Answer :
To solve the problem of finding the acceleration of the wagon, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. This can be expressed with the formula:
[tex]\[ F = ma \][/tex]
Where:
- [tex]\( F \)[/tex] is the net force acting on the object
- [tex]\( m \)[/tex] is the mass of the object
- [tex]\( a \)[/tex] is the acceleration of the object
Let's go through the solution step-by-step:
1. Identify the forces exerted by the horses:
- The first horse exerts a force of 235 N.
- The second horse exerts a force of 134 N.
2. Calculate the total force exerted by both horses:
Since both horses are pulling the wagon in the same direction, you can simply add the forces together:
[tex]\[
\text{Total Force} = 235 \, \text{N} + 134 \, \text{N} = 369 \, \text{N}
\][/tex]
3. Determine the mass of the wagon:
The mass of the wagon is given as 372 kg.
4. Calculate the acceleration of the wagon:
Use the formula for Newton’s second law rearranged to solve for acceleration ([tex]\( a \)[/tex]):
[tex]\[
a = \frac{F}{m}
\][/tex]
Substitute the known values:
[tex]\[
a = \frac{369 \, \text{N}}{372 \, \text{kg}} \approx 0.9919 \, \text{m/s}^2
\][/tex]
Therefore, the acceleration of the wagon is approximately [tex]\( 0.9919 \, \text{m/s}^2 \)[/tex].
[tex]\[ F = ma \][/tex]
Where:
- [tex]\( F \)[/tex] is the net force acting on the object
- [tex]\( m \)[/tex] is the mass of the object
- [tex]\( a \)[/tex] is the acceleration of the object
Let's go through the solution step-by-step:
1. Identify the forces exerted by the horses:
- The first horse exerts a force of 235 N.
- The second horse exerts a force of 134 N.
2. Calculate the total force exerted by both horses:
Since both horses are pulling the wagon in the same direction, you can simply add the forces together:
[tex]\[
\text{Total Force} = 235 \, \text{N} + 134 \, \text{N} = 369 \, \text{N}
\][/tex]
3. Determine the mass of the wagon:
The mass of the wagon is given as 372 kg.
4. Calculate the acceleration of the wagon:
Use the formula for Newton’s second law rearranged to solve for acceleration ([tex]\( a \)[/tex]):
[tex]\[
a = \frac{F}{m}
\][/tex]
Substitute the known values:
[tex]\[
a = \frac{369 \, \text{N}}{372 \, \text{kg}} \approx 0.9919 \, \text{m/s}^2
\][/tex]
Therefore, the acceleration of the wagon is approximately [tex]\( 0.9919 \, \text{m/s}^2 \)[/tex].
