Question

1. (9 points) an apple crate of mass 23 kg accelerates along a surface as the crate is pulled with a force of 14.5 n as shown in the drawing. there is a friction force of 7.0 n. (a) show a complete free - body diagram with all forces acting on the box. (b) what is the weight of the crate? (c) what is the x - component (horizontal) of the 14.5 n force? (you will need trigonometry to answer this question!!)

Explanation:

Step1: Calculate the weight of the crate

The weight formula is \(W = mg\), where \(m = 23\space kg\) and \(g=9.8\space m/s^{2}\).

$$W=23\times9.8$$

Step2: Calculate the x - component of the force

The formula for the x - component of a force \(F\) at an angle \(\theta\) is \(F_{x}=F\cos\theta\). Here \(F = 14.5\space N\) and \(\theta = 19^{\circ}\)

$$F_{x}=14.5\times\cos(19^{\circ})$$

Answer:

• (b) \(W = 23\times9.8=225.4\space N\)
• (c) \(F_{x}=14.5\times\cos(19^{\circ})\approx14.5\times0.946 = 13.727\space N\)