Question

for these problems, sketch a force diagram (fbd), use newtons 2nd law and forces to answer the questions posed.

1. a 200 - kg crate is pushed horizontally with a force of 700 n. if the coefficient of friction is 0.20, calculate the acceleration of the crate.

Explanation:

Step1: Calculate the normal force

The normal force \(N\) on the crate is equal to its weight since there is no vertical acceleration. Using \(N = mg\) (where \(m = 200\space kg\) and \(g=9.8\space m/s^{2}\)):
\(N=200\times9.8 = 1960\space N\)

Step2: Calculate the frictional force

The frictional force \(f=\mu N\), with \(\mu = 0.20\) and \(N = 1960\space N\)
\(f=0.20\times1960=392\space N\)

Step3: Apply Newton's second law (\(F_{net}=ma\))

The net force \(F_{net}=F - f\), where \(F = 700\space N\) and \(f = 392\space N\)
\(F_{net}=700 - 392=308\space N\)
Since \(F_{net}=ma\), then \(a=\frac{F_{net}}{m}\)
Substituting \(F_{net}=308\space N\) and \(m = 200\space kg\)
\(a=\frac{308}{200}=1.54\space m/s^{2}\)

Answer:

The acceleration of the crate is \(1.54\space m/s^{2}\)