Question

question 1
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an object is placed on an adjustable ramp. as the angle is increased from 0 degrees towards 90 degrees...
the normal force increases, and the component of the weight down the ramp decreases
the normal force increases, and the component of the weight down the ramp increases
the normal force decreases, and the component of the weight down the ramp increases
the normal force decreases, and the component of the weight down the ramp decreases
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Explanation:

Step1: Resolve weight into components

Let the weight of the object be \(W = mg\). The normal force \(N\) and the component of weight down the ramp \(F\) can be found by resolving \(W\) into components perpendicular (\(N\)) and parallel (\(F\)) to the ramp.
If the angle of the ramp with the horizontal is \(\theta\), then \(N=mg\cos\theta\) and \(F = mg\sin\theta\).

Step2: Analyze the effect of increasing \(\theta\)

As \(\theta\) increases from \(0^{\circ}\) to \(90^{\circ}\):

• For \(N = mg\cos\theta\), since \(\cos\theta\) is a decreasing function in the interval \([0,\frac{\pi}{2}]\) (where \(\theta\) is in radians, and \(0^{\circ}=0\) radians, \(90^{\circ}=\frac{\pi}{2}\) radians), as \(\theta\) increases, \(N\) decreases.
• For \(F=mg\sin\theta\), since \(\sin\theta\) is an increasing function in the interval \([0,\frac{\pi}{2}]\), as \(\theta\) increases, \(F\) increases.

Answer:

The Normal Force decreases, and the component of the weight down the ramp increases.