Scientists are experimenting with a kind of gun that may eventually be used to fire payloads directly into orbit. In one test, this gun accelerates a 8.9-kg projectile from rest to a speed of 4.2 × 103 m/s. The net force accelerating the projectile is 1.4 × 105 N. How much time is required for the projectile to come up to speed?
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To find the time required for the projectile to come up to speed, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
In this case, we are given the mass of the projectile (8.9 kg) and the net force acting on it (1.4 × 10^5 N). We can use this information to find the acceleration of the projectile.
Using the formula: force = mass x acceleration
1.4 × 10^5 N = 8.9 kg x acceleration
Now we can solve for the acceleration:
acceleration = (1.4 × 10^5 N) / (8.9 kg)
acceleration ≈ 1.57 × 10^4 m/s^2
Next, we can use the formula for acceleration to find the time it takes for the projectile to reach the given speed.
Using the formula: final velocity = initial velocity + (acceleration x time)
4.2 × 10^3 m/s = 0 + (1.57 × 10^4 m/s^2) x time
Now we can solve for time:
time = (4.2 × 10^3 m/s) / (1.57 × 10^4 m/s^2)
time ≈ 0.267 seconds
Therefore, it takes approximately 0.267 seconds for the projectile to come up to speed.
I hope this explanation helps! Let me know if you have any other questions.