A box of mass 8.0 kg rests on a horizontal, rough surface. A string attached to the box passes over a smooth pulley and supports a 2.0kg mass at its other end. When the box is released, a friction force of 6.0N acts on it. What is the acceleration of the box?
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Answer: 1.4ms-2
Explanation: In picture using F=m.a
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The acceleration of the box is 1.36 m/s²
Given :
In a box of mass ( m2) = 8kg, a string attached to the box passes over a smooth pulley and supports a mass (m1) 2.0kg at its other end.
Friction force = 6N
To find :
The acceleration of the box
Solution :
For m1,
m₁g - T = m₁a
2g - T = 2a {equation 1}
For m2,
T - 6 = m₂a
T - 6 = 8a {equation 2}
by adding equations 1 and 2 we get
2g - T + T - 6 = 2a + 8a
2(g-3) = 10a
g-3 = 5a
9.8 - 3 = 5a { g = 9.8 m/s² }
a = 1.36 m/s²
Therefore, the acceleration of the box is 1.36 m/s²
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