The force that friction exerts on a car is proportional to its mass. Suppose friction exerts $6272\,\text{N}$ of force on a $1600\,\text{kg}$ car on a wet road. How many newtons of force would friction exert on a $2400\,\text{kg}$ car under the same conditions?

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Q. The force that friction exerts on a car is proportional to its mass. Suppose friction exerts

6272\,\text{N}

of force on a

1600\,\text{kg}

car on a wet road. How many newtons of force would friction exert on a

2400\,\text{kg}

car under the same conditions?

Establish Relationship: First, we need to establish the relationship between the force of friction and the mass of the car. We are given that the force of friction is proportional to the mass of the car. This means that if we know the force exerted on a car of a certain mass, we can use a ratio to find the force exerted on a car of a different mass.
Set Up Proportion: We are given that a $1600\,\text{kg}$ car experiences a force of $6272\,\text{N}$ . We can set up a proportion to find the force on a $2400\,\text{kg}$ car. Let $F$ be the force on the $2400\,\text{kg}$ car. The proportion is: $\newline$ $(\text{Force on } 1600\,\text{kg car}) / (\text{Mass of } 1600\,\text{kg car}) = (\text{Force on } 2400\,\text{kg car}) / (\text{Mass of } 2400\,\text{kg car})$ $\newline$ $6272\,\text{N} / 1600\,\text{kg} = F / 2400\,\text{kg}$
Cross-Multiply and Solve: To find $F$ , we cross-multiply and solve for $F$ : $6272 \, \text{N} \times 2400 \, \text{kg} = F \times 1600 \, \text{kg}$
Perform Multiplication: Now we perform the multiplication on the left side of the equation: $15,052,800 \, \text{N} \cdot \text{kg} = F \cdot 1600 \, \text{kg}$
Divide and Solve: Next, we divide both sides of the equation by $1600 \, \text{kg}$ to solve for $F$ : $\newline$ $\frac{15,052,800 \, \text{N} \cdot \text{kg}}{1600 \, \text{kg}} = F$
Divide and Solve: Next, we divide both sides of the equation by $1600 \, \text{kg}$ to solve for $F$ : $\newline$ $\frac{15,052,800 \, \text{N} \cdot \text{kg}}{1600 \, \text{kg}} = F$ Performing the division gives us: $\newline$ $F = \frac{15,052,800 \, \text{N} \cdot \text{kg}}{1600 \, \text{kg}}$ $\newline$ $F = 9408 \, \text{N}$