A vehicle that weighs 400N on the surface of the earth is traveling in outer space at a speed of 400m/s. it can be stopped by applying a constant force of 20N for?
To determine the time required to stop the vehicle in outer space, we need to apply Newton's second law of motion. This law states that the force applied to an object is equal to its mass multiplied by its acceleration: F = m * a.
Here, we are given the weight of the vehicle, which is the force due to gravity acting on it. Weight can be calculated using the formula: weight = mass * gravitational acceleration (w = m * g). On the surface of the Earth, the gravitational acceleration is approximately 9.8 m/s².
Given that the weight of the vehicle is 400N, we can calculate the mass (m) by dividing the weight by the gravitational acceleration:
m = w / g
m = 400N / 9.8 m/s²
m ≈ 40.82 kg
Since the vehicle is already moving in outer space, we can assume that there are no other forces acting on it (such as friction or air resistance). Therefore, the only force that will cause the vehicle to decelerate is the applied force of 20N.
To calculate the acceleration (a), we can use Newton's second law:
F = m * a
20N = 40.82 kg * a
a ≈ 0.49 m/s²
Now that we have the acceleration, we can calculate the time required to stop the vehicle using the equation of motion:
v = u + at
where:
v = final velocity (0 m/s for a complete stop)
u = initial velocity (400 m/s)
a = acceleration (-0.49 m/s², as it acts in the opposite direction)
t = time (unknown)
Rearranging the equation, we have:
t = (v - u) / a
t = (0 - 400 m/s) / (-0.49 m/s²)
t ≈ 816.33 s
Therefore, it will take approximately 816.33 seconds (or about 13 minutes and 36 seconds) to stop the vehicle by applying a constant force of 20N in outer space.