A bicyclist is coasting down a road that is sloped downward at an angle of 8°. The bicycle and bicyclist have a total mass of 80 kg. If the bicycle wheels roll freely, without any effect from friction or air resistance slowing the motion, how fast would the bicyclist accelerate?

Wc = mg = 80kg * 9.8N/kg = 784N. = Weight of bicyclist and bike.

Fc = 784N. @ 8deg.
Fp = 784sin8 = 109.1N.. = Force parallel to hill.

Fn = Fp = 1o9.1N.
Fn = ma,
a = Fn / m = 109.1 / 80 = 1.36m/s^2.

Well, I have to say, it sounds like this cyclist is in quite a rush to go downhill! Now, let's do the math here.

We know that the angle of the slope is 8°, which means we need to break out our trigonometry skills. The force of gravity acting on the cyclist and the bike can be split into two components: the force pulling the cyclist down the slope (in the direction of motion) and the force perpendicular to the slope (opposing the normal force).

The force of gravity pulling the cyclist down the slope can be calculated using the formula: F = m * g * sin(θ), where m is the mass (80 kg), g is the acceleration due to gravity (9.8 m/s²), and θ is the angle of the slope (8°).

So, the force pulling the cyclist down the slope is: F = 80 kg * 9.8 m/s² * sin(8°).

Now, we can use Newton's second law of motion, which states that force is equal to mass times acceleration (F = m * a), to find the acceleration of the cyclist.
So, a = F / m.

By plugging in the values we know, we can find the acceleration:
a = (80 kg * 9.8 m/s² * sin(8°)) / 80 kg.

After doing the math, we find that the acceleration is roughly 1.073 m/s². So, the bicyclist would accelerate at about 1.073 meters per second squared while coasting down that slope. Just make sure they don't pedal too fast or things might get a little wheely out of control!

To find the acceleration of the bicyclist, we need to determine the force acting on the bicycle and then use Newton's second law of motion (F = ma) to find the acceleration.

In this case, the force acting on the bicycle is the component of the gravitational force pulling the bicyclist downhill, which can be calculated as:

Force = mass * acceleration due to gravity * sin(angle)

Where:
Mass = 80 kg (total mass of the bicycle and bicyclist)
Acceleration due to gravity = 9.8 m/s^2
Angle = 8°

Let's plug in the values to calculate the force:

Force = 80 kg * 9.8 m/s^2 * sin(8°)

Calculating this value gives us:

Force = 80 kg * 9.8 m/s^2 * 0.139173101

Force = 109.765804 N

Now, we can use Newton's second law (F = ma) to find the acceleration:

109.765804 N = 80 kg * a

Solving for acceleration:

a = 109.765804 N / 80 kg

a ≈ 1.372 N/kg

Therefore, the bicyclist would accelerate at approximately 1.372 m/s^2 while coasting down the road.

To find the acceleration of the bicyclist, we need to consider the forces acting on the system.

First, we need to determine the component of the gravitational force that is acting parallel to the slope. We can do this by multiplying the mass of the system (80 kg) by the acceleration due to gravity (9.8 m/s^2) and then by the sine of the angle of the slope (8°).

Parallel force = m * g * sin(theta)
= 80 kg * 9.8 m/s^2 * sin(8°)

Next, we need to find the net force acting on the system. Since there is no friction or air resistance, the net force is simply the parallel force determined in the previous step.

Net force = Parallel force

Finally, we can calculate the acceleration of the system using Newton's second law of motion: F = ma, where F is the net force and a is the acceleration.

Acceleration = Net force / mass
= Parallel force / mass

Let's calculate the acceleration: