A woman weighing 500 N stands in an elevator that is traveling upward. At a given instant the speed of the elevator as well as the women is 10m/s and both are decreasing at a rate of 2 m/s2 at that instant the elevator is exerts a force on the woman that is
To find the force exerted by the elevator on the woman, we can use Newton's second law of motion, which states that the force (F) acting on an object is equal to the object's mass (m) multiplied by its acceleration (a):
F = m * a
First, we need to find the mass of the woman. We can use the equation for weight (W), which is given by the formula:
W = m * g
where W is the weight of the object in Newtons (N), m is the mass in kilograms (kg), and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Since the weight of the woman is given as 500 N, we can rearrange the equation to solve for mass:
m = W / g
m = 500 N / 9.8 m/s^2
m ≈ 51 kg
Now, let's find the acceleration of the woman. Since both the speed and the acceleration are decreasing, the acceleration of the woman is the difference between the acceleration of the elevator and the acceleration due to gravity:
a = a_elevator - g
a = -2 m/s^2 - (-9.8 m/s^2)
a ≈ 7.8 m/s^2 (upward)
Finally, we can calculate the force exerted by the elevator on the woman using Newton's second law:
F = m * a
F = 51 kg * 7.8 m/s^2
F ≈ 397.8 N
Therefore, the force exerted by the elevator on the woman is approximately 397.8 Newtons (N) in the upward direction.
To determine the force exerted by the elevator on the woman, we need to consider the forces acting on her.
1. The gravitational force (weight) acting on the woman is given by W = mg, where m is the mass of the woman and g is the acceleration due to gravity (approximately 9.8 m/s^2). In this case, the weight of the woman is W = 500 N.
2. The force exerted by the elevator on the woman is equivalent to the net force acting on her. Net force can be calculated using Newton's second law of motion, which states that F = ma, where F is the net force, m is the mass, and a is the acceleration.
Given:
Initial speed (u) = 10 m/s
Acceleration (a) = -2 m/s^2 (since both the elevator and woman are decreasing in speed)
At this instant, the acceleration is negative because the speed is decreasing. Therefore, acceleration due to the upward motion is considered negative in this case.
To find the force exerted by the elevator on the woman, we need to calculate her mass first:
Using Newton's second law:
F = ma
Rearranging the equation:
m = F/a
Plugging in the given weight and acceleration:
m = 500 N / (-9.8 m/s^2)
m ≈ -51 kg (the negative sign indicates downward direction, as mentioned above)
Now we can calculate the force exerted by the elevator on the woman:
F = ma
F = (-51 kg) * (-2 m/s^2)
F = 102 N
Therefore, the elevator exerts a force of 102 N on the woman at that instant.
a↓ mg↓ N↑
ma =mg-N
N=mg-ma =
=W-(W/g) •a=
=500 –(500/9.8) •2 =398 N