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Consider a circus act where the actor (of mass m) slides without friction under the
influence of gravity on a wire that makes an angle a with the upward verticle axis,
and rotates with constant angular velocity w.
(i) Write the Lagrangian using the appropriate generalized coordinates.
(ii) Write down the equation of motion for the generalized coordinates and discuss
the motion of the stunt actor.
State the Hamilton’s principle. In what is known as folk’s physics analogues
principles are often phrased to describe every day’s experience. For example, water
is said to take a path of least resistance while flowing from one point to another
point*. Likewise, example of least action/effort is also seen in human pathways as
shown in the following bicycle-lane! Discuss if these behaviors somehow relate to
Hamilton’s principle or simply human’s innate behavior of least effort! Have you
acted in similar ?
a vehicle of mass m moving without friction with speed v.suddenly, rain starts falling vertically(relative to the road) such that per unit time,mass b falls on the vehicle,comes to rest relative to it, and says within it. determine the vehicle velocity as a function of time, up to a time it can contain all the falling
a rod of length l varies linearly with position along its length, such that it increas to thrice its value from one end to the other. this rod is paleced on a frictionless horizontal surface and a horizontal force of magnitude f is applied to a point on the rod. at what point should this force be applied such that the rod slides on the surface without rotating
Rigid tank contains a hot fluid that is cooled while being stirred by a paddle wheel. Initially, the internal energy of the fluid is 800 kJ. During the cooling process, the fluid loses 500 kJ of heat, and the paddle wheel does 100 kJ of work on the fluid. Determine the final internal energy of the fluid. Neglect the energy stored in the paddle wheel.
2. A child pulls a wagon by the handle along a flat sidewalk. She exerts a force of 76.0 N at an angle of 27 degrees ° above the horizontal while she moves the wagon 22.0 m forward. The force of friction on the wagon is 17.0 N. a) Calculate the mechanical work done by the child on the wagon. b) Calculate the total work done on the wagon.
A group of bike riders took a trip that lasted a total of 10 hours. During the first 7 hours, they traveled a total of 100 kilometers north. during the last 3 hours, they traveled 30 kilometers south. what was the groups distance traveled for the entire trip?
1.For a body dropped from a height, h, the speed, V,with which it strikes the ground depends only on h and g and a dimensionless numerical factor. Obtain an expression connecting v, h and g.
Two rockets A and B depart from earth at a steady speed of 0.6c in opposite directions, having synchronized clocks with each other and with earth at departure. After one year as measured in Earth’s frame, rocket B emits a light signal. At what time, in the frames of earth and rockets A and B, does rocket A receive the signal? Work out the problem in all three frames and verify the answers are same. Use unit of distance as light year and that of time as year.
An object is attached to a lift. The mass of the object is 3 kg.
Two spring balances S1 and S2 are attached to the upper and lower string
to measure their tensions.
The strings are light and inextensible. The lift is initially at rest.
Assume g=10m per sec sq.
(a) If the reading in S1 is 40N, Find the reading in S2.
(b) The lift starts to move and accelerate upwards with a magnitude of 5m per sec sq.
What is the readings of S1 and S2?
(c) When the lift approaches the end of its journey, it decelerates at a magnitude
of 5m per sec sq, what is the readings of S1 and S2 ?
