A person stands on a bathroom scale in a motionless elevator. When the elevator begins to move, the scale briefly reads only 0.69 of the person's regular weight. Calculate the magnitude of the acceleration of the elevator.
m= 0.69
a=mg-g
a=(0.69)(9.80)-9.80
a=-3.038 m/s^2
Acceleration is 3.038 m/s^2 downward
Fnet = ma
ma = Fn-Fg
Fn = 0.69Fg = 0.69mg
Fg = mg
ma = 0.69mg - mg
cancel out all m in equation and left with:
a=0.69g-g
a=-.31g=-.31*9.8= -3.04 m/s^2
ANSWER: a = -3.04 m/s^2
Well, it seems like this person went on a diet without even trying! Let's have some fun calculating the magnitude of the elevator's acceleration.
First, we need to understand the significance of this weight reading. When the scale shows 0.69 of the person's regular weight, it means that there is a force acting on the person that is equal to 0.31 (1 - 0.69) times their weight, which is canceled out by the normal force from the scale.
Now, let's get to the acceleration. We know that weight is equal to the mass of an object multiplied by the acceleration due to gravity. Since the person's weight is canceled out, we can say that the scale is only showing the normal force, which equals the person's weight. Therefore, the normal force is equal to 0.69 times the person's weight.
Next, we need to translate this normal force into the force generated by the acceleration of the elevator. According to Newton's second law, force equals mass times acceleration (F = ma). In this case, the force exerted by the acceleration is equal to the normal force, which is equal to 0.69 times the person's weight.
Now we have all the information we need. We can set up an equation: F = ma, where F is the force exerted by the acceleration, m is the mass of the person, and a is the acceleration. Since we're trying to find the magnitude of the acceleration, we can write a = F/m. Substituting in the values, we get:
a = (0.69 * person's weight) / person's mass
So, to calculate the magnitude of the acceleration, we would need to know the person's mass and weight. But hey, keep in mind that this equation is only applicable if the person isn't wearing a clown nose or juggling while standing on the scale in the elevator!
To calculate the magnitude of the acceleration of the elevator, we can use the concept of Newton's Second Law of Motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m * a). In this case, the person standing on the scale is the object.
1. First, let's consider the forces acting on the person in this situation. The two forces are the gravitational force (weight) and the normal force exerted by the scale.
2. When the elevator is motionless, these two forces are equal in magnitude and opposite in direction, resulting in a net force of zero.
3. When the elevator starts to move, the scale briefly reads only 0.69 of the person's regular weight, which means that the normal force exerted by the scale is reduced to 0.69 times the person's weight.
4. Using this information, we can set up the equation for the net force:
Net force (F_net) = Normal force (N) - Weight (W)
= 0.69 * Weight - Weight
5. Since weight is equal to mass multiplied by the acceleration due to gravity (W = m * g), we can substitute in this equation:
F_net = 0.69 * m * g - m * g
6. Simplifying the equation, we get:
F_net = m * g * (0.69 - 1)
= m * g * (-0.31)
7. Now, according to Newton's Second Law (F_net = m * a), the net force is also equal to the mass of the person multiplied by the acceleration of the elevator:
m * g * (-0.31) = m * a
8. We can cancel out the mass from both sides of the equation:
g * (-0.31) = a
9. Finally, we can calculate the magnitude of the acceleration by taking the absolute value of both sides of the equation:
|g * (-0.31)| = |a|
Therefore, the magnitude of the acceleration of the elevator is equal to |-0.31 * g|.
A person stand on bathroom scale in motionless elevator. When elevator begins to move the briefly reads
only 0.54 of the person's regular weight. Calculate acceleration of elevator.