Chapter 7: Q. 7 (page 177)

Block B in the figure rests on a surface for which the static and kinetic coefficients of friction are $0.60$ and $0.40$ respectively. The ropes are massless.
What is the maximum mass of block A for which the system remains in equilibrium?

Short Answer

Expert verified

The maximum mass of the block A for which the system remains in equilibrium is $12 k g .$

Step by step solution

Part (a) Step 1 : Given information

Static friction coefficient $μ_{s} = 0.60,$ kinetic friction coefficient $μ_{k} = 0.40,$ mass of block $m_{B} = 20 kg .$

Part (a) Step 2 : Calculation

Here, the tension in the rope is the same at all points. Block B must not slide to be in equilibrium.

That means that the tension T in the rope must not exceed the maximum static friction force acting on B.

$T = μ_{s} \times m_{B} \times g T = 0.6 \times 20 k g \times 9.8 m / s^{2} T = 117.6 N$

Tension in the rope at 45⁰ is T . Also, equilibrium requires that block A not to move, so

localid="1650266822568" $T \sin 45 = m_{A} g T = \sqrt{2} m_{A} g m_{Λ} = T / \sqrt{2} g T \cos 45 = 117.6 N T = \sqrt{2} \times 117.6 N m_{Λ} = \frac{\sqrt{2} \times 117.6 N}{\sqrt{2} \times g} 117.6 N / 9.8 m / s^{2} m_{Λ} = 12 kg$

Part (a) Step 3 : Final answer

The maximum mass of the block for which the system remains in equilibrium is $12 k g .$

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Block B in the figure rests on a surface for which the static and kinetic coefficients of friction are $0.60$ and $0.40$ respectively. The ropes are massless.
What is the maximum mass of block A for which the system remains in equilibrium?

Short Answer

Step by step solution

Part (a) Step 1 : Given information

Part (a) Step 2 : Calculation

Part (a) Step 3 : Final answer

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Block B in the figure rests on a surface for which the static and kinetic coefficients of friction are 0.60and 0.40respectively. The ropes are massless.What is the maximum mass of block A for which the system remains in equilibrium?

Short Answer

Step by step solution

Part (a) Step 1 : Given information

Part (a) Step 2 : Calculation

Part (a) Step 3 : Final answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Solid State Physics

Medical Physics

Famous Physicists

Circular Motion and Gravitation

Fluids

Torque and Rotational Motion

Study anywhere. Anytime. Across all devices.

Block B in the figure rests on a surface for which the static and kinetic coefficients of friction are $0.60$ and $0.40$ respectively. The ropes are massless.
What is the maximum mass of block A for which the system remains in equilibrium?