Question

question 9 (1 point)
an object is on a frictionless inclined plane. the plane is inclined at an angle of 30° with the horizontal. what is the objects acceleration?
0.50 g
0.56 g
0.87 g
1.0 g

Explanation:

Step1: Analyze forces on the object

The object on a frictionless inclined plane has gravitational force \( F_g = mg \) acting vertically downwards. We resolve this force into components parallel (\( F_{\parallel} \)) and perpendicular (\( F_{\perp} \)) to the inclined plane. The angle of inclination is \( \theta = 30^\circ \). The component of gravity parallel to the plane is \( F_{\parallel}=mg\sin\theta \).

Step2: Apply Newton's second law

Newton's second law is \( F = ma \). Along the inclined plane, the net force is \( F_{\parallel} \) (since friction is zero). So, \( ma = mg\sin\theta \). We can cancel \( m \) from both sides, giving \( a = g\sin\theta \).

Step3: Calculate the acceleration

Substitute \( \theta = 30^\circ \) into the formula. We know that \( \sin30^\circ=\frac{1}{2} = 0.5 \). So, \( a = g\times0.5= 0.50g \).

Answer:

0.50 g (corresponding to the first option: 0.50 g)