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Answer :
Sure, let's work through the problem step by step to find the acceleration of the mass.
### Step 1: Understand the Forces Involved
- Mass of the object: 18.0 kg
- Applied force: -23355 N (The negative sign indicates the direction of the force.)
- Frictional force: 163 N
### Step 2: Calculate the Net Force
The net force acting on the object is the result of the applied force and the frictional force. Since friction usually opposes the direction of motion, when the applied force is negative, the frictional force tends to counteract it.
[tex]\[ \text{Net Force} = \text{Applied Force} + \text{Frictional Force} \][/tex]
Substituting the values:
[tex]\[ \text{Net Force} = -23355 \, \text{N} + 163 \, \text{N} \][/tex]
[tex]\[ \text{Net Force} = -23192 \, \text{N} \][/tex]
### Step 3: Use Newton's Second Law to Find Acceleration
Newton's second law states that:
[tex]\[ F = ma \][/tex]
Where [tex]\( F \)[/tex] is the net force, [tex]\( m \)[/tex] is the mass, and [tex]\( a \)[/tex] is the acceleration. We can rearrange this formula to solve for acceleration:
[tex]\[ a = \frac{F}{m} \][/tex]
Substituting the known values:
[tex]\[ a = \frac{-23192 \, \text{N}}{18.0 \, \text{kg}} \][/tex]
[tex]\[ a = -1288.44 \, \text{m/s}^2 \][/tex]
### Conclusion
The acceleration of the mass is [tex]\(-1288.44 \, \text{m/s}^2\)[/tex]. The negative sign indicates that the acceleration is in the opposite direction of the applied force.
### Step 1: Understand the Forces Involved
- Mass of the object: 18.0 kg
- Applied force: -23355 N (The negative sign indicates the direction of the force.)
- Frictional force: 163 N
### Step 2: Calculate the Net Force
The net force acting on the object is the result of the applied force and the frictional force. Since friction usually opposes the direction of motion, when the applied force is negative, the frictional force tends to counteract it.
[tex]\[ \text{Net Force} = \text{Applied Force} + \text{Frictional Force} \][/tex]
Substituting the values:
[tex]\[ \text{Net Force} = -23355 \, \text{N} + 163 \, \text{N} \][/tex]
[tex]\[ \text{Net Force} = -23192 \, \text{N} \][/tex]
### Step 3: Use Newton's Second Law to Find Acceleration
Newton's second law states that:
[tex]\[ F = ma \][/tex]
Where [tex]\( F \)[/tex] is the net force, [tex]\( m \)[/tex] is the mass, and [tex]\( a \)[/tex] is the acceleration. We can rearrange this formula to solve for acceleration:
[tex]\[ a = \frac{F}{m} \][/tex]
Substituting the known values:
[tex]\[ a = \frac{-23192 \, \text{N}}{18.0 \, \text{kg}} \][/tex]
[tex]\[ a = -1288.44 \, \text{m/s}^2 \][/tex]
### Conclusion
The acceleration of the mass is [tex]\(-1288.44 \, \text{m/s}^2\)[/tex]. The negative sign indicates that the acceleration is in the opposite direction of the applied force.
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