a 225 kg crate initially at rest slides down a frictionless ramp that is inclined at 34.3°. what is the…

a 225 kg crate initially at rest slides down a frictionless ramp that is inclined at 34.3°. what is the acceleration of the crate as it slides down the ramp? a = ? m/s²

a 225 kg crate initially at rest slides down a frictionless ramp that is inclined at 34.3°. what is the acceleration of the crate as it slides down the ramp? a = ? m/s²

Answer

Explanation:

Step1: Analyze the force along the ramp

The force causing the acceleration along the friction - less ramp is the component of the gravitational force parallel to the ramp. The gravitational force is $F_g = mg$, and the component of the gravitational force along the ramp is $F_{parallel}=mg\sin\theta$, where $m$ is the mass of the crate, $g = 9.8\ m/s^2$ is the acceleration due to gravity, and $\theta$ is the angle of the incline. According to Newton's second law $F = ma$, and $F = F_{parallel}=mg\sin\theta$. So $ma=mg\sin\theta$.

Step2: Solve for the acceleration

We can cancel out the mass $m$ from both sides of the equation $ma = mg\sin\theta$. We get $a = g\sin\theta$. Substitute $g = 9.8\ m/s^2$ and $\theta = 34.3^{\circ}$ into the formula. $\sin(34.3^{\circ})\approx0.563$. Then $a=9.8\times0.563\ m/s^2$. $a = 5.52\ m/s^2$.

Answer:

$5.52$