Dreadful rotation!!!
To kill the German soldiers in the trench, the American sent there a boulder(solid sphere) of mass 2kg with only a initial linear velocity of 343 m/s (means with no initial angular velocity, only initial linear velocity) on a surface with coefficient of friction as 0.1 . The boulder moved until it started rolling without sliding and for 2 more seconds till it reached the edge as shown in the figure and then started projectile. The trench is of depth 20m . Find the distance OA as given in the figure.
Details and Assumptions
- Enter your answer as OA with OA in kilometers upto 5 significant figures.
- Take value of g as 10m/s .
- The dotted sphere is the position of the boulder when it striked the ground .
- Ignore air resistance.
- The surface with friction ends just before the edge(at edge no friction is present). After that all surfaces are frictionless.
The answer is 29.792.
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1 solution
linear acceleration, a= M f . (1)
angular acceleration, α = 2 M R 5 f . (2)
When pure rolling starts, if v' is initial velocity
v=v'-at . (3)
ω = α t . (4)
now, when pure rolling starts, ω R=a . (5)
by (1), (2), (3), (4) and (5)
v= 7 5 v'
v=245m/s
by (1)
a=-1m/s 2
displacement till rolling starts
s 1 = 2 a v 2 − v ′ 2
s 1 =28812 m
displacement till edge
s 2 =s 1 +2v
s 2 =29302 m
time taken by sphere to fall down, as there is no friction at edge and after that
t'= g 2 h
t'=2s
range of projectile
s'=vt'
s'=490m
Distance OA
OA=s 2 +s'
OA=29792 m
OA=29.792 km