Classical Mechanics Answers

A box of length 2m lies on the top of a rough wooden plank of length 10m. The coefficient of friction between the box and the plank is 0.1. The plank accelerates to the right at the rate of a=3m/s^2. If g=10m/s^2 then find the minimum time needed for the box to fall off the plank.

A disc of radius 12 m is rotating in the clockwise direction with an angular speed of 10 rad/sec. A small, smooth ball bearing capable of sliding along the rectangular slot moves with a speed of 10m/s with respect to an observer at O. The mass of the ball is 100gm. The perpendicular distance of the slot from the centre of disc is 8m. Moreover OP=10 m at an instant t. What is the relative velocity of the ball bearing for an observer on the ground at that instant? What is the centrifugal force on the ball? What is the coriolis force on the ball?

If ur^•• = - k/r^2 and prove that the first integral of the equation of motion is 1/2ur^•2 = - c[1/R - 1/r]

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A parachutist weights 1000N. When she opens her parachute it pulls upwards on her with a force of 2000N.a. draw a diagram to show the forces acting on the parachute. b.Calculate the resultant forces acting on the parachute. C.what effect will this force have on her

Ted and his iceboat (combined mass = 240 kg) rest on the frictionless surface of a frozen lake. A heavy rope (mass of 80 kg and length of 100 m) is laid out in a line along the top of the lake. Initially, Ted and the rope are at rest. At time t= 0, Ted turns on a wench which winds 0.5 m of rope onto the boat every second. a) What is Ted’s velocity just after the wench turns on?

A 1967 Corvette of mass 1450 kg moving with a velocity of 100 mph (= 44.7 m/s) slides on a slick street and collides with a Hummer of mass 3250 kg which is parked on the side of the street. The two vehicles interlock and slide off together. What is the speed of the two vehicles immediately after they join?

A pitcher throws a 0.145 so that it crosses home plate kg baseball horizontally with a speed of 40 m/s. It is hit straight back at the pitcher with a final speed of 50 m/s. a) What is the impulse delivered to the ball? b) Find the average force exerted by the bat on the ball if the two are in contact for 2.0 x 103 s. c) What is the acceleration experienced by the ball?

A body constrained to move along the z-axis of a coordinate system is subject to a constant force F given by F = −i + 2 j + 3 k N where i, j, k are unit vectors along the x-, y- and z-axis of the system respectively. What is the work done by this force in moving the body a distance of 4 m along the z-axis?

In a nuclear reactor a neutron of high speed (typically 107 m s–1) must be slowed to 103 m s–1 so that it can have a high probability of interacting with isotope 92235U and causing it to fission. Show that a neutron can lose most of its kinetic energy in an elastic collision with a light nuclei like deuterium or carbon which has a mass of only a few times the neutron mass. The material making up the light nuclei, usually heavy water (D2O) or graphite, is called a moderator.

A block of mass m = 1 kg, moving on a horizontal surface with speed vi = 2 ms–1 enters a rough patch ranging from x = 0.10 m to x = 2.01 m. The retarding force Fr on the block in this range is inversely proportional to x over this range, Fr = -k/x for 0.1 < x < 2.01 m = 0 for x < 0.1m and x > 2.01 m where k = 0.5 J. What is the final kinetic energy and speed vf of the block as it crosses this patch?