Find the location of the point at which the kinetic energy and the potential energy are equal in terms of the constants of the spring and the body
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- Show that when a body of mass m is dropped from a height h, the sum of its kinetic and potentialenergies is constant at any instant and is equal to mgh.Compute the maximum velocity, maximum acceleration, and the maximum force.A concentrated force of 8 kN and a uniform load of 3 kN/m act on the frame shown. Determinethe resultant force and specify where its line of action intersects the horizontal line passing through Ameasured from point A.
- a block of mass M released from height h,friction coefficient k down on an inclined planeit is moving. The speed at which an object of mass M will have height h / 3Find the statement that gives.Find the maximum speed of the mass.An object moves with constant velocity. Is it safe to conclude thatno force acts on the object? Why, or why not?
- A particle of mass m has speed υ = α/x, where x is its displacement. Find the force F(x) responsible.A block of wood is projected up an inclined plane with initial speed vo . If the inclination of the plane is 30 and the coefficient of sliding friction mu_{k} = 0 , find the total time for the block to return to the point of projection ?What is the total nomentum of the two model systems and what is the final velocity?
- On October 14, 2012, Felix Baumgartner became the first human being to break the soundbarrier while falling freely. He jumped from a capsule that was lofted by a balloon to analtitude of 127,852 ft (38.96 km). The speed of sound at that altitude is 690 mi/h.(a) Assuming that air friction (drag) is negligible at such altitudes, how far would he haveto fall to reach the speed of sound? (The approximation for the gravitational potentialenergy near the Earth’s surface, Ug ≈ mgy, is accurate to better than 1% even at suchaltitudes. Track units carefully, though!). Draw energy bar charts of your system atthe start of Felix’s jump and when he reaches the speed of sound to support youranswer.(b) Friction is not negligible, even at this altitude. Baumgartner actually reached thespeed of sound at an altitude of 109,731 ft (33.45 km). What fraction of the system’schange in gravitational energy was converted to thermal energy (mostly thermal energyin the air) by the time Baumgartner reached the…Consider a projectile fired vertically in a constant gravitauonal field. For the same initial velocities, compare the times required the projectile to reach its maximum height (a) for zero resisting force, (b) for a resisting force proportional to the instantaneous velocity of the projectile.In a particle accelerator, a proton has mass 1.6710-27kg and an initial speed of 2.00105m/s . It moves in a straight line, and its speed increases to 9.00105m/s in a distance of 10.0 cm. Assume that the acceleration Is constant. Find the magnitude of the force exerted on the proton.