Complete the following exercises. (Assume g = 9.80 m/s 2 .) (a) A small block is

Question

Complete the following exercises. (Assume g = 9.80 m/s2.)

(a) A small block is released from rest at a height of 3.91 m above the ground and moves downward in free fall.

(i) How long does it take the block to reach the ground?


(ii) What is the speed of the block just before it strikes the ground?

(b) A frictionless incline is 5.00 m long (the distance from the top of the incline to the bottom, measured along the incline). The vertical distance from the top of the incline to the bottom is 3.91 m. A small block is released from rest at the top of the incline and slides down the incline.

(i) How long does it take the block to reach the ground?


(ii) What is the speed of the block just before it strikes the ground?

(c) How do the answers in part (b) compare to the answers in part (a)? (Select all that apply. Speeds are considered approximately equal if they are within 5% of each other.)

The speed of the block in (b) is greater.The speed of the block in (a) is greater.The speeds are approximately equal.It takes the block in (a) longer to reach the ground.It takes the block in (b) longer to reach the ground.

Explanation / Answer

a)

i) Since the block is released from rest ,So the initial Velocity is zero i.e Vo=0 m/s & acceleration due to gravity of a free falling body is a=g=9.8 m/s2

From equation of motion

S=Vot +(1/2)at2 =0+(1/2)at2

3.91 =(1/2)*9.8*t2

t=0.8934 s

b)

Speed of the block just before it stikes the ground is

V=Vo+at =0+9.8*0.8934

V=8.75 m/s

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b)

i)

angle of incline

X=Sin-1(3.91/5) =51.44o

acceleration of the block

a=gSin(x) =9.8sin51.44 =7.664 m/s

From equation of motion

S=Vot +(1/2)at2 =0+(1/2)at2

5 =(1/2)*7.664*t2

t=1.14 s

ii)

Speed of the block just before it strikes the ground is

V=Vo+at =0+7.664*1.14

V=8.75 m/s

c)

By comparing answers,The speeds are approximately equal.,It takes the block in (b) longer to reach the ground.

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