Respuesta :
Answer:
The maximum angle of tilt is 26.56°.
Explanation:
Given that,
Mass of book = 5 kg
Coefficient of static friction = 0.50
The normal force of plank on book
[tex]F_{n}=mg\cos\theta[/tex]
The friction force holding book against moving
[tex]f_{\mu}=\mu F_{n}[/tex]....(I)
The force induced by gravity is
[tex]F_{g}=mg\sin\theta[/tex]....(II)
We need to calculate the angle
Now, both forces are equal
[tex]f_{\mu}=F_{g}[/tex]
[tex]\mu\ mg\cos\theta=mg\sin\theta[/tex]
Put the value into the formula
[tex]0.50\times5\times9.8\cos\theta=5\times9.8\sin\theta[/tex]
[tex]\tan\theta=\dfrac{0.50\times5\times9.8}{5\times9.8}[/tex]
[tex]\theta=\tan^{-1}{0.5}[/tex]
[tex]\theta=26.56^{\circ}[/tex]
Hence, The maximum angle of tilt is 26.56°.
Answer: The maximum angle of tilt is 26.57°
Explanation:
mass of book = 5 kg
weight = mass × acceleration due to gravity
wgt of book = 5 × 9.8 = 49 N
coefficient of static friction = Fs = 0.50
let maximum angle of tilt = A
force parallel to the plank = Fp
force perpendicular to the plank = Fn
Fp = 49 × sin A
Fn = 49 × cos A
Fs = u × Fn = 0.5 × 49 × cos A
Fp - Fs = m × a
49 × sin A - 0.5 × 49 × cos A = m × 0 = 0
49 × sin A = 0.5 × 49 × cos A
(divide both sides by 49)
sin A = 0.5 × cos A
(divide both sides by cos A)
sin A/cos A = 0.5
NOTE: sin A/cos A = tan A
replace sin A/cos A with tan A
∴ tan A = 0.5
A =\tan^{-1}{0.5}
A = 26.565°
(note that to get A, take the arctan of 0.5, where arctan is tan raised to the power of -1)
The maximum angle of tilt is 26.57°.
