Numerical Problems 7.1: A 100 g body hung on a spring, which elongates the spring by 4 cm. When a certain object is hung on the spring and set vibrating, its period is 0.568 s. What is the mass of the object pulling the spring? (Ans: 0.20 kg)
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Numerical Problems 7.2: A load of 15 g elongates a spring by 2 cm. If body of mass 294 g is attached to the spring and is set into vibration with an amplitude of 10 cm, what will be its (i) period (ii) spring constant (iii) maximum speed of its vibration. (Ans: (a) 1.26 s, (b) 7.35 N m⁻¹, (c) 49.0 cm s⁻¹)
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Numerical Problems 7.3: An 8 kg body executes SHM with amplitude 30 cm. The restoring force is 60 N when the displacement is 30 cm. Find.
(i) Period.
(ii) Acceleration, speed, kinetic energy and potential energy when the displacement is 12cm.
(Ans: (i) T = 1.3 s (ii) `\vec a` = 3 m s⁻² , `\vec v` = 1.4 m s , K.E = 7.6 J , PE = 1.44 J) )
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Numerical Problems 7.4: A block of mass 4 kg is dropped from a height of 0.8 m on to a spring of spring constant k = 1960 N m⁻¹, Find the maximum distance through which the spring will be compressed. (Ans: 0.18 m)
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Numerical Problems 7.5: A simple pendulum is 50 cm long. What will be its frequency of vibration at a place where g = 9.8 m s⁻². (Ans: 0.70 Hz)
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Numerical Problems 7.6: A block of mass 1.6 kg is attached to a spring with spring constant 1000 N m⁻¹, as shown is figure on book 7.14. The spring is compressed through a distance of 2 cm and the block is released from rest. Calculate the velocity of the block as it passes through the equilibrium position, x = 0, if the surface is frictionless. (Ans: 0.50 m s⁻¹)
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Numerical Problems 7.7: A car of mass 1300 kg is constructed using a frame supported by four springs. Each spring has a spring constant 20,000 N m⁻¹. If two people riding in the car have a combined mass of 160 kg, find the frequency of vibration of the car, when it is driven over a pot hole in the road. Assume the weight is evenly distributed. (Ans: 1.18 Hz 0.6 Hz)
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Numerical Problems 7.8: Find the amplitude, frequency and period of an object vibrating at the end of a spring, if the equation for its position, as a function of time, is:
x = 0.25 cos(`\frac {π}{8}`) tWhat is the displacement of the object after 2s?
(Ans: 0.25 m, `\frac {1}{16}`Hz, 16 s, x = 0.18 m )
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3. Website for Single National Curriculum Pakistan - All Subjects Notes
© 2022-Onwards by Academic Skills and Knowledge (ASK)
Note: Write me in the comment box below for any query and also Share this information with your class-fellows and friends.
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