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 determine the force required to move a 2 N box up a 5° ramp, we need to consider two main forces acting on the box:
1. The gravitational force acting down the ramp.
2. The frictional force opposing the motion.
**Step 1: Calculate the gravitational force component down the ramp.**
The force due to gravity acting on the box can be calculated using the formula:
\[
F_{\text{gravity}} = mg
\]
In this case, the weight of the box is given as 2 N. Since the weight is already the force due to gravity, we can break it down into components along and perpendicular to the ramp.
The component of the weight acting down the ramp (parallel to the ramp) can be calculated as:
\[
F_{\text{gravity, parallel}} = F_{\text{gravity}} \cdot \sin(\theta)
\]
Where \(\theta\) is the angle of the ramp.
Substituting the values, we have:
\[
F_{\text{gravity, parallel}} = 2 \, \text{N} \cdot \sin(5^\circ)
\]
Calculating \(\sin(5^\circ)\):
\[
\sin(5^\circ) \approx 0.0872 \, (\text{using a calculator})
\]
Now substituting:
\[
F_{\text{gravity, parallel}} \approx 2 \, \text{N} \cdot 0.0872 \approx 0.1744 \, \text{N}
\]
**Step 2: Calculate the total force required to overcome friction and gravity.**
The total force required (\(F_{\text{required}}\)) to push the box up the ramp must overcome both the component of gravitational force acting down the ramp and the frictional force.
Thus, we have:
\[
F_{\text{required}} = F_{\text{gravity, parallel}} + F_{\text{friction}}
\]
Where:
- \(F_{\text{friction}} = 0.5 \, \text{N}\)
Substituting the values:
\[
F_{\text{required}} = 0.1744 \, \text{N} + 0.5 \, \text{N} \approx 0.6744 \, \text{N}
\]
**Conclusion:**
The total force required to get the box to move up the ramp is approximately **0.6744 N**. Thus, you should apply a force of at least **0.6744 N** to initiate movement of the box up the ramp.
1. The gravitational force acting down the ramp.
2. The frictional force opposing the motion.
**Step 1: Calculate the gravitational force component down the ramp.**
The force due to gravity acting on the box can be calculated using the formula:
\[
F_{\text{gravity}} = mg
\]
In this case, the weight of the box is given as 2 N. Since the weight is already the force due to gravity, we can break it down into components along and perpendicular to the ramp.
The component of the weight acting down the ramp (parallel to the ramp) can be calculated as:
\[
F_{\text{gravity, parallel}} = F_{\text{gravity}} \cdot \sin(\theta)
\]
Where \(\theta\) is the angle of the ramp.
Substituting the values, we have:
\[
F_{\text{gravity, parallel}} = 2 \, \text{N} \cdot \sin(5^\circ)
\]
Calculating \(\sin(5^\circ)\):
\[
\sin(5^\circ) \approx 0.0872 \, (\text{using a calculator})
\]
Now substituting:
\[
F_{\text{gravity, parallel}} \approx 2 \, \text{N} \cdot 0.0872 \approx 0.1744 \, \text{N}
\]
**Step 2: Calculate the total force required to overcome friction and gravity.**
The total force required (\(F_{\text{required}}\)) to push the box up the ramp must overcome both the component of gravitational force acting down the ramp and the frictional force.
Thus, we have:
\[
F_{\text{required}} = F_{\text{gravity, parallel}} + F_{\text{friction}}
\]
Where:
- \(F_{\text{friction}} = 0.5 \, \text{N}\)
Substituting the values:
\[
F_{\text{required}} = 0.1744 \, \text{N} + 0.5 \, \text{N} \approx 0.6744 \, \text{N}
\]
**Conclusion:**
The total force required to get the box to move up the ramp is approximately **0.6744 N**. Thus, you should apply a force of at least **0.6744 N** to initiate movement of the box up the ramp.