Questions: A 6.3 kg statue is sitting on an incline plane at a 70.0° angle. Draw a force diagram. Label all the forces. Find the holding force and normal of the block.

A 6.3 kg statue is sitting on an incline plane at a 70.0° angle. Draw a force diagram. Label all the forces. Find the holding force and normal of the block.

Transcript text: A 6.3 kg statue is sitting on an incline plane at a $70.0^{\circ}$ angle. Draw a force diagram. Label all the forces. Find the holding force and normal of the block.

Solution

Solution Steps

Step 1: Identify the Forces Acting on the Statue

The statue is subject to the following forces:

Gravitational Force ($F_g$): Acts vertically downward. The magnitude is given by $F_g = mg$, where $m = 6.3 \, \text{kg}$ and $g = 9.81 \, \text{m/s}^2$.
Normal Force ($F_n$): Acts perpendicular to the surface of the incline.
Holding Force ($F_h$): Acts parallel to the incline, preventing the statue from sliding down.

Step 2: Calculate the Gravitational Force

The gravitational force is calculated as follows: \[ F_g = mg = 6.3 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 61.803 \, \text{N} \]

Step 3: Resolve the Gravitational Force into Components

The gravitational force can be resolved into two components:

Parallel to the Incline ($F_{g,\parallel}$): $F_{g,\parallel} = F_g \sin \theta$
Perpendicular to the Incline ($F_{g,\perp}$): $F_{g,\perp} = F_g \cos \theta$

Given $\theta = 70.0^\circ$: \[ F_{g,\parallel} = 61.803 \, \text{N} \times \sin(70.0^\circ) = 58.048 \, \text{N} \] \[ F_{g,\perp} = 61.803 \, \text{N} \times \cos(70.0^\circ) = 21.137 \, \text{N} \]

Step 4: Determine the Normal Force

The normal force ($F_n$) is equal in magnitude and opposite in direction to the perpendicular component of the gravitational force: \[ F_n = F_{g,\perp} = 21.137 \, \text{N} \]

Step 5: Determine the Holding Force

The holding force ($F_h$) is equal in magnitude and opposite in direction to the parallel component of the gravitational force: \[ F_h = F_{g,\parallel} = 58.048 \, \text{N} \]