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Two identical objects P and Q with a mass of 10 kg each, are moving side by side with an initial velocity of 5,5 m·s⁻¹ east on a horizontal surface - NSC Physical Sciences - Question 9 - 2016 - Paper 1
Question 9
Two identical objects P and Q with a mass of 10 kg each, are moving side by side with an initial velocity of 5,5 m·s⁻¹ east on a horizontal surface. The following gr... show full transcript
Worked Solution & Example Answer:Two identical objects P and Q with a mass of 10 kg each, are moving side by side with an initial velocity of 5,5 m·s⁻¹ east on a horizontal surface - NSC Physical Sciences - Question 9 - 2016 - Paper 1
Step 1
Bereken die totale impuls wat voorwerp Q in 10 s ondervind.
Answer
To calculate the total impulse experienced by object Q in 10 seconds, we need to find the area under the graph of the force versus time. The graph shows a linear force change from 0 N to 10 N over the first 2 seconds, then from 10 N to -10 N over 6 seconds, and finally remains at -10 N during the last 2 seconds:
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Calculate Area for 0 to 2 seconds: Area of the triangle = ( \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2 \times 10 = 10 , \text{Ns} )
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Calculate Area for 2 to 8 seconds: Area of the trapezium = ( \frac{1}{2} \times (\text{base1} + \text{base2}) \times \text{height} = \frac{1}{2} \times (10 + (-10)) \times 6 = 0 , \text{Ns} )
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Calculate Area for 8 to 10 seconds: Area of the rectangle = ( ext{length} \times ext{height} = 2 \times (-10) = -20 , \text{Ns} )
Thus, the total impulse is: [ 10 + 0 - 20 = -10 , \text{Ns} ] Therefore, the total impulse for object Q in 10 seconds is -10 Ns.
Step 2
Vergelyk, sonder berekening, die totale impuls vir voorwerp P aan dié van voorwerp Q. Skryf iets neer: GROTER AS, KLEINER AS OF GELYK AAN.
Answer
The total impulse for object P is greater than that of object Q. This is due to the shape and area under the corresponding force-time graph for object P indicating a greater net area, reflecting a larger impulse.
Step 3
Bereken die eindsnelheid van voorwerp Q.
Answer
To find the final velocity of object Q, we use the impulse-momentum theorem, which states that impulse equals the change in momentum:
[ ext{Impulse} = m(v_f - v_i) ]
Given that:
- Mass (m) = 10 kg
- Initial velocity (v_i) = 5.5 m/s
- Impulse calculated previously = -10 Ns
Substituting these values gives: [ -10 = 10(v_f - 5.5) ]
Dividing both sides by 10: [ -1 = v_f - 5.5 ]
Thus: [ v_f = 5.5 - 1 = 4.5 , \text{m/s} ] Therefore, the final velocity of object Q is 4.5 m/s.