3 part question:

A 52-kg girl weighs herself by standing on a scale in an elevator. What does the scale read when:

a.)the elevator is accelerating downward at 2.5 m/s2?

b.)the elevator is accelerating upward at 2.5 m/s2?

c.)the elevator is ascending at 10 m/s but its speed is decreasing by 6 m/s in each second?

I assume the scale reads in kg.

a) [(g-2.5)/g] x 52 = 38.7 kg
b) [(g + 2.5)]/g x 52 =
c) [(g -6)/g] x 52 =
The speed does not matter but the accleration does. 6 m/s^2 is the deceleration rate.

Thanks for your help but the answers were wrong some how. On my homework it says to answer in Newtons. I know F=ma but w/ these stipulations i don't know how to solve it

I've never seen a weight scale that reads in Newtons. If you want Newtons, multiply my previous answers by 9.8 m/s^2 (same as 9.8 N/kg)

To answer these questions, we need to consider the forces acting on the girl in each scenario. The weight of the girl is the force she exerts on the scale, which is equal to her mass multiplied by the acceleration due to gravity (9.8 m/s^2), expressed as W = m * g.

a.) When the elevator is accelerating downward at 2.5 m/s^2, we need to consider the net force acting on the girl. In this case, there are two forces acting on her: her weight (downward) and the force due to the elevator's acceleration (upward). The net force is the difference between these forces. So, the net downward force will be:

F_net = (m * g) - (m * a_elevator)
= m * (g - a_elevator)
= 52 kg * (9.8 m/s^2 - 2.5 m/s^2)
= 52 kg * 7.3 m/s^2
= 379.6 N

Since the scale measures the normal force acting on the girl, which is equal in magnitude but opposite in direction to the net downward force she experiences, the scale will read 379.6 N.

b.) When the elevator is accelerating upward at 2.5 m/s^2, the net force acting on the girl will be the sum of her weight and the force due to the elevator's acceleration:

F_net = (m * g) + (m * a_elevator)
= m * (g + a_elevator)
= 52 kg * (9.8 m/s^2 + 2.5 m/s^2)
= 52 kg * 12.3 m/s^2
= 639.6 N

In this case, the scale will read 639.6 N.

c.) When the elevator is ascending at 10 m/s but its speed is decreasing by 6 m/s in each second, we can calculate the net force by considering the equation F_net = m * a. The acceleration is the rate of change of velocity, so we need to subtract the elevator's deceleration from its initial acceleration.

Initial acceleration = 10 m/s
Deceleration = -6 m/s (negative because it's in the opposite direction of the initial acceleration)

Net acceleration = Initial acceleration + Deceleration
= 10 m/s - 6 m/s
= 4 m/s

F_net = m * a
= 52 kg * 4 m/s^2
= 208 N

Therefore, the scale will read 208 N.

In summary:
a.) The scale will read 379.6 N when the elevator is accelerating downward at 2.5 m/s^2.
b.) The scale will read 639.6 N when the elevator is accelerating upward at 2.5 m/s^2.
c.) The scale will read 208 N when the elevator is ascending at 10 m/s but its speed is decreasing by 6 m/s in each second.