Laws of Motion

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1. A smooth inclined plane of length L, having an inclination α with horizontal is inside a lift which is moving down with retardation 'a'. The time taken by the body to slide down the inclined plane from rest will be?
2. A block of mass m lying on a horizontal surface is to be brought into motion by a pulling force F. At what angle "A" with horizontal should the force F be applied so that its magnitude is minimum ? Also find this minimum magnitude.
3.  A 921-kg sports car is moving rightward with a speed of 29.0 m/s. The driver suddenly slams on the brakes and the car skids to a stop over the course of 3.20 seconds with the wheels locked. Determine the average resistive force acting upon the car.
4. A tow truck exerts a 18300-N force upon a 1210-kg car to drag it out of a mud puddle onto the shoulder of a road. A 17900 N force opposes the car's motion. The plane of motion of the car is horizontal. Determine the time required to drag the car a distance of 6.90 meters from its rest position.
5. For the next several questions, consider the velocity-time plot below for the motion of an object along a horizontal surface. The motion is divided into several time intervals, each labeled with a letter. 
   22. During which time interval(s), if any, are there no forces acting upon the object? List all that apply.
   23. During which time interval(s), if any, are the forces acting upon the object balanced? List all that apply.
   24. During which time interval(s), if any, is there a net force acting upon the object? List all that apply.
   25. During which time interval(s), if any, is the net force acting upon the object directed toward the right? List all that apply.
   26. During which time interval(s), if any, is the net force acting upon the object directed toward the left? List all that apply.
   6.  The centre of gravity of a car is at height h and the distance between its wheel is 2a. What is the maximum speed with which this car can go around a level curve of radius r without overturning ?
   7.   A 4.44-kg bucket suspended by a rope is accelerated upwards from an initial rest position. If the tension in the rope is a constant value of 83.1 Newtons, then determine the speed (in m/s) of the bucket after 1.59 seconds.
   8.   A lift of mass 1000 kg, which is moving with an acceleration of 1 m/s² in upward direction has tension developed in its string equal to____________
   9.   A light string passes over a smooth light pulley connects two blocks of masses m_a and m_b. If the acceleration of the system is (g/8), then ratio of masses is_________
   10.  The total mass of a lift and passengers is 1000 kg. The variation of velocity with me is given in the graph with velocity being positive in the upward direction.
   (a)    What is the tension in the rope pulling the left at t = 1 sec.
   (b)    What is the tension at t = 3 sec.
   (c)    What is the tension at t = 9 sec.
   
   
   11.  A man pulls himself, and the cradle he is sitting in, by pulling down on the rope which is tied to the cradle and would over a fixed pulley. If the man weights 60 kg and the cradle weighs 25 kg then how much force must the man exert on the rope to pull himself up at an acceleration of l m/s².
   
   
   
   
   
   
   
   12.  A mass m₁ is placed at an inclined plane which makes a angle θ with the horizontal. A string is attached to the mass. The other end of the string supports mass m₂ hanging freely. The string passes over a friction less pulley. Calculate acceleration of blocks.
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   13. In the system shown in figure, acceleration of cart is a = g/7; such that m₂ is in a critical equilibrium of just to go upwards. For ideal pulley and string find on the contact surface of m₂ (Also m₁ rests on a friction less surface). Find the co-efficient of friction between m₂ and cart.
   
   
   
   14. In a configuration as shown in figure masses of 10, 20, 40 kg are hanging by pulley's all strings and pulleys are ideal. Find the acceleration of the masses.
   
   
   
   15.  A small block of mass m is placed on a wedge lying on a horizontal table. The wedge has mass M and face of the wedge is inclined at angle θ with the horizontal. Neglecting any friction, find the acceleration of two blocks.
   
   
   
   
   
   16. A block of mass 0.1 kg is held against a wall by applying a horizontal force of 5N on the block. If the coefficient of friction between the block and the wall is 0.5. Find the magnitude of the frictional force acting on the block.
   
   
   17. Physical independence of force is a consequence of which law of motion ?
   
   
   18. A car travelling at a speed of 30 km/h is brought to a halt in 8 mtr by applying brakes. If the same car is travelling at 60 km/h, it can be brought to halt with the same breaking power in_______mtr.
   
   
   19. A chain is lying on a rough table with a friction (1/n) of its length hanging down from the edge of the table. It is just on the point of sliding down from the table, then the coefficient of friction between the table and chain is___________
   
   
   20. Two masses m₁ and m₂ are placed touching each other on an inclined plane forming an angle θ with the horizontal the coefficient of friction between the inclined plane and m₁ is μ₁ and that of between plane and m₂ is μ₂ where μ₁ > μ₂.
         (a)    Find the interaction force between the two masses.
         (b)    What is the minimum angle θ at which masses start sliding.