Question

an object with a mass of m kilograms is placed on a ramp at an angle of θ degrees from the horizontal. what must the component of the objects weight that points parallel to the ramps surface be equal to?
mg sin θ
mg cos θ
tan θ
g sin θ
g cos θ
tan^{-1}(θ)

Explanation:

Step1: Analyze the weight of the object

The weight of the object is \( W = mg \), where \( m \) is the mass and \( g \) is the acceleration due to gravity.

Step2: Resolve the weight into components

When resolving the weight vector \( \vec{W} = mg \) into components parallel and perpendicular to the ramp. Using trigonometry, if the ramp makes an angle \( \theta \) with the horizontal, the component of the weight parallel to the ramp is \( mg\sin\theta \). The component perpendicular to the ramp is \( mg\cos\theta \). The other options: \( \tan\theta=\frac{\sin\theta}{\cos\theta} \) (a ratio, not a force component), \( g\sin\theta \) and \( g\cos\theta \) lack the mass \( m \) (weight is \( mg \)), and \( \tan^{- 1}(\theta) \) is an inverse - tangent function (not a force component).

Answer:

A. \( mg\sin\theta \)