A student walks 350 m [S], then 400 m [E20°N], and finally 550 m [N10°W]. Using the component method, find the resultant (total)
1 answer:
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Answer:
Its speed is maximum and its acceleration is zero
Explanation:
- Concerning the speed:
In a simple harmonic motion, the speed can be determined through the law of conservation of energy. In fact, we have that the total mechanical energy of the system, which is sum of elastic potential energy U and kinetic energy K, is constant:
where k is the spring constant, x is the displacement, m is the mass and v is the speed.
We see that when the displacement is 0, x = 0: this means that the elastic potential energy U is also 0, therefore the kinetic energy K is maximum, and so the speed v is also maximum.
- Concerning the acceleration:
According to Newton's second law, the acceleration of the system is proportional to the net force:
the net force is just the restoring force of the spring, given by Hooke's law:
So, the acceleration is
and we see that when the displacement is zero, x = 0, and so the acceleration is also zero.
Question 7.
Given:
Mass, m = 2200 kg
Time, t = 8 s
Velocity = 12 m/s
Let's find the average net force required to stop the car.
To find the average net force required to stop the car, let's first find the acceleration of the car.
Where:
Initial velocity, vo = 12 m/s
Final velocity, v = 0 m/s (velocity of car when it stops)
t is the time = 8 seconds
a is the acceleration.
Rewrite the formula for a:
Hence, we have:
The acceleration is -1.5 m/s² (negative because the car is deccelerating).
Now, to find the net force, we have:
Where:
m is the mass = 2200 kg
a is the acceleration = -1.5 m/s²
Hence, we have:
The negative sign indicates that the force acts in the opposite direction the car is travelling.
Therefore, average net force required to stop the car is 3300 Newtons in the opposite direction.
ANSWER:
3300 N in the opposite direction