Newton's Law of Motion for a Straight Line Motion

In summary, the conversation discusses a scenario where an oil tanker's engines break down and it is headed towards a reef. The wind dies down and the engineer gets the engines going again, but the rudder is stuck. The ship tries to accelerate backwards to avoid hitting the reef, and the mass of the tanker and cargo is given. The question asks if the ship will hit the reef and if the oil will be safe. The attempt at a solution involves finding the acceleration of the ship's engines, calculating the time it takes for the ship to hit the reef, and determining the distance traveled. However, the calculation for acceleration is incorrect, and the correct answer is that the ship will hit the reef at a speed of 0.17 m
  • #1
!!!
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Homework Statement


An oil tanker's engines have broken down, and the wind is blowing the tanker straight toward a reef at a constant speed of 1.5 m/s. When the tanker is 500 m from the reef, the wind dies down just as the engineer gets the engines going again. The rudder is stuck, so the only choice is to try to accelerate straight backward away from the reef. The mass of the tanker and cargo is 3.6 x 107 kg, and the engines produce a net horizontal force of 8.0 x 104N on the tanker. Will the ship hit the reef? If it does, will the oil be safe? The hull can withstand an impact at a speed of 0.2 m/s or less. You can ignore the retarding force of the water on the tanker's hull.


Homework Equations


F = ma
vx = v0x + axt
x = x0 + v0xt + 1/2 axt2
vx2= v0x2 + 2ax(x-x0)
x - x0 = (v0x + vx / 2)t

The Attempt at a Solution


I don't exactly know what to do first, so I first found the acceleration of the ship's engines.
a = f/m = 8.0 x 104N / 3.6 x 107 kg = 2.22 x 103 m/s2

Then I tried to find the time it takes for the ship to hit the reef:
vx = v0x + axt
1.5 = 0 + (2.22 x 103)(t)
t = 6.757 x 10-4 s.

And plugged it into the distance traveled:
x = x0 + v0xt + 1/2 axt2
x = 0 + 0 + 1/2 (2.22 x 103)(6.757 x 10-4)2
x = 5.02 x 10-4 m.

The book's answer said that it's 506 m so the ship will hit the reef, and the speed at which the ship hits the reef is 0.17 m/s, so the oil should be safe.
But I don't know how to get to the correct answers. :(
 
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  • #2
! said:

The Attempt at a Solution


I don't exactly know what to do first, so I first found the acceleration of the ship's engines.
a = f/m = 8.0 x 104N / 3.6 x 107 kg = 2.22 x 103 m/s2
Is it reasonable that the ship will receive an acceleration of 2220 m/s2? No, it's certainly not. Check your calculation in this step.
 
  • #3
! said:
a = f/m = 8.0 x 104N / 3.6 x 107 kg = 2.22 x 103 m/s2

shouldn't it be:
a = f/m = 8.0 x 104N / 3.6 x 107 kg = 2.22 x 10-3 m/s2
 

1. What is Newton's Law of Motion for Straight Line Motion?

Newton's Law of Motion for Straight Line Motion, also known as the First Law of Motion, states that an object will remain at rest or in constant velocity unless acted upon by an external force.

2. How is this law different from the other two laws of motion?

The other two laws of motion, the Second and Third Laws, deal with the changes in motion of objects when acted upon by external forces. The First Law specifically focuses on the concept of inertia and how objects will maintain their state of motion unless acted upon by a force.

3. What is the role of inertia in Newton's Law of Motion for Straight Line Motion?

Inertia is the tendency of an object to resist changes in its state of motion. According to the First Law, objects will maintain their state of rest or constant velocity due to inertia, unless acted upon by an external force.

4. Can this law be applied to both stationary and moving objects?

Yes, this law can be applied to both stationary and moving objects. For stationary objects, it explains why they remain at rest unless a force is applied. For moving objects, it explains why they continue to move with constant velocity, unless a force is applied to change their motion.

5. How does Newton's Law of Motion for Straight Line Motion relate to everyday life?

This law is applicable in many everyday situations, such as when a book remains on a table until someone picks it up, or when a car continues to move forward on a flat road unless the brakes are applied. It also explains why objects in space continue to move in a straight line at a constant speed unless acted upon by a force, such as gravity or a change in direction from a rocket engine.

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