tutorial sheet 6 - PAP111/PHYS1A Claus-Dieter Ohl Tutorial...

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PAP111/PHYS1A Tutorial Sheet 6 29 th of September 2010 Claus-Dieter Ohl 1 The power is defined as the time rate of energy transfer. The instantaneous power P =d E /d t can also expressed as the scalar product F · v . Why? 1) Power ful car A car with mass m having an automatic gear box accelerates from rest with a constant power P . Determine and sketch the position x ( t ), the velocity v ( t ), and the acceleration a ( t ). How long does a car with mass m = 1000 kg applying a power P of 100 kW to reach a velocity of 100 km/h. Hint: You need to solve an ordinary differential equation. Use a trial solution v ( t ) = A t 1/2 , where A is a constant. 2) Slider on a sphere A point mass m starts from rest and slides down the surface of a frictionless solid sphere of radius r as in shown in the figure. Measure angles from the vertical and potential energy from the top. Find a) the change in potential energy of mass with angle; b) the kinetic energy as a function of angle; c) the radial and tangential accelerations as a function of angle; d) the angle at which the mass flies off the sphere.
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