Question

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**.