An airplane is experiencing turbulence and at some point you feel like feeling lighter. If at that moment your apparent weight is 70% of your normal weight, what is the size and direction of the acceleration of the plane?
the acceleration is in the same direction as gravity (downward)
it is 30% of gravity
.3 g = ?
To find the size and direction of the acceleration of the plane, we can use the concept of apparent weight.
Apparent weight is the perceived weight of an object when it undergoes acceleration or deceleration. In this case, the apparent weight of the person on the plane is 70% of their normal weight. This means that the person feels lighter than usual.
Let's denote the person's normal weight as W (in newtons) and their apparent weight as Wa. We can express the relationship between apparent weight, normal weight, and acceleration using the following formula:
Wa = W + ma
Where m is the mass of the person (in kilograms) and a is the acceleration of the plane (in meters per second squared).
Since the person feels lighter, their apparent weight is 70% of their normal weight:
Wa = 0.7W
Substituting this into the formula, we get:
0.7W = W + ma
Now, we can solve for the acceleration (a):
0.7W - W = ma
-0.3W = ma
a = (-0.3W) / m
The size of the acceleration of the plane is given by (-0.3W) / m. Since the apparent weight is less than the normal weight, the acceleration must be negative (directed opposite to the force of gravity).
Note: The negative sign indicates that the acceleration is in the opposite direction to the person's weight. The magnitude of the acceleration can be calculated by substituting the known values for W (weight) and m (mass) into the equation.