Two identical billiard balls strikes a rigid wall with a same speed but at different angles, and get deflected without any change in speed as shown in figure. What is (a) Direction of the force on the wall due to each ball. (b) The ratio of the magnitude of impulse imparted to the balls by the wall?
Ans:(a) \(along\left(-Ve\right)X\) and (b) \(1.2\).
A lift of mass \(2000kg\) is supported by thick steel ropes. If maximum upward acceleration of the lift is \(1.2 ms^{-2}\) and the breaking stress for the steel ropes is \(\left(2.8\times 10^{8}\right)N.m^{-2}\). What should be the maximum diameter of the rope?
Ans: \(d_{max}=0.01m\).
A \(75kg\) man stands on the lift. What force does the floor of the lift exerts on the man when the lift is moving upwards with a acceleration of \(2.0m.s^{-2}\)? Take: \(g=10 m.s^{-2}\).
Ans: \(R=90kgf\).
Find the apparent weight of a man weighing \(60kg\) on the earth when he stands on a lift which is, (a) Rising with an acceleration of \(1.2m.s^{-2}\)? (b) Going down with the same acceleration? (c) Falling freely under the acceleration due to gravity? and (d) Going up or down with an uniform velocity? Given: \(g=9.8m.s^{-2}\).
Ans:(a) \(55kgf\), (b) \(0\left(Zero\right)kgf\) and (c) \(49kgf\).
An elevator and its load weighing a total of \(800kg\). Find: the tension T in the supporting cable when the elevator, originally moving downward at \(20m.s^{-1}\) is brought to rest with an constant retardation with in a distance of \(50m\).
Ans: \(T=\left(1.104\times10^{8}\right)N\)
A balloon with a mass M is descending down with a =n acceleration of a, where a<g. What is the amount of mass m of its content mass be removed so that it starts moving up with an acceleration a?
Ans: \(m=\frac{2Ma}{g+a}\).
A light string is passing over a smooth and light pulley connects two blocks of masses \(m_{1}\) and \(m_{2}\) vertically. Calculate: the ratio of masses if the acceleration of the system is \(\frac{g}{8}\).
Ans: \(\frac{m_{1}}{m_{2}}=\frac{7}{9}\).
A helicopter of mass \(500kg\) rises with a vertical acceleration of \(10 m.s^{-2}\). The weight of the pilot is \(60kg\). Give: the magnitude and direction of; (a) Force on the floor of the helicopter by the pilot. (b) Action of the rotor of the helicopter on the surrounding air. (c) Force on the helicopter due to the surrounding air. TAKE: \(g=10m.s^{-2}\).
Ans: (a) \(R=1200N\), (b) \(F_{surrounding}=11200N\) and \(11200N\).
A block of mass M is pulled along a horizontal frictionless surface by a rope of mass m. If a force of P is applied at free end of the rope, then calculate; the force exerted by the rope on the block.
Ans: \(T=\frac{MP}{M+m}\).
A block of mass \(kg\) lies on a horizontal frictionless plane. A string attached to it passes over a smooth pulley fixed to the edge of the plane and carries a load of mass \(1kg\). Find: acceleration of the system.
Ans: \(a=1.63\frac{m}{s^{2}}\).
A string passes over a smooth frictionless light pulley with masses \(4kg\) and \(5kg\) attached to the end of a string and hanging vertically. Find: the acceleration of the either mass and tension in the string.
Ans: \(a=1.09\frac{m}{s^{2]}\) and \(T=43.55N\).
Three identical blocks of mass \(m=2kg\) are drawn by a force \(F=10.2N\) with an acceleration of \(0.6m.s^{-2}\) on a frictionless surface as shown in below figure. Calculate: the tension in the string between the blocks B and C.
Ans: \(7.8N\).
A person of mass \(60kg\) is inside a lift of mass \(940kg\) and presses the button on control panel. The lift starts moving upwards with an acceleration of \(1.0m.s^{-2}\). Find: the tension in the supporting cable if \(g=10m.s^{-2}\).
Ans: \(Tension=\left(11\times10^{}\right)N\)
Two blocks of masses \(m_{1}\) and \(m_{2}\) in contact lie on a smooth horizontal surface as shown in below diagram: The blocks are pushed by a force of F. If, the two blocks are always in contact, what is the force on their common interface?
Three blocks are connected together as shown below figure and lie on a horizontal frictionless table and pulled to the right with a force of \(F=50N\). If,\(m_{1}=5kg\), \(m_{2}=10kg\) and \(m_{3}=15kg\). Find: the tension \(T_{1}\) and \(T_{2}\).
Ans: \(T_{1}=8.33N\) and \(T_{2}=25N\)
Four blocks of same mass m connected by cords are pulled by a force F on smooth horizontal surface as shown in figure. Determine: the tensions \(T_{1}\), \(T_{2}\) and \(T_{3}\) in cords.
Ans: [late]T_{1}=\frac{3}{4}F[/latex], \(T_{2}=\frac{1}{2}F\) and \(T_{3}=\frac{1}{4}F\).
A system consisting two blocks as shown in figure moves over a horizontal smooth surface when a horizontal force of \(10N\) is applied on it. Find: the tension in the connecting string and the acceleration of the system. (Neglect Friction).
Ans: \(a=2.5\frac{m}{s^{2}}\) and \(T=5N\).
A wooden block of mass \(2kg\) rests on a smooth horizontal floor. When an iron cylinder of mass \(25kg\) is placed on the top of the block, the floor yields steadily and the block and the cylinder together go down with an acceleration of \(0.1m.s^{-2}\). What is the action of the block on the floor? (a) Before and (b) after the floor yields? take: \(g=10m.s^{-2}\).
Ans:(a) \(20N\) Downward and (b) \(267.3N\) Downward.
The masses \(m_{1}\), \(m_{3}\) and \(m_{3}\) of the three bodies shown in figure is 5, 2 and 3kg respectively. Calculate: the value of \(T_{1}\), \(T_{2}\) and \(T_{3}\) when; (a) The whole system going upwards with an acceleration of \(2.0m.s^{-2}\). (b) Whole system is stationary. Take: \(g=9.8m.s^{-2}\).
Ans:(I) \(T_{1}=118N\), \(T_{2}=59N\) and \(T_{3}=35.4N\). (ii) \(T_{1}=98N\), \(T_{2}=49N\) and \(T_{3}=29.4N\).
A block of mass \(100kg\) is set into motion on a frictionless horizontal surface with the help of frictionless pulley and a rope system as shown in figure; What is the horizontal force should be applied on the to produce an acceleration of \(10 cm.s^{-2}\) in the block?
Ans: \(F=5N\).
Three identical blocks, each having a mass of m are pushed by a force of F on a frictionless table as shown. What will be the acceleration of the blocks? What is net force on block A? What force does A applies on block B? What force B applies on the block C? Show the action reaction pairs on the contact surface.
Ans: \(\frac{F}{3m}\), \(\frac{F}{3}\), \(\frac{2F}{3}\) and \(\frac{F}{3}\).
