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Zorluk: OrtaNewton's Second Law (F=ma)

Match each modification of a transport vehicle's engine thrust (net force) and cargo load (mass) to its resulting effect on the vehicle's acceleration. Assume all other conditions remain constant, based on Newton's Second Law (F=maF = ma).

  • Engine thrust is doubled, and vehicle mass is unchanged.Acceleration increases to twice the original value.
  • Engine thrust is halved, and vehicle mass is doubled.Acceleration decreases to one-fourth of the original value.
  • Engine thrust is doubled, and vehicle mass is reduced to half.Acceleration increases to four times the original value.
  • Both engine thrust and vehicle mass are doubled.Acceleration remains exactly the same as the original value.

Cevap

Each scenario is solved by substituting the modified multipliers for Force (FF) and mass (mm) into the acceleration formula a=Fma = \frac{F}{m}.
Newton's Second Law dictates that acceleration is directly proportional to net force and inversely proportional to mass (a=Fma = \frac{F}{m}). By applying the respective multipliers given in each scenario to the numerator and denominator, the resulting change in acceleration can be accurately calculated as a multiple of the original state.

Adım Adım Çözüm

1
Rearrange Newton's Second Law to solve for acceleration.
a=Fma = \frac{F}{m}
This isolates the variable we need to evaluate to compare proportional changes.
2
Evaluate the first condition: doubled thrust, unchanged mass.
anew=2Fm=2aa_{new} = \frac{2F}{m} = 2a
Force increases by a factor of 2, directly doubling acceleration.
3
Evaluate the second condition: halved thrust, doubled mass.
anew=0.5F2m=0.25aa_{new} = \frac{0.5F}{2m} = 0.25a
Reducing the numerator by half and doubling the denominator divides the overall quotient by 4.
4
Evaluate the third condition: doubled thrust, halved mass.
anew=2F0.5m=4aa_{new} = \frac{2F}{0.5m} = 4a
Dividing by 0.5 in the denominator is equivalent to multiplying by 2, which compounds with the doubled force in the numerator.
5
Evaluate the fourth condition: doubled thrust, doubled mass.
anew=2F2m=1aa_{new} = \frac{2F}{2m} = 1a
The equal proportional increases in both the numerator and denominator cancel each other out entirely.

Anahtar Kavram

Proportional Reasoning using Newton's Second Law
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Konular

Newton's Second Law (F=ma)

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