a box that has a mass of 80 kg slides down a ramp with a 30 - degree angle. the free - body diagram shows…

Answer:

B. $4.9\ m/s^{2}$

Explanation:

Step1: Identify the force causing acceleration

The component of gravitational - force along the ramp causes acceleration. The gravitational force is $F_g = mg$, and its component along the ramp is $F = mg\sin\theta$.

Step2: Apply Newton's second - law

Newton's second - law is $F = ma$. Since $F = mg\sin\theta$ and $F = ma$, we can equate them: $mg\sin\theta=ma$.

Step3: Solve for acceleration

Cancel out the mass $m$ on both sides of the equation $mg\sin\theta = ma$. We get $a = g\sin\theta$. Given $g = 9.8\ m/s^{2}$ and $\theta = 30^{\circ}$, then $a=9.8\times\sin30^{\circ}$.

Step4: Calculate the value of acceleration

Since $\sin30^{\circ}=\frac{1}{2}$, then $a = 9.8\times\frac{1}{2}=4.9\ m/s^{2}$.