Friction between plane and object

Classical Mechanics Level 3

In the above diagram, a box with mass $m_{1} (= 8 \text{ kg}$ ) is on a slope with $60^{\circ}$ inclination. This box is connected with another box with mass $m_{2} (= 13 \text{ kg}$ ) by a wire on a frictionless pulley. What is the magnitude of the acceleration of the two boxes when the coefficient of kinetic friction between the first box $( 8 \text{ kg} )$ and the slope is $0.2?$

Gravitational acceleration is $g=10\text{ m/s}^{2}.$

1.26 \text{ m/s}^2

2.51 \text{ m/s}^2

5.02 \text{ m/s}^2

3.05 \text{ m/s}^2

2 solutions

Paola Ramírez
Mar 9, 2015

Sum of forces of the first mass are:

$T-F_{fr}-m_1g\sin 60°=m_1a$

$F_N-m_1g\cos 60°=0$

Sum of forces of the second mass are:

$m_2g-T=m_2a$

Solving the sistem we get

$a=\frac{0.2(8)g\cos 60°-8g\sin 60°+13g}{21}=2.46 m/s^2 \approx 2.51 m/s^2$

Just a small remark, you got the answer 2.460171826 at first because you assumed that g=9.8 However if you substitute it with g=10 just as the question says the answer will exactly be 2.510379414 without approximation. :D

Mohamed Yasser - 6 years, 1 month ago

Diptangshu Sen
May 29, 2014

Let the tension in the string be T and the acc of the system be a . 13g-T=13a ,T=13(g-a). Again, T-8gsin60-8gcos60 *(0.2)=8a Solving, a=2.51m/s^2.

Friction between plane and object

2 solutions

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