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 4.8-kg projectile from rest to a speed of 3.9 103 m/s. The net force accelerating the projectile is 4.8 105 N. How much time is required for the projectile to come up to speed?
V = Vo + a*t.
a = Fn/m = 4.8*10^5/4.8 = 1*10^5 m/s^2.
t=(V-Vo)/a = (3900-0)/1*10^5 = 0.039 s.
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 its mass multiplied by its acceleration.
Here's how you can calculate the time required:
1. Identify the known variables:
- The mass of the projectile (m) = 4.8 kg
- The net force acting on the projectile (F) = 4.8 × 10^5 N
- The final velocity of the projectile (v) = 3.9 × 10^3 m/s
- The initial velocity of the projectile (u) is given as "from rest," which means u = 0.
2. Apply Newton's second law to find the acceleration (a):
F = m × a
a = F / m
Substitute the given values:
a = (4.8 × 10^5 N) / (4.8 kg)
a = 10^5 m/s^2
3. Use the formula for final velocity (v) in uniformly accelerated motion:
v = u + a × t
Substitute the known values:
3.9 × 10^3 m/s = 0 + (10^5 m/s^2) × t
4. Solve the equation for time (t):
t = v / a
Substitute the known values:
t = (3.9 × 10^3 m/s) / (10^5 m/s^2)
t = 0.039 s
Therefore, the time required for the projectile to come up to speed is approximately 0.039 seconds.