Question

a+small+1000-kg+suv+has+a+wheel+base+of+3.0+m.+if+60%+if+its+weight+rests+on+the+front+wheels,+how+far+behind+the+front+wheels+is+the+wagon’s+center+of+mass?

Answer 1

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:

`\[ \text{COM} = \frac{(\text{Weight on front wheels} * \text{Distance to front wheels})}{\text{Total weight}} \]`

Given that 60% of the SUV's weight rests on the front wheels, the weight on the front wheels
`(\(W_{\text{front}}\))` is 0.6 times the total weight
`(\(W_{\text{total}}\))`. The distance to the front wheels
`(\(d_{\text{front}}\))` is the wheelbase divided by 2. The total weight of the SUV
`(\(W_{\text{total}}\))` is 1000 kg. Thus, the formula becomes:

`\[ \text{COM} = \frac{(0.6 * 1000 \, \text{kg} * \frac{3.0 \, \text{m}}{2})}{1000 \, \text{kg}} \]`

Solving this equation yields:

`\[ \text{COM} = \frac{(600 \, \text{kg} * 1.5 \, \text{m})}{1000 \, \text{kg}} = 0.9 \, \text{m} \]`

The COM is the distance from the front wheels, so to find the distance from the rear wheels, subtract this from the wheelbase:

`\[ \text{Distance from rear wheels} = \text{Wheelbase} - \text{COM} \]`

`\[ \text{Distance from rear wheels} = 3.0 \, \text{m} - 0.9 \, \text{m} = 2.1 \, \text{m} \]`

Therefore, the wagon's center of mass is located 1.2 m behind the front wheels.