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Write the note on central force motion.
Let the force of gravity to be constant for small distances above the surface of the earth. A body is dropped from rest at a height h above the earth surface. What will be its kinetic energy just before it strikes the ground?
Four Minute Mile. As part of your training regiment for your eventual pro sports career, you are attempting to complete the famous “4-minute mile”, completing 4 laps of a 400 m track (which is not quite a mile, but it’s close) in a time of 4 minutes or less. As part of your training, you have been running several 3250 m races to improve your sustained long distance speed, and have completed them in an average time of 500 seconds. You have also run several 200 m sprints to improve your sprinting speed, and have completed those sprints in an average time of 25.0 seconds.
a) What are your average sustained long distance speed, and your average sprinting speed? (4)
b) Assuming that you run uniformly at the sustained speed from part a) for the first part of the race, and sprint at the sprinting speed from a) for the final part of the race, at what time should you start sprinting in order to complete the 1.60 km race in 4.00 minutes? How much distance have you covered in this time?
In A = B" C" expression, A has a dimension of [LT], and B has a dimension of [L*T| IfC has a dimension of [L'T), find the value of m+n.
A particle of mass m is attached to the end of a string and moves in a circle of radius r on a frictionless horizontal table. The string passes through a frictionless hole in the table and, initially, the other end is fixed. a) if the string is pulled so that the radius of the circular orbit decreases, how does the angular velocity change if it is ω0 when r = r0? b) what work is done when the particle is pulled slowly in from a radius r0 to a radius r0/2?
A force f is expressed with respect to the basis e1 and e2 by equation 2(3e1+4e2) N. If the directions of e1 makes an angle of 30 degree with f, find the vector e2.
A beam LO weighing 50N rests against a wall, the lower part of the beam extending 15 m from the base of the wall. Calculate the minimum value of the force F that can be applied to keep the beam in equilibrium. The coefficient of friction at L and O is 0.30.
A force f is expressed with respect to the basis e1 and e2 by equation 2(3e1+4e2) N. If the directions of e1 makes an angle of 30 degree with f, find the vector e2.
A rock ejected from a volcano with a speed of 25m/s and at an angle of 35 degrees above the horizontal. If the rock hits the side of the volcano at an altitude 20m lower than the starting point, how long does it take the rock to reach the starting point?
