107 145
Assignments Done
100%
Successfully Done
In January 2023

# Answer to Question #104508 in Mechanics | Relativity for havefun7741

Question #104508
1
2020-03-05T09:37:02-0500

(i)

According to the second Newton's low

"-T+m_a\\cdot g\\cdot \\sin40\u00b0=m_a\\cdot a"

"T-\\mu_s\\cdot (m_b\\cdot g+T_0\\cdot \\sin30\u00b0)-T_0\\cdot \\cos30\u00b0=m_b\\cdot a"

"T_0\\cdot \\cos30\u00b0-\\mu_s\\cdot (m_c\\cdot g-T_0\\cdot \\sin30\u00b0)=m_c\\cdot a"

"a(m_a+m_b+m_c)=m_a\\cdot g\\cdot \\sin 40\u00b0-(m_b+m_c)\\cdot g\\mu_s" ;

"m_a\\cdot g\\cdot \\sin 40\u00b0-(m_b+m_c)\\cdot g\\mu_s="

"=12\\cdot 9.8\\cdot \\sin 40\u00b0-(10+5)\\cdot 9.8\\cdot 0.4=16.8 N"

The block will move.

(ii)

"a=\\frac{m_a\\cdot g\\cdot \\sin 40\u00b0-(m_b+m_c)\\cdot g\\mu_k}{m_a+m_b+m_c}="

"=\\frac{12\\cdot 9.8\\cdot \\sin 40\u00b0-(10+5)\\cdot 9.8\\cdot 0.3}{12+10+5}=1.17 m\/s^2"

(iii)

"T=m_a\\cdot g\\cdot \\sin40\u00b0-m_a\\cdot a=12\\cdot 9.8\\cdot \\sin40\u00b0-12\\cdot 1.17\\approx61.6N"

"T_0=\\frac{m_ca+\\mu_km_cg}{\\cos30\u00b0+\\mu_k\\sin30\u00b0}=\\frac{5\\cdot 1.17+0.3\\cdot 5\\cdot 9.8}{\\cos30\u00b0+0.3\\cdot \\sin30\u00b0}\\approx20.2N"

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!