Question

a skateboard weighing 29 n, represented by force g, lies on a hill that is inclined 33° to the horizontal, as shown. the figure is not drawn to scale. complete the following. do not round any intermediate computations, and round your answers to the nearest hundredth. (a) find the magnitude of the force q required to prevent the skateboard from rolling down the hill. n (b) find the magnitude of the force c of the skateboard against the hill. n

Explanation:

Step1: Analyze the force components

When a force \(G\) acts on an inclined plane at an angle \(\theta = 33^{\circ}\) with the horizontal. The force \(Q\) (parallel - to - the - plane component) and \(C\) (perpendicular - to - the - plane component) can be found using trigonometry.
The force of gravity \(G = 29\space N\). The component of \(G\) parallel to the inclined plane (force \(Q\)) is given by \(Q=G\sin\theta\), and the component perpendicular to the inclined plane (force \(C\)) is given by \(C = G\cos\theta\).

Step2: Calculate the magnitude of \(Q\)

Substitute \(G = 29\space N\) and \(\theta=33^{\circ}\) into the formula \(Q = G\sin\theta\).
We know that \(\sin(33^{\circ})\approx0.5446\), so \(Q=29\times\sin(33^{\circ})=29\times0.5446 = 15.7934\approx15.79\space N\)

Step3: Calculate the magnitude of \(C\)

Substitute \(G = 29\space N\) and \(\theta = 33^{\circ}\) into the formula \(C=G\cos\theta\).
We know that \(\cos(33^{\circ})\approx0.8387\), so \(C = 29\times\cos(33^{\circ})=29\times0.8387=24.3223\approx24.32\space N\)

Answer:

(a) \(15.79\space N\)
(b) \(24.32\space N\)