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

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

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

Answer

Explanation:

Step1: Resolve gravitational force

The gravitational - force component along the ramp is $F = mg\sin\theta$, where $m = 80$ kg, $g=9.8$ m/s², and $\theta = 30^{\circ}$. According to Newton's second - law $F = ma$. Since $F = mg\sin\theta$ and $F = ma$, we can equate them: $ma=mg\sin\theta$.

Step2: Solve for acceleration

Cancel out the mass $m$ on both sides of the equation $ma = mg\sin\theta$. We get $a = g\sin\theta$. Substitute $g = 9.8$ m/s² and $\theta = 30^{\circ}$ into the formula. Since $\sin30^{\circ}=\frac{1}{2}$, then $a=9.8\times\frac{1}{2}=4.9$ m/s².

Answer:

$4.9$ m/s²