A rocket sled exerts 3.00(10^4) N of thrust and has a mass of 2.00(10^3) kg. What does it do "zero to sixty" in? How many g's does it achieve?
To determine how long it takes for the rocket sled to go from zero to sixty and the number of g's it achieves, we can use the equations of motion. Let's break it down into steps:
Step 1: Calculate the acceleration of the rocket sled.
The net force acting on an object can be found by using Newton's second law of motion, which states that force equals mass multiplied by acceleration (F = m*a). In this case, the force is the thrust exerted by the rocket sled, which is 3.00x10^4 N, and the mass is 2.00x10^3 kg. Thus, we have:
3.00x10^4 N = (2.00x10^3 kg) * a
Divide both sides by 2.00x10^3 kg to solve for acceleration:
a = (3.00x10^4 N) / (2.00x10^3 kg)
Step 2: Calculate the time taken to reach the desired velocity.
To find the time it takes for the rocket sled to go from zero to sixty, we can use the equation of motion that relates final velocity (v), initial velocity (u), acceleration (a), and time (t):
v = u + a*t
In this case, the final velocity is 60 m/s (since we want to reach 60), the initial velocity is 0 m/s (starting from zero), and we already know the acceleration from Step 1. Thus, the equation becomes:
60 m/s = 0 m/s + (a from Step 1) * t
Simplifying the equation:
60 m/s = (3.00x10^4 N) / (2.00x10^3 kg) * t
Now, solve for t:
t = (60 m/s) * (2.00x10^3 kg) / (3.00x10^4 N)
Step 3: Calculate the number of g's achieved.
The acceleration due to gravity (g) is approximately 9.8 m/s². To find the number of g's achieved, divide the acceleration calculated in Step 1 by the acceleration due to gravity:
Number of g's = a / g
Plug in the values:
Number of g's = ((3.00x10^4 N) / (2.00x10^3 kg)) / 9.8 m/s²
Simplify the equation:
Number of g's ≈ ((3.00x10^4 N) / (2.00x10^3 kg)) / 9.8 m/s²
Now, calculate the result to find the number of g's achieved.