) mg – T1 – (mv12)/R mg + T2+(mv12)/R Here T1, T2 (and v1, v2) denote the tension in Q.34 "It is reasonable to consider the Earth as an inertial frame for any laboratory scale terrestrial experiments, but the Earth is a non-inertial frame of reference for astronomical observations". Explain this statement. Do you see how the same frame of the string (and the speed of the stone) at the lost reference is approximately inertial for one purpose, and the highest point respectively. and non-inertial for the other ? NEWTON LAW OF MOTION Page # 20 Q.35 A block of mass 25 kg is raised by a 50 kg man in two different ways as shown in figure 5.22. What is the action on the floor by the man in the two cases ? A If the floor yields to a normal force of 700 N, which mode should the man adopt to lift the block without B 200N the floor yielding ? Q.38 A block of mass 15 kg is placed on a long trolley. The co-efficient of static friction between the block and the trolley is 0.18. The trolley accelerates from rest with 0.5 m s–2 for 20 s and then moves with uniform velocity. Discuss the motion of the block as viewed by (a) a stationary observer on the ground, 25kg 25kg (b) an observer moving with the trolley. Q.36 A monkey of mass 40 kg climbs on a rope as Q.39 The rear side of a truck is open and a box of 40 shown in figure which can bear a maximum tension of kg mass is placed 5 m away from the open end as 600 N. In which of the following cases will the rope shown in Fig. The co-efficient of friction between the break : The monkey box and the truck below it is 0.15. On a straight road, (a) climbs up with an acceleration of 6 m s–2 the truck starts from rest and accelerates with a (b) climbs down with an acceleration of 4 m s–2 constant acceleation of 2 m s–2. At what distance (c) climbs up with a uniform speed of 5 m s–1 from the starting point does the box fall off the truck (d) falls down the rope nearly freely under gravity ? ? (Ignore the size of the box) \ (Ignore the mass of the rope) Q.37 Two bodies A and B of masses 5 kg and 10 kg in contact with each other rest on a table against a rigid partition (figure). The co-efficient of friction between the bodies and the table is 0.15. A force of 200 N is applied horizontally at A. What are (a) the reaction of the partition (b) the action-reaction forces between A and B? What happens when, the partition is removed ? Does the answer to (b) change, when the bodies are in motion ? Ignore the difference between s and k.