As shown, a small, heavy block of mass M rests a top a smooth, curved track whos

Question

As shown, a small, heavy block of mass M rests a top a smooth, curved track whose lowest end is a height h_2 above a level, horizontal floor. when released from a height of h_2, above the tabletop, the block accelerates down the track, leaves it horizontally, and strikes the floor at a location that is distance D from the base of the table. Express your leaves it horizontally, and strikes the floor at a location that is distance answers in terms of h_1, and h_2 and any necessary physical constants. Derive an expression for the speed of the block the moment it leaves the track. Derive an expression for the distance D the block travels before it strikes the floor. A student performing this experiment takes the following measurements: h_1 = 0.25 m and h_2 =0.90 m. Although the student's calculation of theoretical D is 0 45 m, he measures the average location of the actual impact of the ball with the floor (after 5 trials) as D_avg = 0.86 m. Based upon your answer to parts a.) and b) Dan explain the discrepancy in the student's results.

Explanation / Answer

1. The speed of the block after it leaves the track is ( 2. g. h1) 1/2

this can be derived by conversation of energy

potential energy = kinetic energy

Mgh1 + Mgh2 = 1/2 Mv2 + Mgh2

Then solving v, we get the answer

2.

D = Vxt

= ( 2. g. h1) 1/2 x t

t can be substituted as ( 2h2/g ) 1/2

So D = Root ( ( 2 g x h1 ) x 2 h2 /g)

= Root ( 4 x h1 x h2)

= 2 x root ( h1 x h2)

3. if we keep h1 and h2 as the values given , D = 0.94 m

But practically it is coming as D =0.86 m

This may be due to

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