Question

a box that has a mass of 80 kg slides down a ramp with a 30 degree angle. the free - body diagram shows the forces acting on the box. ignoring friction and air resistance, what is the acceleration of the box, to the nearest tenth? 0.5 m/s² 4.9 m/s² 8.5 m/s² 9.8 m/s²

Explanation:

Step1: Resolve gravitational force

The gravitational force $F_g = mg$, and the component of the gravitational force along the ramp is $F = mg\sin\theta$. According to Newton's second - law $F = ma$. So $ma=mg\sin\theta$.

Step2: Solve for acceleration

Cancel out the mass $m$ on both sides of the equation $ma = mg\sin\theta$, we get $a = g\sin\theta$. Given $g = 9.8\ m/s^2$ and $\theta = 30^{\circ}$, then $a=9.8\times\sin30^{\circ}$. Since $\sin30^{\circ}=0.5$, so $a = 9.8\times0.5=4.9\ m/s^2$.

Answer:

$4.9\ m/s^2$