Answer :
The magnitude of the resulting acceleration is 16.66 m/s².
The Breakdown
Mass of the block: 22 kg
Force provided by Scarlett: 218 N
Force provided by Hunter Johansson: 218 N
Coefficient of friction: 0.322
Acceleration of gravity: 9.8 m/s²
Calculating the net force acting on the block.
The net force is the vector sum of the applied forces and the frictional force.
Frictional force = μ × N
Where μ is the coefficient of friction and N is the normal force.
Since the block is on a horizontal surface, the normal force is equal to the weight of the block.
N = mg = (22 kg) × (9.8 m/s²) = 215.6 N
Frictional force = 0.322 × 215.6 N = 69.4 N
Net force = Scarlett's force + Hunter's force - Frictional force
Net force = 218 N + 218 N - 69.4 N = 366.6 N
Calculating the magnitude of the resulting acceleration.
Using Newton's second law: F = ma
a = F / m
a = 366.6 N / 22 kg = 16.66 m/s²
Therefore, the magnitude of the resulting acceleration is 16.66 m/s².
The magnitude of the resulting acceleration is approximately [tex]\(16.66 \, \text{m/s}^2\).[/tex]
1. Calculate the frictional force:
[tex]\[N = mg = (22 \, \text{kg}) \times (9.8 \, \text{m/s}^2) = 215.6 \, \text{N}\] \[f_{\text{friction}} = \mu \times N = 0.322 \times 215.6 \, \text{N} = 69.4152 \, \text{N}\][/tex]
2. Calculate the net force:
[tex]\[ \text{Net force} = (436 \, \text{N}) - (69.4152 \, \text{N}) = 366.5848 \, \text{N}\][/tex]
3. Calculate the acceleration:
[tex]\[a = \frac{F}{m} = \frac{366.5848 \, \text{N}}{22 \, \text{kg}} = 16.6639 \, \text{m/s}^2\][/tex]
So, the magnitude of the resulting acceleration is approximately [tex]\(16.66 \, \text{m/s}^2\).[/tex]
