What will a spring scale read for the weight of a 75 kg woman in an elevator that moves upward with acceleration 0.30 g? w=?
W=m(g+a)
To solve this problem, we need to consider the forces acting on the woman in the elevator. The weight of the woman is a force pointing downward and is given by the equation w = m * g, where w represents the weight, m is the mass of the woman, and g is the acceleration due to gravity.
First, let's calculate the weight of the woman:
w = m * g
w = 75 kg * (9.8 m/s^2)
w = 735 N
Next, we need to consider the additional force acting on the woman due to the upward acceleration of the elevator. The equation for this force is F = m * a, where F represents the force, m is the mass of the woman, and a is the acceleration.
The acceleration of the elevator is given as 0.30g, where g is the acceleration due to gravity. Since g is a positive value (pointing downward), the upward acceleration can be calculated as follows:
Upward acceleration = 0.30 * g
Now, let's calculate the upward force on the woman:
Upward force = m * (0.30 * g)
Upward force = 75 kg * (0.30 * 9.8 m/s^2)
Upward force = 220.5 N
To find the reading on the spring scale, we need to consider the net force acting on the woman. The net force is the difference between the upward force due to acceleration and the downward force of the woman's weight.
Net force = Upward force - Weight
Net force = 220.5 N - 735 N
Net force = -514.5 N
In this case, the negative sign indicates that the net force is pointing downward. Therefore, the spring scale will read the magnitude of the net force, which is 514.5 N.