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A small solid ball of mass M and radius R rolls without slipping on the track whose height y as a function of horizontal position x is given by y=ax^2 where a is a constant with the units of inverse length. The mass is given an initial displacement from the bottom of the track and then released. Find an expression for the period of the resulting motion. Express your answer in terms of a, g, M, and R.
T=
A skateboarder, starting from rest, rolls down a 12.2-m ramp. When she arrives at the bottom of the ramp her speed is 8.61 m/s. Determine the magnitude of her acceleration, assumed to be constant
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A garden plot must have a central planting area of length 13 m and width 8 m. There is to be a sidewalk around its edge of width w. If the total area, planting area plus sidewalk area, is 150 m^2, what is the sidewalk width w in meters.
Suppose that the Earth's orbit around the Sun is perfectly circular. Employing conservation arguments, find the value of the eccentricity e of the orbit
An object falls off of a pier and into the ocean (sea water) where it displaces a total volume of 2.2 cubic meters of sea water. What is the buoyant force acting on the object in newtons
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