6a) Acceleration of the bullet:
6b) Final velocity of the bullet: 360 m/s
7a) Acceleration of the truck:
7b) Net force on the truck: 54,000 N
7c) The acceleration will triple
Explanation:
6a)
The acceleration of the bullet can be found by using Newton's second law, which states that the net force acting on an object is equal to the product between the mass of the object and its acceleration:
where
F is the force
m is the mass
a is the acceleration
For the bullet in this problem, we have
F = 3600 N (force)
m = 0.025 kg (mass of the bullet)
Therefore, the acceleration is
6b)
The motion of the bullet is a uniformly accelerated motion, so we can use the following suvat equation:
where
u is the initial velocity
v is the final velocity
a is the acceleration
t is the time elapsed
In this problem, we have:
u = 0 (the bullet starts from rest)
t = 0.0025 s (time)
(acceleration)
So we can solve to find v, the final velocity of the bullet as it leaves the rifle:
7a)
The acceleration of a body is defined as the rate of change of its velocity:
where
u is the initial velocity
v is the final velocity
t is the time taken for the velocity to change from u to v
a is the acceleration
For the truck in this problem, we have
u = 0 (it starts from rest)
v = 28 m/s (final velocity)
t = 18.7 s (time elapsed)
Substituting, we find the acceleration
7b)
The net force on the truck can be calculated using Newton's second law:
where
F is the force
m is the mass
a is the acceleration
For the truck in this problem,
m = 36,000 kg is the mass of the truck
is the acceleration
So, the net force on the truck is
7c)
We said that the relationship between the net force on the truck and its acceleration is
The equation can be rewritten as
We notice that the acceleration is directly proportional to the acceleration.
Here we are told that the net force on the truck is tripled, therefore
As a consequence, the new acceleration of the truck would be
So, the acceleration also triples.
Learn more about force, acceleration and Newton's second law:
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