You press down on the gas on your car and accelerate through the mob of zombies in front of you. As you move 65 m through the swarm to get out of the place you've been hiding in, you estimate that the force of your car increases from 200 N to 780 N. Determine how much work your car did to the zombies.
To determine the work done by your car on the zombies, we need to calculate the work done by the changing force as you accelerate through the swarm.
Work (W) is defined as the product of force (F) and displacement (d) in the direction of the force. Mathematically, it can be expressed as:
W = F * d * cos(theta)
In this case, the displacement (d) is given as 65 m, and the initial force (F1) is 200 N, while the final force (F2) is 780 N. To find the work done, we can use the average force, which is equal to the sum of the initial and final forces divided by 2.
Average force (Favg) = (F1 + F2) / 2
Now, let's calculate the average force:
Favg = (200 N + 780 N) / 2
= 980 N / 2
= 490 N
We can now calculate the work done:
W = Favg * d * cos(theta)
Since the force and displacement are in the same direction (forward through the swarm), the angle (theta) between them is 0 degrees. The cosine of 0 degrees is 1, so we can simplify the equation:
W = 490 N * 65 m * cos(0°)
W = 490 N * 65 m * 1
W = 31,850 N·m
Therefore, your car did 31,850 joules of work on the zombies as it accelerated through the swarm.
To determine the work done by your car to move through the swarm of zombies, you need to calculate the work done by the net force acting on the car. Work is defined as the product of force and displacement, given by the equation:
Work = Force x Displacement x cos(theta).
In this case, the force experienced by your car increased from 200 N to 780 N. However, it is not clear from the question whether this force is the net force or the applied force. So, we'll assume it as the net force since it is not explicitly mentioned.
The displacement of your car through the swarm of zombies is given as 65 m. The angle (theta) in the equation represents the angle between the force vector and the displacement vector. Since the car moves straight ahead, the angle between the force and displacement vectors is 0 degrees. Therefore, the cosine of theta is 1.
Plugging in the values into the formula, we get:
Work = (780 N - 200 N) x 65 m x cos(0)
= 580 N x 65 m
Now, multiply the force difference and displacement:
Work = 37700 N·m
Therefore, your car did approximately 37700 Joules of work to the zombies.