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A boy sitting on his horse whips it. The horse speeds up at an average acceleration of 2.0 m/s 2 . If the boy does not slide back, what is the force of friction exerted by the horse on the boy ? If the boy slides back during acceleration, what can be said about the coefficient of static friction between the horse and the boy.

A boy sitting on his horse whips it. The horse speeds up at an average acceleration of 2.0 m/s.
  1.  If the boy does not slide back, what is the force of friction exerted by the horse on the boy ?
  2. If the boy slides back during acceleration, what can be said about the coefficient of static friction between the horse and the boy.

Grade:12th pass

1 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
9 years ago
Dear student,
The Forces acting on the horse are
(i) the weight Mg
(ii) the normal contact force and
(iii) the static friction f.

(a) As the boy does not slide back, its acceleration a is equal to the acceleration of the horse. As friction is theonly horizontal force, it must act along the acceleration and its magnitude is given by Newton’s second law
f_{s}=Ma=30\times 2=60 N

(b) When the boy slides back, the horse is unable to exert the force of 60 N on the boy. Hence the maximum force that the horse may exert on the boy is:
f_{s}=\mu _{s}mg=\mu _{s}\times 30\times 10=300\mu _{s}
Theerefore300\mu _{s}<60\Rightarrow \mu _{s}<\frac{60}{300}=0.2
Regards
Sumit

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