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A particle P of mass m is free to move inside a sphere with centre O and radius r. The particle starts from the lowest point, directly below O, with a speed v. As long as the particle stays on the inner surface of the sphere, its position can be described in terms of the angle ? between the line OP and the vertical.(a) Find the particle speed as a function of ?.(b) Find the normal reaction between the particle and the surface of the sphere.(c) Show that the particle remains in contact with the sphere through a complete revolution as long as v = v 5rg.(d) Show that if v 2rgNov 04 2015 10:38 PM
A stable and highly soluble pollutant is dumped into a lake at the rate of 0.19 tonnes per day. The lake volume is 2E7 m3 and the average water flow-through rate is 8E4 m3 per day
A tiny 0.0250 -microgram oil drop containing 15 excess electrons is suspended between to horizontally closely-spaced metal plates, Which plate must be positive, the upper one or the lower one
Water is pumped steadily out of a flooded basement at a speed of 5.47 m/s through a uniform hose of radius 1.00 cm. The hose passes out through a window 3.35 m above the waterline. What is the power of the pump?
A 1500 kg vehicle is making a circular turn on a flat roadway. What is the max speed the vehicle can travel before it starts to slide
A long, current-carrying solenoid with an air core has 1640 turns per meter of length and a radius of 0.0173 m. What is the mutual inductance of this system
A 55.4 g arrow traveling at 64.7 m/s hits a bale of hay and stops after entering 0.37 m into the hay. Assuming constant acceleration, find the magnitude of the force in N by the bale on the arrow.
a merry-go-round r=2m, initially at rest is given a constant tangential push that depends on time. F(t) =β(t) applied on the rim. β=10N/s, Calculate angular acceleration as a function of time
At the Earth's surface a projectile is launched straight up with aspeed of 10.1 km/s. To what height will it rise. Ignore airresistance and the rotation of the Earth.
A 5.00-kg object is initially at rest. The object is acted on by a 9.00-N force toward the east for 3.00 s. No force acts on the object for the next 4.00 s. How far has the object moved during this 7.00 s interval
A 5.0 kg mass is held between two springs of unstretched length 0.1m so that the springs are horizontal. What angle do the springs make with the vertical at equilibrium
A submarine dives 110.0 m at an angle of 10.0° below the horizontal. Illustrate what are the horizontal and vertical components of the submarine's displacement?
Charges of 3.0 nC, -2.0 nC, -7.0 nC, and 1.0 nC are contained inside a rectangular box with length 1.0 m, width 2.0 m, What is the electric flux through the surface of the box
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