Question

the diagram shows a 15-kg box resting on a wedge which has an angle of inclination of 30° and a coefficient of friction of 0.15. which equation correctly gives the value of ( f_f ), the force due to friction?
a ( f_f = 0.15f_n )
b ( f_f = 0.15f_g )
c ( f_f = 0.15f_{||} )
d ( f_f = 0.15f_{||}f_{perp} )

Explanation:

Step1: Recall Friction Formula

The formula for frictional force is \( F_f = \mu F_N \), where \( \mu \) is the coefficient of friction and \( F_N \) is the normal force. Here, \( \mu = 0.15 \), so \( F_f = 0.15 F_N \).

Step2: Analyze Options

• Option A: Matches \( F_f = 0.15 F_N \) (from \( F_f=\mu F_N \), \( \mu = 0.15 \)).
• Option B: \( F_g \) is weight, \( F_f \) isn't proportional to \( F_g \) directly here (since \( F_N

eq F_g \) on an incline).

• Option C: \( F_{\parallel} \) is parallel component of weight, \( F_f \) formula doesn't involve \( F_{\parallel} \) as \( 0.15 F_{\parallel} \).
• Option D: Incorrect relation, \( F_f \) is \( \mu F_N \), not related to \( F_{\parallel} \) and \( F_{\perp} \) as \( 0.15 F_{\parallel} F_{\perp} \).

Answer:

A. \( F_f = 0.15F_N \)