Question

multiple choice question
the illustration represents the force on, and acceleration of, vehicles with different masses.
suppose that the vehicles have the same acceleration. according to newtons second law of motion, how must the force on the two vehicles compare?
the force on the car must be greater.
the force on them is the same.
there is not enough information to tell.
the force on the truck must be greater.

Explanation:

Step1: Recall Newton's second law

Newton's second law is \(F = ma\) (where \(F\) is force, \(m\) is mass, and \(a\) is acceleration).

Step2: Analyze the relationship between force, mass and acceleration

Given \(a_{car}=a_{truck}\) (same acceleration). Let \(m_{car} = 900\space kg\), \(F_{car}=9000\space N\), so \(a=\frac{F_{car}}{m_{car}}=\frac{9000}{900}= 10\space m/s^{2}\). For the truck with \(m_{truck}=1200\space kg\) and \(a = 10\space m/s^{2}\), using \(F=ma\), we get \(F_{truck}=m_{truck}\times a=1200\times10 = 12000\space N\). Since \(m_{truck}>m_{car}\) and \(a\) is the same, from \(F = ma\), \(F_{truck}>F_{car}\).

Answer:

The force on the truck must be greater.