Question

A 1700 kg truck traveling on a flat road at 35 m/s applies its brakes and skids for 78 m before coming to rest. Calculate the friction force between the tires and the pavement. Round to the whole number.

Answer 1

The magnitude of the frictional force that brings a 1700 kg truck traveling at 35 m/s to rest over a distance of 78 m is approximately 13,350 N.

Step-by-step explanation:

To calculate the friction force between the tires and the pavement when a 1700 kg truck skids to a stop, we can use the work-energy principle. The work done by friction is equal to the change in kinetic energy of the truck. Since the truck comes to rest, its final kinetic energy is 0, and its initial kinetic energy can be calculated using ½mv², where m is mass and v is velocity.

The initial kinetic energy is ½(1700 kg)(35 m/s)² = 1,041,250 Joules. The work done by friction is the force of friction multiplied by the distance over which it acts (78 m). The work-energy principle states that the work done by the friction force is equal to the change in kinetic energy, which is -1,041,250 Joules (since the truck is losing energy).

Hence, we can write: Friction Force × 78 m = -1,041,250 J. This will allow us to solve for the friction force: Friction Force = -1,041,250 J / 78 m ≈ -13,350 N. Since friction always opposes motion, it acts in the opposite direction of the truck's movement; however, when reporting the magnitude of a force, we usually report the absolute value. Therefore, the magnitude of the frictional force is about 13,350 N, rounded to a whole number.

Answer 2

The friction force between the tires and the pavement is approximately 13,333 N.

Step-by-step explanation:

To calculate the friction force between the tires and the pavement, we can use the equation:

Friction force = mass x deceleration

Given that the mass of the truck is 1700 kg and the truck comes to rest after skidding for 78 m, we can calculate the deceleration of the truck using the equation:

Deceleration = (final velocity^2 - initial velocity^2) / (2 x distance)

Substituting the given values, we get:

Deceleration = (0 - 35^2) / (2 x 78)

After calculating the deceleration, we can substitute it back into the original equation to find the friction force:

Friction force = 1700 x deceleration

Calculating the value, we get:

Friction force = 1700 x (-12.19)

Therefore, the friction force between the tires and the pavement is approximately 13,333 N (rounded to the nearest whole number).