a) The launch velocity of the rocket is 5.48 m/s
b) The maximum height is 1.53 m
Explanation:
a)
We can solve this part by applying the law of conservation of energy, by considering the kinetic energy and the elastic potential energy only, since there is no change in gravitational potential energy and no friction is involved.
The total energy when the spring is compressed is:
with
(initial kinetic energy is zero)
is the elastic potential energy stored in the spring, with
k = 450 N/m (spring constant)
x = 0.10 m (compression of the spring)
The total energy when the spring is relased is:
with
(final kinetic energy), with
m = 0.15 kg (mass of the rocket)
v = velocity of launch of the rocket
(elastic potential energy is zero when the spring is released)
Combining the two equations we get
And solving for v,
b)
In this part instead we consider only the kinetic energy and the gravitational potential energy, since the spring is at rest so its energy is now zero.
The total energy at the launch is:
where
(initial kinetic energy), with
m = 0.15 kg (mass of the rocket)
v = 5.48 m/s (velocity of launch of the rocket)
(initial gravitational potential energy is zero)
The total energy at the point of maximum height is:
where
(kinetic energy is zero since speed is zero)
(final gravitational potential energy), with
m = 0.15 kg
(acceleration of gravity)
h = ? (maximum height)
Combining the two equations we find
And solving for h,
Learn more about potential energy and kinetic energy:
#LearnwithBrainly
Answer:
Explanation:
The main equation to solve this is F = ma, where F is the force applied to the brakes with respect to its acceleration. We have the mass that we need, but we do not have the acceleration. That's the first thing we have to find. However, our velocity needs to be stated in m/s and right now it's in km/h. Converting that:
Now we're ready to find the acceleration:
where the top line there translates to the final velocity minus the initial velocity.
so the acceleration is -8.3 m/s/s
We can use that now in the force equation above:
F = 1200(-8.3) and
F = -1.0 × 10⁴ N (that's 10,000 N to the correct number of sig dig's; the negative sign means that the force is being applied in the direction opposite to that which the van is currently moving)