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3.1 A 160 g ball, bowled with a velocity of 40 m·s⁻¹, is struck by a cricket bat - NSC Technical Sciences - Question 3 - 2022 - Paper 1

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3.1 A 160 g ball, bowled with a velocity of 40 m·s⁻¹, is struck by a cricket bat. The ball leaves the cricket bat with a velocity of 65 m·s⁻¹ in the opposite directi... show full transcript

Worked Solution & Example Answer:3.1 A 160 g ball, bowled with a velocity of 40 m·s⁻¹, is struck by a cricket bat - NSC Technical Sciences - Question 3 - 2022 - Paper 1

Step 1

Define the term impulse.

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Answer

Impulse is defined as the product of the resultant/net force acting on an object and the time that the net force acts on the object. Mathematically, it is expressed as:

Impulse = F_{net} imes riangle t

Where:

$F_{net}$ is the net force
$riangle t$ is the time duration.

Step 2

Calculate the impulse of the cricket bat on the ball.

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Answer

To calculate the impulse, we first need to determine the change in momentum ( $riangle p$ ).

The initial velocity of the ball ( $v_i$ ) is -40 m/s (considering direction) and the final velocity ( $v_f$ ) is 65 m/s. Therefore, the change in velocity is:

riangle v = v_f - v_i = 65 - (-40) = 105 ext{ m/s}

Next, we calculate the mass of the ball in kg:

m = 160 ext{ g} = 0.16 ext{ kg}$$ Now we can find the impulse:

Impulse = m imes riangle v = 0.16 imes 105 = 16.8 ext{ kg·m/s}

Step 3

Calculate the magnitude of the net force exerted on the ball.

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Answer

The net force ( $F_{net}$ ) can be calculated using Newton's second law:

F_{net} = m imes a

We need to first find the acceleration. Using:

a = rac{v_f - v_i}{ riangle t} = rac{65 - (-40)}{4 imes 10^{-3}} = rac{105}{4 imes 10^{-3}} = 26250 ext{ m/s}^2

Now substituting this back into the force equation gives:

F_{net} = 0.16 imes 26250 = 4200 ext{ N}

Step 4

State the principle of conservation of linear momentum in words.

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Answer

The total linear momentum in an isolated system is conserved in both magnitude and direction. This means that the total momentum before a collision or explosion is equal to the total momentum after the collision or explosion.

Step 5

Calculate the velocity of the 1 kg block after the collision.

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Answer

Using the law of conservation of momentum:

ext{Total momentum before} = ext{Total momentum after}

Before collision:

m_1 v_{1i} + m_2 v_{2i} = (1)(5) + (1.8)(2.5) = 5 + 4.5 = 9.5 ext{ kg·m/s}

After collision:

m_1 v_{1f} + m_2 v_{2f} = (1)(v) + (1.8)(3)

Setting both equations equal:

9.5 = v + 5.4 ightarrow v = 4.1 ext{ m/s to the right}

Step 6

Determine, by means of calculations, if the above collision is elastic or inelastic.

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Answer

To determine whether the collision is elastic or inelastic, we compare the total kinetic energy before and after the collision: Before collision:

KE_{initial} = rac{1}{2}m_1 v_{1i}^2 + rac{1}{2}m_2 v_{2i}^2 = rac{1}{2}(1)(5^2) + rac{1}{2}(1.8)(2.5^2)

Calculate:

KE_{initial} = 12.5 + 5.625 = 18.125 ext{ J}

After the collision:

KE_{final} = rac{1}{2}(1)(v^2) + rac{1}{2}(1.8)(3^2)

Substituting in $v = 4.1:

KE_{final} = rac{1}{2}(1)(4.1^2) + rac{1}{2}(1.8)(9) = 8.41 + 8.1 = 16.51 ext{ J}

Since $KE_{initial} > KE_{final}$ , the collision is inelastic.

3.1 A 160 g ball, bowled with a velocity of 40 m·s⁻¹, is struck by a cricket bat - NSC Technical Sciences - Question 3 - 2022 - Paper 1

Worked Solution & Example Answer:3.1 A 160 g ball, bowled with a velocity of 40 m·s⁻¹, is struck by a cricket bat - NSC Technical Sciences - Question 3 - 2022 - Paper 1

Define the term impulse.

Calculate the impulse of the cricket bat on the ball.

Calculate the magnitude of the net force exerted on the ball.

State the principle of conservation of linear momentum in words.

Calculate the velocity of the 1 kg block after the collision.

Determine, by means of calculations, if the above collision is elastic or inelastic.

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