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? Explain not sure

The component of weight down the plank is equal to mg*sinTheta. What does sin Theta do as theta increases?

Does sin Theta remain the same as theta increases

If the value of theta changes, then the value of sin(theta) will change (every 2pi radians or 360 degrees).

Yes but does it increase, decrease or remain the same in reference to original question posted

Picture a plank lying flat on the ground. The angle between the grown and the plank is now zero. The question tells you that the plank is inclined with reference to the ground. Do you think the angle is now zero or do you think the angle is greater than zero? What do you think the angle between the plank and the ground is when the plank has been inclined so that the plank is vertical?

If the angle between the plank and the ground increases, then the component of the weight of the box parallel to the plank will also increase.

When the angle between the plank and the horizontal increases, the component of the weight of the box parallel to the plank actually decreases. Let me explain why.

The weight of an object is the force exerted on it due to gravity, and it acts vertically downward. When the box rests on the inclined plank, the weight can be resolved into two components: one perpendicular to the plank and one parallel to the plank.

The component of the weight parallel to the plank can be calculated using the equation mg * sinΘ, where m is the mass of the box, g is the acceleration due to gravity, and Θ is the angle between the plank and the horizontal.

Now, let's focus on sinΘ. As the angle Θ increases, sinΘ also increases. This is because sinΘ is a trigonometric function that outputs values between -1 and 1, with its maximum value of 1 reached at 90 degrees (or π/2 radians).

So, as the angle Θ increases, sinΘ increases, and therefore, the component of the weight parallel to the plank decreases. This is because the weight is now acting more perpendicular to the plank, with a smaller component acting parallel to it.

To summarize, as the angle between the plank and the horizontal increases, the component of the weight of the box parallel to the plank decreases.

The angle between the plank and the ground is greater than zero when the plank is inclined. When the plank is vertical, the angle between the plank and the ground is 90 degrees.