Two blocks, A, of mass 4 kg, and B, of mass 9 kg, are connected by a light inextensible string. The blocks are held at rest on a plane which is inclined at an angle of 35° with the horizontal. A constant force, F, acting parallel to the plane, is applied to block B, as shown in the diagram below. The blocks now accelerate up the plane at 2 m s⁻². 2.1 State Newton's Second Law of Motion in words. The kinetic frictional forces acting on blocks A and B are 5,88 N and 13,23 N respectively. 2.2 Draw a labelled free-body diagram showing all the forces acting on block A. 2.3 Calculate the magnitude of: 2.3.1 The tension in the string. 2.3.2 Force F. 2.4 The angle that the plane makes with the horizontal is now decreased. 2.4.1 How will this change the kinetic frictional force acting on block A? Choose from INCREASES, DECREASES or REMAINS THE SAME. 2.4.2 Explain the answer to QUESTION 2.4.1.

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Two blocks, A, of mass 4 kg, and B, of mass 9 kg, are connected by a light inextensible string - NSC Physical Sciences - Question 2 - 2023 - Paper 1

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Two blocks, A, of mass 4 kg, and B, of mass 9 kg, are connected by a light inextensible string. The blocks are held at rest on a plane which is inclined at an angle ... show full transcript

Worked Solution & Example Answer:Two blocks, A, of mass 4 kg, and B, of mass 9 kg, are connected by a light inextensible string - NSC Physical Sciences - Question 2 - 2023 - Paper 1

Step 1

2.1 State Newton's Second Law of Motion in words.

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Answer

Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This can be expressed mathematically as:

$F_{net} = m imes a$

where $F_{net}$ is the net force, $m$ is the mass, and $a$ is the acceleration.

Step 2

2.2 Draw a labelled free-body diagram showing all the forces acting on block A.

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Answer

In the free-body diagram for block A, the following forces should be labeled:

Normal force ( $F_N$ ) acting perpendicular to the inclined plane.
Gravitational force ( $W$ ) acting downwards, which can be resolved into two components: one parallel to the incline ( $W imes ext{sin}(35°)$ ) and the other perpendicular ( $W imes ext{cos}(35°)$ ).
Tension in the string ( $T$ ) acting upwards along the incline.
Kinetic frictional force ( $f_k$ ) acting downwards along the incline, opposing the motion.

Step 3

2.3.1 The tension in the string.

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Answer

To find the tension in the string (T) for block A, we start with the equation:

$F_{net} = T - f_k - W imes ext{sin}(35°) = m imes a$

Substituting the known values, we have: $T - 5,88 - 4g imes ext{sin}(35°) = 4 imes 2$

Calculating the components gives: $T = 4 imes 2 + 5,88 + 4 imes 9.81 imes ext{sin}(35°)$ $T = 8 + 5,88 + 4 imes 9.81 imes 0,5736$ $T ≈ 36,36 ext{ N}$

Step 4

2.3.2 Force F.

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Answer

Using the equation for block B:

$F - T - f_B = m_B imes a$

where $f_B$ is the kinetic friction for block B. Now substituting:

$F - 36,36 - 13,23 = 9 imes 2$

Solving for F gives: $F = 18 + 36,36 + 13,23$ $F ≈ 118,18 ext{ N}$

Step 5

2.4.1 How will this change the kinetic frictional force acting on block A?

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Answer

The kinetic frictional force acting on block A will DECREASE as the angle of inclination is decreased.

Step 6

2.4.2 Explain the answer to QUESTION 2.4.1.

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Answer

As the angle of the incline decreases, the normal force acting on block A also decreases. Since the kinetic frictional force is directly proportional to the normal force, this means the frictional force will decrease. The formula for kinetic friction is:

$f_k = ext{μ}_k imes F_N$

where $F_N$ is the normal force, which is reduced with a lower incline angle.

Two blocks, A, of mass 4 kg, and B, of mass 9 kg, are connected by a light inextensible string - NSC Physical Sciences - Question 2 - 2023 - Paper 1

Worked Solution & Example Answer:Two blocks, A, of mass 4 kg, and B, of mass 9 kg, are connected by a light inextensible string - NSC Physical Sciences - Question 2 - 2023 - Paper 1

2.1 State Newton's Second Law of Motion in words.

2.2 Draw a labelled free-body diagram showing all the forces acting on block A.

2.3.1 The tension in the string.

2.3.2 Force F.

2.4.1 How will this change the kinetic frictional force acting on block A?

2.4.2 Explain the answer to QUESTION 2.4.1.

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