Who won?

Classical Mechanics Level 3

Particles $\text{a}$ and $\text{b}$ races from $\text{ Point P}$ to $\text{Point Q}$ . Particle $\text{a}$ moves along strainght line Path A with constant velocity.

Particle $\text{b}$ slides down a circular Path B with horizontal component of its initial velocity equal to that of Particle $\text{a}$ .

Let $t_{\text{a}}$ and $t_{\text{b}}$ be the time taken by Particles $\text{a}$ and $\text{b}$ to reach Q from P respectively, then

\frac{t_{\text{a}}}{t_{\text{b}}} = \frac{\text{Length of PQ}}{\text{Length of arc PQ}}

t_{\text{a}}=t_{\text{b}}

t_{\text{a}}>t_{\text{b}}

t_{\text{a}}<t_{\text{b}}

1 solution

Kushal Patankar
Oct 2, 2016

Particle b has a normal force from Path B acting on it which increases its horizontal velocity till it reaches the very bottom of the path and then decreases to its initial value, Thus horizontal velocity component of b always remains greater than a, which moves with constant velocity. So b wins.

But we should also consider the fact that particle 'b' is taking a larger route to its destination ( point Q )

Sabhrant Sachan - 4 years, 8 months ago

That may be, but horizontal displacement is same.

Kushal Patankar - 4 years, 8 months ago

It's going faster at the start - it's only going at the same rate with respect to the x axis

Alex Li - 4 years, 8 months ago

i suppose particle wont reach the destination due to effect of gravity

Himanshu Patil - 4 years, 8 months ago

i mean particle a

Himanshu Patil - 4 years, 8 months ago

Yes, it will, conservation of energy could show that.

And, besides, then it wouldnt be much of a question. Would it?

Kushal Patankar - 4 years, 8 months ago

wont the normal force affect the motion of particle b while going up?

Sparsh Sarode - 4 years, 8 months ago

Its from DC pandey

Dhruv Joshi - 4 years, 2 months ago

Who won?

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