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A truck of mass 2.1 × 10³ kg tows a car of mass 1.3 × 10³ kg along a horizontal road - AQA - A-Level Physics - Question 24 - 2022 - Paper 1

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A truck of mass 2.1 × 10³ kg tows a car of mass 1.3 × 10³ kg along a horizontal road. The total resistive force on the car is 1100 N. The acceleration of the car and... show full transcript

Worked Solution & Example Answer:A truck of mass 2.1 × 10³ kg tows a car of mass 1.3 × 10³ kg along a horizontal road - AQA - A-Level Physics - Question 24 - 2022 - Paper 1

Step 1

Calculate the total mass being towed

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Answer

The total mass of the system (truck + car) is calculated as:

extTotalmass=extmassoftruck+extmassofcar=2.1imes103extkg+1.3imes103extkg=3.4imes103extkg ext{Total mass} = ext{mass of truck} + ext{mass of car} = 2.1 imes 10^3 ext{ kg} + 1.3 imes 10^3 ext{ kg} = 3.4 imes 10^3 ext{ kg}

Step 2

Determine the total force acting on the system

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Answer

The net force acting on the system can be determined using Newton's second law:

Fnet=extTotalmassimesextacceleration=3.4imes103extkgimes2.3extm/s2=7820extNF_{net} = ext{Total mass} imes ext{acceleration} = 3.4 imes 10^3 ext{ kg} imes 2.3 ext{ m/s}^2 = 7820 ext{ N}

Step 3

Calculate the tension in the tow rope

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Answer

The tension in the tow rope can be found by considering the resistive forces acting on the car:

T=Fnet+Fresistive=7820extN+1100extN=8920extNT = F_{net} + F_{resistive} = 7820 ext{ N} + 1100 ext{ N} = 8920 ext{ N}

However, checking the options given:

  • A: 3000 N
  • B: 4100 N
  • C: 7800 N
  • D: 8900 N

The closest option, considering rounding effects, is D: 8900 N.

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