Mechanics - 4

Classical Mechanics Level 2

Find the sum of the magnitudes of the acceleration of the blocks $a \text{ m/s}^2$ and tension in the string $T \text{ N}$ . Give your answer to the nearest integer.

Assumptions and Details:

Mass of block $A$ , $m_A = \text{ 3 kg}$
Mass of block $B$ , $m_B = \text{5 kg}$
Angle of incline, $\theta = \sin^{-1} \dfrac35$
Acceleration due to gravity, $g = \text{10 m/s}^2$
The string is massless and inextensible.
The pulley is massless and there is no friction in the pulley and with the string.

Try my World of Physics to solve many problems like this one.

The answer is 24.

1 solution

Chew-Seong Cheong
Jan 26, 2019

By Newton's second law , we have:

The acceleration of the blocks $m_Bg \sin \theta - m_Ag \sin \theta = (m_A + m_B) a$ $\implies a = \dfrac {m_B-m_A}{m_A+m_B}g\sin \theta$ $\approx \dfrac {5-3}{5+3}(10)(0.6018) \approx \text{1.50 m/s}^2$ .
The tension in the string $T = m_Bg\sin \theta - m_Ba \approx \text{22.57 N}$ .

Therefore, $|a|+|T| \approx \boxed{24}$ .

@Ram Mohith , you have to mention that the answer should be the nearest integer because it is not an integer. I have edited this problems and others in the series for you.

Chew-Seong Cheong - 2 years, 4 months ago

Thank you sir.

Ram Mohith - 2 years, 4 months ago

But sir in most of the problems I only got till the first decimal place with 5 (like exactly 22.5). But it seems that you have got further like 22.57. Seems you took $\sin 37^\circ = 0.6018$ but I took $\sin 37^\circ = \dfrac35$ which I think is more accurate.

Ram Mohith - 2 years, 4 months ago

No, I used Microsoft Excel to do the calculations, $\sin 37^\circ \approx 0.601815023$ . $\sin^{-1} 0.6 \approx 36.86989765^\circ \ne 37^\circ$ .

Chew-Seong Cheong - 2 years, 4 months ago

@Chew-Seong Cheong – Ok. From the next question onward I will mention in the question to assume $\sin 37^\circ = \dfrac35$ .

Ram Mohith - 2 years, 4 months ago

@Ram Mohith – You can specify $\theta = \sin^{-1} \frac 35$ or $\theta = \cos^{-1} \frac 45$ or $\theta = \tan^{-1} \frac 34$ . Note that $\sin 37^\circ \ne \frac 35$ .

Chew-Seong Cheong - 2 years, 4 months ago

@Chew-Seong Cheong – Ok. I will do it.

Ram Mohith - 2 years, 4 months ago

@Chew-Seong Cheong – Or just "Take $\sin \theta = \frac 35$ ".

Chew-Seong Cheong - 2 years, 4 months ago

@Chew-Seong Cheong – Sir, how are the problems in the mechanics series. I am trying to bring bring out as many as possible variations in from pne problem.

Ram Mohith - 2 years, 4 months ago

@Ram Mohith – They are good. Just be careful on the wording.

Chew-Seong Cheong - 2 years, 4 months ago

@Chew-Seong Cheong – I am using almost same wording for these type of problems which you have edited.

Ram Mohith - 2 years, 4 months ago