You and a friend push horizontally on a 40 kg crate with a force of 500 N. The friction force between the floor and the crate is 260 N. Calculate the acceleration of the crate.
To calculate the acceleration of the crate, we can use Newton's second law of motion, which states:
\[
F_{\text{net}} = m \cdot a
\]
where \( F_{\text{net}} \) is the net force acting on the object, \( m \) is the mass of the object, and \( a \) is the acceleration.
1. **Determine the forces acting on the crate**:
- The applied force from you and your friend is \( F_{\text{applied}} = 500 \, \text{N} \).
- The friction force opposing the motion is \( F_{\text{friction}} = 260 \, \text{N} \).
2. **Calculate the net force**:
The net force \( F_{\text{net}} \) is the applied force minus the friction force:
\[
F_{\text{net}} = F_{\text{applied}} - F_{\text{friction}} = 500 \, \text{N} - 260 \, \text{N} = 240 \, \text{N}
\]
3. **Calculate the mass of the crate**:
Given that the crate has a mass \( m = 40 \, \text{kg} \).
4. **Calculate the acceleration**:
Rearranging the equation \( F_{\text{net}} = m \cdot a \) to solve for acceleration gives:
\[
a = \frac{F_{\text{net}}}{m} = \frac{240 \, \text{N}}{40 \, \text{kg}} = 6 \, \text{m/s}^2
\]
5. **Final answer**:
The acceleration of the crate is
\[
\boxed{6 \, \text{m/s}^2}
\]
Update (2024-11-06):
To find the acceleration of the crate, we first need to determine the net force acting on it. The net force (\( F_{\text{net}} \)) can be calculated using the following formula:
\[
F_{\text{net}} = F_{\text{applied}} - F_{\text{friction}}
\]
Where:
- \( F_{\text{applied}} \) is the total force you and your friend are applying on the crate (500 N), and
- \( F_{\text{friction}} \) is the frictional force opposing the motion (260 N).
Plugging in the values:
\[
F_{\text{net}} = 500 \, \text{N} - 260 \, \text{N} = 240 \, \text{N}
\]
Now, we can use Newton's second law to find the acceleration (\( a \)) of the crate:
\[
F_{\text{net}} = m \cdot a
\]
Rearranging this formula to solve for acceleration gives us:
\[
a = \frac{F_{\text{net}}}{m}
\]
Where \( m \) is the mass of the crate (40 kg). Now we can substitute the values:
\[
a = \frac{240 \, \text{N}}{40 \, \text{kg}} = 6 \, \text{m/s}^2
\]
Thus, the acceleration of the crate is \( 6 \, \text{m/s}^2 \).