An 8.0-newton block is accelerating down a frictionless ramp inclined at 15° to the horizontal, as shown in the diagram below. What is the magnitude of the net force causing the block's acceleration?

Answer 1

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.

1. 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.

2. 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:

• \( W = 8.0 , \text{N} \)
• \( \theta = 15^\circ \)

3. 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, \[ F_{\text{parallel}} = 8.0 , \text{N} \cdot 0.2588 \approx 2.07 , \text{N} \]

4. 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.