A block of mass 0.750 kg starts at rest from a height of 0.650 m and slides down

Question

A block of mass 0.750 kg starts at rest from a height of 0.650 m and slides down a rough ramp inclined at30to the horizontal. The coefcient of kinetic friction between the ramp and the block is 0.200. (a) What isthe work done on the block by gravity till it reaches the bottom of the ramp? (b) What is the work done onthe block by friction till it reaches the bottom of the ramp? (c) What is the speed of the block at the bottomof the ramp?The block continues to move on the horizontal portion of the track. The horizontal portion is frictionless. Theblock compresses the spring till it comes to rest. The spring constant of the spring is 45.0 N/m. (d) What isthe maximum compression of the spring?The spring now rebounds and pushes the block back. (e) What is the total work done on the block as itmoves up the ramp? (f) How high does the block go before it comes to rest?

Explanation / Answer

(a) work done = mgh = 0.750 x 9.81 x 0.65 = 4.78 J
(b)work done by friction = -( x m x g x cos30 ) x 0.65 / sin 30 =(0.2 x 0.750 x 9.81 x cos30 ) x 0.65 / sin30 = 1.66 J

(c) speed = (2 x( g- x g x cos30) x( 0.65/sin30)) = 4.59 m/s

kinetic energy = mv2/2 = 7.91 J

(d) maximum compression = (2 x kinetic energy / k ) = 0.59 m ( k= 45N/m)

(e) total work done = energy of block = 7.91 J

(f) distance = 4.592/2 x (1+cos)x g = 0.915m

height = 0.915 x sin30 = 0.458 m

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