Question

a 1.10 kg glass is on a tray that is inclined at 20.0^{\circ}.

what is the x-component of the weight of the glass?

w_x = ? n

Explanation:

⚡ Using what you learned: newton's laws of motion

Step 1: Calculate the total weight

The total weight \( w \) of the glass is the force due to gravity acting on its mass:

$$ w = m \cdot g $$

Given:

• \( m = 1.10 \text{ kg} \)
• \( g \approx 9.80 \text{ m/s}^2 \)

$$ w = 1.10 \cdot 9.80 = 10.78 \text{ N} $$

Step 2: Find the x-component of the weight

For an object on an inclined plane, the component of gravity parallel to the incline (the x-component, \( w_x \)) is given by:

$$ w_x = w \cdot \sin(\theta) $$

Given:

• \( \theta = 20.0^\circ \)

$$ w_x = 10.78 \cdot \sin(20.0^\circ) $$

$$ w_x \approx 10.78 \cdot 0.34202 $$

$$ w_x \approx 3.69 \text{ N} $$

Answer:

3.69