At a time when mining asteroids has become feasible, astronauts have connected a line between their 3400 kg space tug and a 6000 kg asteroid. Using their ship's engine, they pull on the asteroid with a force of 490 N. Initially the tug and the asteroid are at rest, 420 m apart. How much time does it take for the ship and the asteroid to meet?
Please Help! I don't even know where to start. Thanks!
To solve this problem, we can use the concept of Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
Let's break down the problem into different steps:
Step 1: Determine the net force acting on the system.
The net force is the force applied by the space tug (490 N) minus the force of friction or any other opposing force. In this case, we assume there is no friction or opposing force, so the net force is 490 N.
Step 2: Calculate the acceleration of the system.
The acceleration can be calculated using Newton's second law, which states that the force acting on an object is equal to its mass multiplied by its acceleration (F = ma).
Since we know the mass of the system (space tug + asteroid), we can rearrange the equation to solve for acceleration:
a = F/m
The mass of the system is the sum of the mass of the space tug and the mass of the asteroid:
Mass of space tug = 3400 kg
Mass of asteroid = 6000 kg
Mass of system = Mass of space tug + Mass of asteroid
Step 3: Calculate the acceleration:
a = F/m
a = 490 N / (3400 kg + 6000 kg)
Step 4: Calculate the time it takes for the two objects to meet.
We can use the equations of motion to determine the time it takes for the tug and the asteroid to meet.
The equation we can use is:
d = v0t + (1/2)at^2
Since the tug and the asteroid start from rest (v0 = 0), and the distance between them is given as 420 m, the equation simplifies to:
d = (1/2)at^2
Rearranging the equation to solve for time (t):
t = sqrt((2d) / a)
Now, you can substitute the values and calculate the time it takes for the ship and the asteroid to meet.
I hope this explanation helps! Let me know if you have any further questions.