Question

question 5 of 10
an object of mass m slides down an incline with angle θ. which expression shows the net force on the object along the surface of the incline?
a. mg cos(θ) - f_n
b. mg sin(θ) - f_n
c. mg sin(θ)
d. mg cos(θ)

Explanation:

Step1: Resolve gravitational force

The gravitational force on the object is $F = mg$. Resolve it into components along and perpendicular to the incline. The component of the gravitational - force along the incline is $F_{parallel}=mg\sin(\theta)$, and the component perpendicular to the incline is $F_{perpendicular}=mg\cos(\theta)$.

Step2: Analyze normal force and net - force

The normal force $F_N$ acts perpendicular to the surface of the incline. We are interested in the net - force along the surface of the incline. Since $F_N$ has no component along the incline, the net - force along the surface of the incline is just the component of the gravitational force along the incline, assuming no friction. So, $F_{net}=mg\sin(\theta)$.

Answer:

C. $mg\sin(\theta)$