To find the net force causing the block's acceleration on a frictionless ramp, we can start by analyzing the forces acting on the block.
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Weight of the Block: The weight (force due to gravity) of the block is given as 8.0 N. This can be broken down into two components relative to the inclined plane:
- The component acting parallel to the ramp (down the ramp), which causes the acceleration.
- The component acting perpendicular to the ramp.
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Components of the Weight: The weight can be resolved into two components:
- The component parallel to the incline: \( F_{\text{parallel}} = W \sin(\theta) \)
- The component perpendicular to the incline: \( F_{\text{perpendicular}} = W \cos(\theta) \)
Where:
- \( W = 8.0 , \text{N} \)
- \( \theta = 15^\circ \)
- Calculating the Parallel Component: \[ F_{\text{parallel}} = 8.0 , \text{N} \cdot \sin(15^\circ) \]
Using the sine of 15 degrees: \[ \sin(15^\circ) \approx 0.2588 \]
So, \[ F_{\text{parallel}} = 8.0 , \text{N} \cdot 0.2588 \approx 2.07 , \text{N} \]
- Net Force: Since there is no friction, the net force acting on the block is equal to this parallel component of the weight: \[ F_{\text{net}} = F_{\text{parallel}} \approx 2.07 , \text{N} \]
Thus, the magnitude of the net force causing the block's acceleration is approximately 2.07 newtons.