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A particle moves in a one-dimensional potential given by V(x) = Vo(e^-ax + bx),(V(x) is potential not velocity) where Vo, a and b are all positive constants.
(a) Find the force on the particle at any point x.
(b) Sketch the potential and the force as functions of x. Make a Taylor expansion of the potential about the equilibrium point.
(c) What condition must be satisfied by the constants if the harmonic approximation is to be valid?
(d) If the equilibrium point is a stable one, find the frequency for small oscillations about this point. WELL EXPLAINED ANSWERS GET BETTER RATINGS.
A horse is capable of moving at four different speeds: walk (1.9 m/s), trot (5.0 m/s), canter (7.0 m/s), and gallop (12 m/s). Ann is learning how to ride a horse. She spends 15 minutes riding at a walk and 1.8 minutes at each other speed.
Consider a too-small space station that consists of a 2.7m radius rotating sphere. A man standing inside is 1.9m tall and his feet are at 1g. What is the acceleration of his head.
An object, at the top of a very tall building, is released from rest and falls freely due to gravity. Neglect air resistance and calculate the distance covered by the object between times t1 = 5.57 s and t2 = 7.59 s after it is released.
Water flows through a pipe with circular cross section. The fluid has a radius of 5.0 cm and flows at 2.0m/s. The output has a radius of 2.50 cm. find the output velocity.
A skier wears a jacket filled with goose down that is 15 mm thick. Another skier wears a wool sweater that is 7.00 mm thick. Both have same surface area.
A rifle with a barrel length of 56 cm fires a 14 g bullet with a horizontal speed of 350 m/s/s. The bullet strikes a block of wood and penetrates to a depth of 13 cm.
A 1.2m -long, 900g rope pulls a 9.0kg block of ice across a horizontal, frictionless surface. The block accelerates at 1.0m/s^2, How much force pulls forward on the block of ice
In one design, a large spring with spring constant 2×10^4 N/m was placed behind the cannon. The other end of the spring braced against a post that was firmly anchored to ship's frame.
A charged particle travels undeflected through perpendicular electric and magnetic fields whose magnitudes are 5000N/C, Find the speed of the particle if it is a proton
A ball is released from rest on a no-slip surface, as shown. After reaching its lowest point, the ball begins to rise again, How high does the ball rise on the frictionless side
Using Newton's laws, Evaluate the magnitude of the normal force that the floor exerts on the chair.
The equation of a transverse wave traveling along a very long string is given by y = 6.9 sin(0.025(pi)x + 4.5(pi)t), Determine the transverse displacement
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