A wire. 100 kg. Fig. 1.1

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1 1 Fig. 1.1 shows circulr cylinder of mss 100 kg being rised by light, inextensible verticl wire. There is negligible ir resistnce. wire 100 kg Fig. 1.1 (i) lculte the ccelertion of the cylinder when the tension in the wire is 1000 N. [3] (ii) lculte the tension in the wire when the cylinder hs n upwrd ccelertion of 0.8 m s 2. [2] The cylinder is now rised inside fixed smooth verticl tube tht prevents horizontl motion but provides negligible resistnce to the upwrd motion of the cylinder. When the wire is inclined t 30 to the verticl, s shown in Fig. 1.2, the cylinder gin hs n upwrd ccelertion of 0.8 m s 2. tube kg wire Fig. 1.2 (iii) lculte the new tension in the wire. [3] 2 oxes nd slide on smooth, horizontl plne. ox hs mss of 4 kg nd box mss of 5 kg. They re connected by light, inextensible, horizontl wire. Horizontl forces of 9 N nd 135 N ct on nd in the directions shown in Fig. 5. 9N 4 kg 5 kg 135 N Fig. 5 lculte the tension in the wire joining the boxes. [4] PhysicsndMthsTutor.com

2 3 Fig. 3 shows system in equilibrium. The rod is firmly ttched to the floor nd lso to n object, P. The light string is ttched to P nd psses over smooth pulley with n object Q hnging freely from its other end. verticl light string 20kg P Q smooth pulley 15kg verticl light rod floor Fig. 3 (i) Why is the tension the sme throughout the string? [1] (ii) lculte the force in the rod, stting whether it is tension or thrust. [3] 4 Two trucks, nd, ech of mss kg, re pulled long stright, horizontl trck by constnt, horizontl force of P N. The coupling between the trucks is light nd horizontl. This sitution nd the resistnces to motion of the trucks re shown in Fig N 10000kg 300N 10000kg PN Fig. 4 The ccelertion of the system is 0.2 m s 2 in the direction of the pulling force of mgnitude P. (i) lculte the vlue of P. [3] Truck is now subjected to n extr resistive force of 2000 N while P does not chnge. (ii) lculte the new ccelertion of the trucks. [2] (iii) lculte the force in the coupling between the trucks. [2] PhysicsndMthsTutor.com

3 5 trin consists of n engine of mss kg pulling one truck of mss 4000 kg. The coupling between the engine nd the truck is light nd prllel to the trck. The trin is ccelerting t 0.25 m s 2 long stright, level trck. (i) Wht is the resultnt force on the trin in the direction of its motion? [2] The driving force of the engine is 4000 N. (ii) Wht is the resistnce to the motion of the trin? [1] (iii) If the tension in the coupling is 1150 N, wht is the resistnce to the motion of the truck? [2] With the sme overll resistnce to motion, the trin now climbs uniform slope inclined t 3 to the horizontl with the sme ccelertion of 0.25 m s 2. (iv) Wht extr driving force is being pplied? [3] PhysicsndMthsTutor.com

4 6 box of weight 147 N is held by light strings nd. s shown in Fig. 7.1, is inclined t to the horizontl nd is fixed t ; is held t. The box is in equilibrium with horizontl nd such tht sin 0.6 nd cos 0.8. Fig. 7.1 (i) lculte the tension in string. [3] (ii) Show tht the tension in string is 196 N. [2] s shown in Fig. 7.2, box of weight 90 N is now ttched t nd nother light string D is held t D so tht the system is in equilibrium with still horizontl. D is inclined t b to the horizontl. D b 90N Fig. 7.2 (iii) Explin why the tension in the string is still 196 N. [2] (iv) Drw digrm showing the forces cting on the box t. Find the ngle b nd show tht the tension in D is 216 N, correct to three significnt figures. [7] PhysicsndMthsTutor.com

5 The string section D is now tken over smooth pulley nd ttched to block of mss M kg on rough slope inclined t 40 to the horizontl. s shown in Fig. 7.3, the prt of the string ttched to the box is still t b to the horizontl nd the prt ttched to the block is prllel to the slope. The system is in equilibrium with frictionl force of 20 N cting on the block up the slope. D b Mkg 90N 40 Fig. 7.3 (v) lculte the vlue of M. [4] PhysicsndMthsTutor.com

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