Work, Energy and Power
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A shot travelling at the rate of 100 ms–1 is just able to pierce a plank 4 cm thick. What velocity is required to just pierce a plank 9 cm thick?
A 16 kg block moving on a frictionless horizontal surface with a velocity of 4 m/s compresses an ideal spring and comes to rest. If the force constant of the spring be 100 N m–1, then how much is the spring compressed?
The human heart discharges 75ml of blood at each against a pressure of 0.1 m of Hg. Calculate the power of the heart assuming that the pulse frequency is 80 beats per minute. Given, density of mercury =13.6×103 kg/m3.
A railway carriage of mass 10000 kg moving with a speed of 15 ms–1 strikes a stationary carriages of the same collision, the carriages get coupled and move together. What is their common speed after collision?
Two ball bearings of mass m each moving in opposite directions with equal speed v collide head on with each other. Predict the outcome of the collision, assuming it to be perfectly elastic.
Find the center of mass of the parabolic lamina bounded by the curves y² = 2px and x = a, figure.
A ball of 0.1 kg makes an elastic head on collision with a ball of unknown mass that is initially at rest. If the 0.1 kg ball rebounds at one third of its original speed, what is the mass of the other ball?
Show that moment of a couple does not depend on the point about which you take the moments.
Two masses as shown in figure are released from heir their positions. Calculate the velocity with which the mass of 5 kg touches the surface if its initial height from the surface is 4 m. Also, show that the gain in KE of the system is equal to loss its P.E. Take g = 10 ms–2.
The mass of a pendulum bob is 0.2 kg, and it is suspended by a string 1 m long. It is pulled aside until the thread is at 30° to the vertical. How much work is done? The ball is now released. Find its K.E. at the lowest point? Take g = 10 ms–2.
When an automobile moving with a speed of 36 km/h reaches an upward inclined road of angle 30°, its engine in switches off. If the coefficient of friction is 0.1, how much distance will the automobile move before coming to rest? Take g = 10 ms–2.
A man cycles up a bill whose slope is 1 in 20 with a velocity of 6.4 km h–1 along the hill. The weight of the man and the cycle is 98 kg. What work per minute is the man doing? What is his horse power?
Find the center of mass of three particles of masses m, 2m and 3m which are at the vertices of an equilateral triangle of sides a.