Scientists are experimenting with a kind of gun that may eventually be used to fire payloads...

Question:

Scientists are experimenting with a kind of gun that may eventually be used to fire payloads directly into the orbit. In one test this gun accelerates a 9.2 kg projectile from rest to a speed of {eq}1.4 x 10^{3} {/eq} m/s. The net force accelerating the projectile is {eq}3.6 x 10^{5} {/eq} N. How much time is required for the projectile to come up to speed?

Newton's 2nd Law and Kinematics

For this problem we will need to use both Newton's 2nd Law:

{eq}F_{net}=m*a {/eq}

and the kinematics equation

{eq}v_f=v_i+a*t {/eq}.

When tackling a problem like this, it is helpful to list all the variables that you know. For this problem we know the initial velocity, the final velocity, the mass and the net force. Our goal is to find the time. Once the variables are listed, you can notice that you have enough information to use Newton's 2nd Law to find the acceleration. Once you know the acceleration, you can use your kinematics equations to compute the time it would take to accelerate the payload to the required speed.

Answer and Explanation:

Finding the acceleration

{eq}a= \frac{F_{net}}{m} = \frac {3.6*10^5}{9.2} = 39130 \frac{m}{s^2} {/eq}

Finding the time:

{eq}v_f=v_i+a*t {/eq}

{eq}1.4*10^3=0+39130*t {/eq}

t= 0.036 seconds


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Newton's Laws of Force & Motion

from GED Science: Life, Physical and Chemical

Chapter 7 / Lesson 6
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