A rope inclined at angle 37degree to the horizontal is used to drag a 50kg block along a level floor with an acceleration of 1m/s². The coefficient of friction between the block and floor is 0.2. What is the tension in the rope?
Gives
"\\theta=37\u00b0"
"a=1m\/sec"
m=50kg
"\\mu=.2"
We know that
Horizontal components
"f=Tcos37\u00b0"
Vertical components
Tsin37°+N=mg
N=mg-Tsin37°
We can rewrite horizontal components
f=Tcos37°
"\\mu N=Tcos37\u00b0"
Put N value
"\\mu(mg-Tsin37\u00b0)=Tcos30\u00b0"
"\\mu mg=T(\\mu sin30\u00b0+cos30\u00b0)"
"T=\\frac{\\mu mg}{\\mu sin37\u00b0+cos37\u00b0}"
Put value
"T=\\frac{0.2\\times50\\times9.8}{0.2sin37\u00b0+cos37\u00b0}"
"T=\\frac{98}{0.9189}=106.64" N
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