Final Answer:
The wagon's center of mass is located 1.2 m behind the front wheels.
Step-by-step explanation:
The location of the center of mass (COM) can be determined using the formula:
![\[ \text{COM} = \frac{(\text{Weight on front wheels} * \text{Distance to front wheels})}{\text{Total weight}} \]](https://img.qammunity.org/2024/formulas/physics/high-school/11pz68deqx29du26uulwizh8uxuwcl5e0v.png)
Given that 60% of the SUV's weight rests on the front wheels, the weight on the front wheels
is 0.6 times the total weight
. The distance to the front wheels
is the wheelbase divided by 2. The total weight of the SUV
is 1000 kg. Thus, the formula becomes:
![\[ \text{COM} = \frac{(0.6 * 1000 \, \text{kg} * \frac{3.0 \, \text{m}}{2})}{1000 \, \text{kg}} \]](https://img.qammunity.org/2024/formulas/physics/high-school/midlxdri04yq0uv49bnmngh23mcz7rf823.png)
Solving this equation yields:
![\[ \text{COM} = \frac{(600 \, \text{kg} * 1.5 \, \text{m})}{1000 \, \text{kg}} = 0.9 \, \text{m} \]](https://img.qammunity.org/2024/formulas/physics/high-school/6l9wlo22f9uq9qpjh9rlnkfj114zk3kqsf.png)
The COM is the distance from the front wheels, so to find the distance from the rear wheels, subtract this from the wheelbase:
![\[ \text{Distance from rear wheels} = \text{Wheelbase} - \text{COM} \]](https://img.qammunity.org/2024/formulas/physics/high-school/ir16kp8rwpt5fcanwciluf2ugxyhoprtjz.png)
![\[ \text{Distance from rear wheels} = 3.0 \, \text{m} - 0.9 \, \text{m} = 2.1 \, \text{m} \]](https://img.qammunity.org/2024/formulas/physics/high-school/yh224l1vp2j8iv3kwe7mwqaq9xump25q6w.png)
Therefore, the wagon's center of mass is located 1.2 m behind the front wheels.