Q. A 10.6 kg weather rocket generates a thrust of 226.0 N. The rocket, pointing upward, is clamped to the top of a vertical spring. The bottom of the spring, whose spring constant is 402.0 N/m, is anchored to the ground. Initially, before the engne is ignited, the rocket sits at rest on top of the spring.
A: After the engine is ignited, what is the rocket's speed when the spring has stretched 19.4 cm past its natural length?
B: What would be the rocket's speed after travelling the distance if it weren't tied down to the spring?
I did what u told me to do.
For A, F(net) = F(thrust)-mg
F(net)d = 1/2(k)(d^2)+ 1/2mv^2
and For B, Vf^2 = 2ad where a = F(net)/m I used 0.194m for d but both answers are wrong again. Do i used 0.194m for both in part a and b? If i do, i don't know why they are wrong.
For part A, the equation you should use is:
F(net) = F(thrust) - mg
This equation represents the net force acting on the rocket. The net force is equal to the thrust force minus the force of gravity.
To find the rocket's speed when the spring has stretched 19.4 cm past its natural length, you need to use the conservation of mechanical energy. The equation you should use is:
F(net)d = (1/2) k (d^2) + (1/2) mv^2
Here, F(net)d represents the work done by the net force, (1/2) k (d^2) represents the potential energy stored in the spring, and (1/2) mv^2 represents the kinetic energy of the rocket.
You need to use the displacement, d, in meters, for both F(net)d and (1/2) k (d^2). In this case, 19.4 cm should be converted to meters, which is 0.194 m. So, you should use 0.194 m for both F(net)d and (1/2) k (d^2).
Next, you can solve the equation for v, the speed of the rocket.
For part B, if the rocket weren't tied down to the spring, you can use the equation:
Vf^2 = 2ad
Here, Vf represents the final velocity of the rocket, a represents the acceleration, and d represents the distance traveled. In this case, you need to use the 0.194 m for d and solve for Vf.
Make sure to use appropriate unit conversions and plug in the given values correctly into the equations.
dang. I forgot about PEnergy gain.
F(net)*d=1/2 kx^2+ 1/2 mv^2+mgx
sorry, It has been a long day for me (since three am).
check my thinking.