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We are given a cone of height H and angle alpha with constant density. We want to calculate the center of mass using triple integrals in cylindrical coordinates
The stairs are angled at 45° pointing in the direction of motion as shown. What is the velocity of the passenger relative to the water?
A ball is shot from the ground into the air. At a height of 9.1m, the velocity is observed to be V = 7.9i + 5.1j in m/s (i horizontally, j upward).
Compute the moment of the 100-lb force about A, (a) by using the definition of the moment of a force, (b) by resolving the force
Find its position vector in terms of the vector's magnitude and orientation. What is the magnitude?
What is the minimum coefficient of static friction required between the crate and truck bed, if it is not to slide forward?
What was the average speed of the car between 2 pm and 4pm? That is, what was the average speedometer reading in miles/hour?
Consider a force F acting on a particle that moves with a velocity v for F=(6N)i - (5N)j and v = (-5 m/s)i + (4 m/s)j
Automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calculate (a) its angular acceleration, assumed constant.
A person about to jump from a 1.6m high platform wants to limit the average stopping force on landing to 12 times her weight.
The simple pendulum in a grandfather clock is 1.0 m long. What are (a) the period and (b) the frequency of this pendulum?
Determine the impulse of his foot on the ball. Neglect the impulse caused by the ball's weight while its being kicked.
Jonathan and Jane are sitting in a sleigh that is at rest on frictionless ice. Jonathan's weight is 800 N, Jane's weight is 600 N, and that of the sleigh.
Angular momentum of the stick+puck is conserved about the (stationary) point where the collision occurs.
210Po is used as a source of 5.2 [MeV] alpha particles in a Rutherford experiment. The alpha particles are directed at a gold foil of thickness 2µm
An impulse air turbine has a total (on static) inlet pressure and temperature of 11,25 bar, 600 degrees K.
For zero mass particles, like neutrinos, the relativistic relationship between energy E and momentum p is
What is it's average angular speed in rad/s? (b) What are the tangential speed of two people 4.0 m and 5.0 m from the center, or axis of rotation?
Its displacement varies with time according to the equation x=5(pi/t +pi/3). The velocity (in m/s) of the body at t=1 second is equal to what value?
She then moves in a circle of radius 1M around the pole.What is the force exerted by the rope on her arms?
The position function of a particle is given by s= 1/ t^2 + 2t + t where s is the height in feet and t is the time in seconds.
A billiard ball approaches the rail at a speed of 15 m/s and an angle of 60 degrees, but rebounds at a speed of 10 m/s and an angle of 50 degrees.
An alpha particle has a charge of +3.2 x 10-19 C and a mass of 6.6 x 10-27 kg. The alpha particle travels at a velocity v of magnitude 550 m/s
Translate Noether's theorem into Hamiltonian mechanics. That is, define a symmetry for Hamiltonian mechanics (by translating the Lagrangian-definition).
A radioactive source emits alpha-particles with kinetic energies of 4MeV. What must be the value of an applied magnetic field so that the radius of curvature