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 9.7-kg projectile from rest to a speed of 6.5 × 103 m/s. The net force accelerating the projectile is 8.0 × 105 N. How much time is required for the projectile to come up to speed?
F = m*a
a = F/m = 80000/9.7 = 8247 m/s^2
V = Vo + a*t
t = (V-Vo)/a = (6500-0)/ 8247 = 0.788 s.
At an instant when a soccer ball is in contact with the foot of the player kicking it, the horizontal or x component of the ball's acceleration is 750 m/s2 and the vertical or y component of its acceleration is 990 m/s2. The ball's mass is 0.38 kg. What is the magnitude of the net force acting on the soccer ball at this instant?
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:
net force = mass x acceleration
In this case, the net force is given as 8.0 × 10^5 N and the mass of the projectile is 9.7 kg. The acceleration can be obtained by dividing the final velocity of the projectile (6.5 × 10^3 m/s) by the time it takes to reach that velocity (which we need to find).
So, we have the following equation:
8.0 × 10^5 N = 9.7 kg x (6.5 × 10^3 m/s) / t
Now, we can isolate the variable t (time) by rearranging the equation.
First, multiply both sides of the equation by t to remove it from the denominator:
(8.0 × 10^5 N) * t = (9.7 kg) * (6.5 × 10^3 m/s)
Next, divide both sides of the equation by (8.0 × 10^5 N) to solve for t:
t = (9.7 kg * 6.5 × 10^3 m/s) / (8.0 × 10^5 N)
Calculating this expression will give us the time required for the projectile to come up to speed. Let's do the math:
t = (9.7 kg * 6.5 × 10^3 m/s) / (8.0 × 10^5 N)
t = 62.385 s
Therefore, the projectile takes approximately 62.4 seconds to come up to speed.