6. A block of mas s 0.3 kg starts from rest at position O on the frictionless sl

Question

6. A block of mas s 0.3 kg starts from rest at position O on the frictionless slide shown in the Fig. 5. When the block passes the point A, its speed is 1.5 m/s. a) What is the difference in height, h, of point O and point A? (Ch.7, p.211) b) The block passes the point B which is at the same height as point A. What is the c) What is the magnitude of the acceleration of the block at point B? The circular d) kinetic encrgy of the block at point B? (Ch. 7, pp. 203-206) portion has a radius of 0.2m. (Ch. 6, pp. 162-164) What is the direction of the acceleration of the block at point B? What is the speed of the block when it reaches point C? Assume the height H of point B (and of point A) from point C is Sh.. (Ch.7,p.211). e)

Explanation / Answer

a)

By Conservation of energy

PEA=KEA

mgh = (1/2)mVA2

=>h=V2/2g =1.52/2*9.8

h=0.1148 m

b)

Since Point A and Point B are at same height ,they have same same speed

VA=VB=1.5 m/s

KEB =KEA= (1/2)mVA2 =(1/2)*0.3*1.52

KEB=0.3375 J

c)

Centripetal acceleration of the block at point B is

aB=VB2/r =1.52/0.2 =11.25 m/s2

d)

Since it is centripetal acceleration ,So direction of acceleration is downwards below B

e)

Since the height difference between O and C is

H=h+5h=6h ,

At Point A

VA=sqrt[2gh]

At point C

VC=sqrt[2g*6h]=sqrt[6)*VA

VC=sqrt[6]*1.5 =3.674 m/s

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