Question

exit ticket the box below has a mass of 12 kg. part a: determine the acceleration of the box. ( f_{net}=(m)(a) ) part b: determine the acceleration if the mass of the box triples. (is multiplied by 3). ( f_{net}=(m)(a) ) part c: what is the proportional relationship between mass and acceleration?

Explanation:

Step1: Calculate the net force in the horizontal direction

Since \(F_N\) and \(F_g\) are equal and opposite (\(F_N = 72N\), \(F_g=- 72N\)), they cancel each other out.
The net force \(F_{net}\) is calculated by \(F_{net}=F_A + F_f\).
Substitute \(F_A = 60N\) and \(F_f=-96N\) into the formula:
\(F_{net}=60+( - 96)=-36N\)

Step2: Calculate the acceleration using \(F = ma\)

We know \(m = 12kg\) and \(F_{net}=-36N\).
From \(F_{net}=ma\), we can solve for \(a\) by \(a=\frac{F_{net}}{m}\).
Substitute the values: \(a=\frac{-36}{12}=-3m/s^{2}\)

Step3: Calculate the acceleration when mass triples

The new mass \(m'=3\times12 = 36kg\), and \(F_{net}=-36N\) (remains the same as the horizontal forces are unchanged).
Using \(a'=\frac{F_{net}}{m'}\), substitute \(F_{net}=-36N\) and \(m' = 36kg\):
\(a'=\frac{-36}{36}=-1m/s^{2}\)

Step4: Determine the proportional relationship

From \(F = ma\) (assuming \(F\) is constant), \(a=\frac{F}{m}\).
So mass and acceleration are inversely proportional.

Answer:

• Part A: The acceleration of the box is \(-3m/s^{2}\)
• Part B: The acceleration when mass triples is \(-1m/s^{2}\)
• Part C: Mass and acceleration are inversely proportional.