A box rests on a plank that is inclined to the horizontal. As the angle between the plank and the horizontal increases, does the component of the weight of the box parallel to the plank increase, decrease, or remain the same? Please just answer
Suzanne, you are going to have to think this out. Fill this table out:
Theta SinTheta
0 deg ?
20 deg ?
30 deg ?
THe question I asked, is as theta increases, what does Sine of Theta (SinTheta) do?
That is the answer to your question.
As the angle between the plank and the horizontal (θ) increases, the component of the weight of the box parallel to the plank (Wpara) actually decreases. To understand this, you can analyze the relationship between the angle and the sine function.
When the angle θ is 0 degrees, sinθ is also 0. This means that when the plank is horizontal, there is no component of the weight parallel to the plank.
As the angle θ increases to 20 degrees and 30 degrees, the value of sinθ also increases. You can calculate the sine values using a scientific calculator or a table of trigonometric ratios.
For instance, when θ is 20 degrees, the sinθ is approximately 0.342. And for θ equal to 30 degrees, the sinθ is approximately 0.5.
From this observation, we can conclude that as the angle increases, the value of sinθ also increases. Since the component of the weight parallel to the plank is proportional to sinθ, it will decrease as the angle θ increases.