Question
A 2 N box is pushed up a 5° ramp. The ramp provides a frictional force of 0.5 N. How much force is required to get the box to move?
Answers
GPT-4o mini
To find the force required to move the 2 N box up a 5° ramp, we need to consider both the gravitational force acting on the box and the frictional force.
1. **Calculate the force of gravity parallel to the ramp**:
The gravitational force acting down the ramp can be calculated using the formula:
\[
F_{\text{gravity, parallel}} = mg \sin(\theta)
\]
where:
- \( m \) is the mass of the box,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( \theta \) is the angle of the ramp.
Since we know the weight of the box is 2 N, we can consider weight directly without needing mass:
\[
F_{\text{gravity, parallel}} = 2 \sin(5°)
\]
Using a calculator:
- \( \sin(5°) \approx 0.0872 \)
Thus:
\[
F_{\text{gravity, parallel}} = 2 \times 0.0872 \approx 0.1744 \, \text{N}
\]
2. **Add the frictional force**:
The total force required to overcome both the gravitational component parallel to the ramp and the frictional force can be calculated using:
\[
F_{\text{required}} = F_{\text{gravity, parallel}} + F_{\text{friction}}
\]
Given that the friction force is 0.5 N, we can now add the forces:
\[
F_{\text{required}} = 0.1744 \, \text{N} + 0.5 \, \text{N} = 0.6744 \, \text{N}
\]
Therefore, the force required to start moving the box up the ramp is approximately **0.67 N** (rounded to two decimal places).
1. **Calculate the force of gravity parallel to the ramp**:
The gravitational force acting down the ramp can be calculated using the formula:
\[
F_{\text{gravity, parallel}} = mg \sin(\theta)
\]
where:
- \( m \) is the mass of the box,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( \theta \) is the angle of the ramp.
Since we know the weight of the box is 2 N, we can consider weight directly without needing mass:
\[
F_{\text{gravity, parallel}} = 2 \sin(5°)
\]
Using a calculator:
- \( \sin(5°) \approx 0.0872 \)
Thus:
\[
F_{\text{gravity, parallel}} = 2 \times 0.0872 \approx 0.1744 \, \text{N}
\]
2. **Add the frictional force**:
The total force required to overcome both the gravitational component parallel to the ramp and the frictional force can be calculated using:
\[
F_{\text{required}} = F_{\text{gravity, parallel}} + F_{\text{friction}}
\]
Given that the friction force is 0.5 N, we can now add the forces:
\[
F_{\text{required}} = 0.1744 \, \text{N} + 0.5 \, \text{N} = 0.6744 \, \text{N}
\]
Therefore, the force required to start moving the box up the ramp is approximately **0.67 N** (rounded to two decimal places).