Sliding Down An Inclined Plane

Classical Mechanics Level 4

A small mass slides down an inclined plane of inclination $\theta = 60^\circ$ with respect to the horizontal. The acceleration of the block varies as $a = k x^{2}$ , where $x$ is the distance through which the mass slides down and $k$ is a constant. The coefficient of friction is 1 when the block covers a distance of $\sqrt{10}$ . Find the value of $k$ .

Details and Assumptions :
Take $g=10 \text{ m/s}^2$ .
Every quantity is in SI unit.

The answer is 0.366.

2 solutions

Refaat M. Sayed
Feb 16, 2016

photo To know direction of forces... I solved it by Newton's second law $\displaystyle\sum F = ma = 10m \sin 60 - 10\mu m \cos 60$

Now we have $a= 5+5\sqrt {3}$ this value we have when $\mu=1$ This mean the distance is $\sqrt {10}$ Finally we have $5+5\sqrt {3}=k \times (\sqrt{10})^2$ so $k = \frac{\sqrt{3 } -1}{2} \boxed {\approx 0. 366}$

Same method, easy problem.

Adarsh Kumar - 5 years, 3 months ago

Same way buddy

Kaustubh Miglani - 5 years, 3 months ago

My ans is coming as 3times of your ans I have used work energy theorem pls check

Rahul Malhotra - 5 years, 3 months ago

By integrating acc. v^2=[20 [10]^0.5]/3 *K Putting the value of v^2 in the eq ghsin60-gcos60 [10]^0.5=0.5[v]^2

Rahul Malhotra - 5 years, 3 months ago

My solution is correct.. Show me your work first to check it :)

Refaat M. Sayed - 5 years, 3 months ago

This question is incorrect as if we use nlm eq Mgsin60-umgcos60=ma Remove m from the equation and the value comes out to be a constant. This means that acc is not a function of "x ". Hope u understand.

Rahul Malhotra - 5 years, 3 months ago

u is not constant!!!

Kaustubh Miglani - 5 years, 3 months ago

Read properly it's given 1

Rahul Malhotra - 5 years, 3 months ago

@Rahul Malhotra – Its 1 when it covers the distance not always.I said rightly.

Kaustubh Miglani - 5 years, 3 months ago

Lu Chee Ket
Feb 17, 2016

$a = \frac{F}{m} = \frac{5(\sqrt3 -1) m}{m} = k (\sqrt{10})^2$

$\implies k = \frac{5(\sqrt3 - 1)}{10} \approx 0.366$

Answer: $\boxed{0.366}$

Caution: $a = 0.366~x^2$ does not reflect a logical physics for the whole journey.

Sliding Down An Inclined Plane

The answer is 0.366.

2 solutions

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