A 1300 kg car traveling at a steady speed of 15 m/s initially due northwest round a corner so that after 10s, it is traveling due northeast. What is the magnitude and direction of the net force that must be acting on the car at the instant it is traveling due north?
the car goes through a quarter of a circle in 10 s, at a speed of 15 m/s
so the circumference of the circle is
... 10 * 15 * 4 = 600 m
... the radius is ... 600 / 2π
the centripetal force (which causes the car to travel in a curved path) is
... m v^2 / r
when the car is traveling north, this force is directed east
is gravity part of the "net force"?
To find the magnitude and direction of the net force acting on the car, we need to consider the change in velocity and the period over which the change occurred.
1. Calculate the change in velocity:
The car initially travels due northwest and ends up traveling due northeast. These directions are 90 degrees apart. So, the change in velocity has both a magnitude and a direction.
The magnitude of the change in velocity is given by the difference between the initial and final velocities:
Δv = vf - vi
= (15 m/s) - (-15 m/s) [Since due northwest is -45 degrees and due northeast is +45 degrees]
= 30 m/s
2. Calculate the time period over which the change occurred:
The time period is given as 10 seconds.
3. Calculate the acceleration:
Using the formula for acceleration:
a = Δv / t
= 30 m/s / 10 s
= 3 m/s²
4. Determine the mass of the car:
The given mass is 1300 kg.
5. Calculate the net force:
Using Newton's second law, which states that the net force (F) acting on an object is equal to the mass (m) of the object multiplied by its acceleration (a):
F = m * a
= (1300 kg) * (3 m/s²)
= 3900 N
Therefore, the magnitude of the net force acting on the car is 3900 N.
6. Determine the direction of the net force:
Since the car is traveling due north, the net force must also act in the same direction (due north). So, the direction of the net force is north.
In conclusion, the magnitude of the net force acting on the car when it is traveling due north is 3900 N, and the direction of the net force is north.