To find the force of friction acting on the book as it slides down the ramp at constant velocity, we first need to understand the forces acting on the book.
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Weight of the book (W): The weight of the book is given as 20 N.
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Components of the weight: The weight can be broken down into two components:
- Parallel to the ramp (W_parallel): This is the component of the weight that acts down the ramp.
- Perpendicular to the ramp (W_perpendicular): This is the component of the weight that acts into the ramp.
The formulas for these components are: \[ W_{\text{parallel}} = W \sin(\theta) \] \[ W_{\text{perpendicular}} = W \cos(\theta) \] where \(\theta\) is the angle of the ramp (30° in this case).
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Calculating the components: \[ W_{\text{parallel}} = 20 , \text{N} \cdot \sin(30°) = 20 , \text{N} \cdot 0.5 = 10 , \text{N} \] \[ W_{\text{perpendicular}} = 20 , \text{N} \cdot \cos(30°) = 20 , \text{N} \cdot \left(\frac{\sqrt{3}}{2}\right) \approx 17.32 , \text{N} \]
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Force of friction: Since the book is sliding down the ramp at constant velocity, the net force acting along the ramp is zero. This means that the force of friction (f_friction) must balance out the component of the weight acting down the ramp (W_parallel). Therefore: \[ f_{\text{friction}} = W_{\text{parallel}} = 10 , \text{N} \]
So, the force of friction between the book and the ramp is 10 Newtons.
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