1.An elastic climbing rope is tested by fixing one end of the rope to the top of a crane.The other end of the rope is connected to a block which is initially at position A.The block is released from rest. The mass of the rope is negligible.

The unextended length of the rope is 60.0 m. From position A to position B, the block falls freely.

(a)At position B the rope starts to extend. Calculate the speed of the block at position B.

(b)At position C the speed of the block reaches zero. The time taken for the block to fall between B and C is 0.759 s. The mass of the block is 80.0 kg.

(i)Determine the magnitude of the average resultant force acting on the block between B and C.

(ii)Sketch on the diagram the average resultant force acting on the block between B and C. The arrow on the diagram represents the weight of the block.

(iii)Calculate the magnitude of the average force exerted by the rope on the block between B and C.

(c)For the rope and block, describe the energy changes that take place

(i)between A and B.

(ii)between B and C.

(d)The length reached by the rope at C is 77.4 m. Suggest how energy considerations could be used to determine the elastic constant of the rope.


2.A closed box of fixed volume 0.15 m3 contains 3.0 mol of an ideal monatomic gas.

The temperature of the gas is 290 K.

(a)Calculate the pressure of the gas.

(b)When the gas is supplied with 0.86 kJ of energy, its temperature increases by 23 K. The specific heat capacity of the gas is 3.1 kJ kg-1 K-1.

(i)Calculate, in kg, the mass of the gas.

(ii)Calculate the average kinetic energy of the particles of the gas.

(c)Explain, with reference to the kinetic model of an ideal gas, how an increase in temperature of the gas leads to an increase in pressure.


3.A beam of coherent monochromatic light from a distant galaxy is used in an optics experiment on Earth.

(a)The beam is incident normally on a double slit. The distance between the slits is 0.300 mm. A screen is at a distance D from the slits. The diffraction angle θ is labelled.

(i)A series of dark and bright fringes appears on the screen. Explain how a dark fringe is formed.

(ii)The wavelength of the beam as observed on Earth is 633.0 nm. The separation between a dark and a bright fringe on the screen is 4.50 mm. Calculate D.

(b)The air between the slits and the screen is replaced with water. The refractive index of water is 1.33.

(i)Calculate the wavelength of the light in water.

(ii)State two ways in which the intensity pattern on the screen changes.




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