A block starts at rest and slides down a frictionless track except for a small r

Question

A block starts at rest and slides down a frictionless track except for a small rough area on a horizontal section of the track (as shown in the figure below). It leaves the track horizontally, flies through the air. and subsequently strikes the ground. The acceleration of gravity is 9.81 m/s2 . At what height h above the ground is the block released? Answer in units of m What is the the speed of the block when it leaves the track? Answer in units of m/s What is the total speed of the block when it hits the ground? Answer in units of m/s

Explanation / Answer

A.) The initial height of the block when it is at rest at the top of frictionless track = H Height of the point where the block leaves the track horizontally = h Change in height = H - h Loss in gravitational potential energy of block=mg(H-h) Gain in kinetic energy of block as it leaves the track =Loss in gravitational potential energy of block Gain in kinetic energy =(1/2)mv^2 (1/2)mu^2=mg(H - h) u = sq rt 2g (H - h) A . The ball leaves the track with a speed = sq rt 2g ( H - h) If H and h are in meter then ball leaves the track with a speed = sq rt19.62 (H-h) m/s ______________________________________… B.) As the block leaves the track horizontally,its initial velocity in vertical direction is zero.(u=0) vertical displacement = h using the relation s=ut+ (1/2 )a t^2 h = (1/2 )g T^2 T = sq rt 2 gh =2*9.81*h =19.62 h If h is in meter then T= [19.62 h] second where T is time of flight that is the time the block is in air horizontal distance x the block travels in the air=horizontal velocity*time of flight T x = [ sq rt 2g ( H - h) ]* sq rt 2gh x = 2g [ sq rt (H -h ) h ] the block travels a horizontal distance = 2g [ sq rt( H - h) *h] If H and h are in meter then the block travels a horizontal distance = 19.62 [ sq rt( H - h) *h] is in meter ______________________________________… C.) If V is speed with which block hits the ground, Final kinetic energy of block (KE) =initial potential energy of block (PE) (1/2)mV^2=mgH V= sq rt 2gH the speed of the block when it hits the ground is sq rt 2gH If H is in meter then speed is [ sq rt 19.62 H ] m/s

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