A small block of mass m is placed at height h on a ramp inclined at angle ? . Wh
ID: 2088991 • Letter: A
Question
A small block of mass m is placed at height h on a ramp inclined at angle ?. When released from rest, the block slides down the ramp and then falls y meters to the floor. The ramp and block have friction between them with the coefficient of kinetic friction ?k between their surfaces. A small hole is located x meters from the end of the ramp. Ignore air resistance but do not ignore the kinetic friction force when the block is sliding. Known quantities are ?, x, y, ?k and g. <?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /?>
a) From what height h should the block be released in order to land in the hole?
b) Does your answer depend upon the mass of the block?
c) Compare your answers for h from this problem to problem 7. Do your mathematical answers compare sensibly in light of what the physics would predict?
Explanation / Answer
Solve for h: mgh= (uk)mgsin(theta)h/sin(theta) + ukmgx =>h=uk(h(sin(theta))^2+x)