A 1100 kg car coasts on a horizontal road with a speed of 19 m/s. After crossing a an unpaved, sandy stretch of road 32 m long, its speed decreases to 12 m/s. (a) Was the net force done on the car positive, negative, or zero? Explain (b) Find the magnitude of the average net force on the car in the sandy section.

Equations:

Change in kinetic energy = 1/2m(Vf^2-Vi^2) = Net (total) Work done on the object = F*d

m = 1100 kg
Vi = 19 m/s
Vf = 12 m/s
d = 32m

Calculations:

1/2(1100)(12^2-19^2) = F(net)*32
=119350/32
b) =3730 N

a) ΔEK is negative, meaning that W < 0 meaning that theta > 90 degrees (cos180 for this question)

(a) Well, the car is coasting, meaning there is no engine power involved. So, we can assume that the net force done on the car must be zero. Otherwise, it would be like a magician secretly pulling the car back with an invisible rope, and that's just not realistic.

(b) To find the magnitude of the average net force, we can use the equation: average net force = (change in momentum) / (change in time). However, since we don't have the change in time, we need to find another approach.

Here's a little joke to lighten up the physics mood: Why did the car bring a broom to the sand? Well, it wanted to sweep its problems away!

Getting back to the problem, we can use the work-energy principle. The work done on the car equals the change in kinetic energy. So, we have:

Work = (Change in kinetic energy) = (1/2) * m * (vf^2 - vi^2)

Where:
m = mass of the car = 1100 kg
vf = final velocity = 12 m/s
vi = initial velocity = 19 m/s

Let's plug in the values and calculate the work done.

W = (1/2) * 1100 kg * (12 m/s)^2 - (19 m/s)^2

Simplifying this equation will give us the work done.

(a) In order to determine the direction of the net force, we need to consider the change in the speed of the car. In this case, the car's speed decreases from 19 m/s to 12 m/s. Since the speed is decreasing, the acceleration of the car is directed opposite to its motion, which means that the net force is in the opposite direction of the car's velocity. Therefore, the net force done on the car is negative.

(b) To find the magnitude of the average net force, we can use the equation for average acceleration:

average acceleration = (final velocity - initial velocity) / time

Since the motion occurs over a distance, we can use the equation:

average acceleration = (final velocity^2 - initial velocity^2) / (2 * distance)

Plugging in the values:

initial velocity = 19 m/s
final velocity = 12 m/s
distance = 32 m

average acceleration = (12^2 - 19^2) / (2 * 32)
average acceleration = (-45) / (2 * 32)
average acceleration = -0.7031 m/s^2

Now, we can use Newton's second law of motion:

net force = mass * acceleration

mass = 1100 kg
acceleration = -0.7031 m/s^2

net force = 1100 kg * (-0.7031 m/s^2)
net force = -773.41 N

Therefore, the magnitude of the average net force on the car in the sandy section is 773.41 N.

(a) To determine whether the net force done on the car was positive, negative, or zero, we need to consider the change in the car's speed.

Given that the car's speed decreases from 19 m/s to 12 m/s, we can conclude that the net force done on the car was negative. This is because the car experienced a deceleration due to an opposing force acting against its motion. The negative net force came from the friction between the sandy surface and the car's tires, which acted opposite to the car's direction of motion.

(b) To find the magnitude of the average net force on the car in the sandy section, we can use the concept of work and energy.

The work-energy principle states that the net work done on an object is equal to the change in its kinetic energy. Mathematically, this can be expressed as:

Net work = change in kinetic energy

The change in kinetic energy can be calculated as:

Change in kinetic energy = (1/2) * mass * (final velocity^2 - initial velocity^2)

Given:
Mass of the car (m) = 1100 kg
Initial velocity (v1) = 19 m/s
Final velocity (v2) = 12 m/s

Change in kinetic energy = (1/2) * 1100 kg * ((12 m/s)^2 - (19 m/s)^2)

Calculating this expression will give us the change in kinetic energy.

Since the magnitude of the average net force on the car is equal to the work done on it divided by the displacement, we can use the work-energy principle to determine the average net force.

Average net force = net work / displacement

In this case, the displacement is given as 32 meters.

Therefore, to find the magnitude of the average net force on the car in the sandy section, we need to calculate the work done on the car using the change in kinetic energy we previously found, and then divide it by the displacement of 32 meters.