4. (9 points) an apple crate of mass 23 kg accelerates along a surface as the crate is pulled with a force…
4. (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!!)
Answer
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)