A steroid is moving along a straight line. A force acts along the displacement of the asteroid and slows it down. The asteroid has a mass of 4.5e4kg and the force causes the speed to change from 7100 to 5500m/s. (A) What is the work done by the force? (B) If the asteroid slows down over a distance of 1.8e6m determine the magnitude of the force.

To answer these questions, we can make use of the work-energy principle and Newton's second law of motion.

(A) The work done by a force can be calculated using the formula:

Work = Force x displacement x cos(θ)

We are given the mass of the asteroid, but we need to determine the force. To do this, we can use Newton's second law:

Force = mass x acceleration

The acceleration can be found using the equation:

acceleration = (final velocity - initial velocity) / time

However, the time is not given in the problem. Therefore, we need to find an alternative way to calculate the force.

Let's use a different equation derived from Newton's second law:

force = mass x change in velocity / time

From the problem, we know the mass (4.5e4 kg) and the change in velocity (7100 m/s - 5500 m/s = 1600 m/s). We need to determine the time.

To find the time, we can use the equation of motion:

final velocity = initial velocity + acceleration x time

Given the initial and final velocities, we can find the acceleration. Then, using the acceleration and the change in velocity, we can find the time.

Once we have the force, we can substitute it into the work formula to determine the work done by the force.

(B) To determine the magnitude of the force acting on the asteroid, we can use the equation:

force = mass x acceleration

We have the mass of the asteroid (4.5e4 kg) and the distance over which the asteroid slows down (1.8e6 m).

The acceleration can be found using the equation:

acceleration = change in velocity / time

We know the change in velocity (7100 m/s - 5500 m/s = 1600 m/s), but we need to determine the time.

Similar to part (A), we can use the equation of motion to relate time and acceleration. Once we have the time, we can calculate the acceleration and then find the force using the mass and acceleration.

Please let me know if you would like me to explain the calculation process in more detail or if you need any further assistance!

Let's calculate the work done by the force and the magnitude of the force step-by-step.

(A) To find the work done by the force, we can use the equation:

Work = Force * Distance * cos(θ)

where θ is the angle between the force and the displacement.

Since the force is acting opposite to the displacement, the angle between them is 180 degrees, so cos(θ) = -1.

Given:
Mass of the asteroid (m) = 4.5e4 kg
Initial speed (vi) = 7100 m/s
Final speed (vf) = 5500 m/s

First, let's calculate the change in kinetic energy (ΔKE):

ΔKE = (1/2) * m * (vf^2 - vi^2)

Substitute the given values:

ΔKE = (1/2) * 4.5e4 kg * (5500^2 - 7100^2)

Now, let's calculate the work done:

Work = ΔKE = (1/2) * 4.5e4 kg * (5500^2 - 7100^2)

Calculating this will give you the work done by the force.

(B) To find the magnitude of the force, we can use the equation:

Work = Force * Distance * cos(θ)

Given:
Distance (d) = 1.8e6 m

Rearranging the equation, we have:

Force = Work / (Distance * cos(θ))

Since cos(180) = -1, we can simplify the equation:

Force = - Work / Distance

Substitute the calculated value of the work into the equation:

Force = - Work / Distance

Calculating this will give you the magnitude of the force.

Please note that without the value of the work done, it is not possible to provide an exact numerical value for either the work or the magnitude of the force.