Please help due in less than 2 hours!!
A person whose mass is m = 86.0 kg steps on a mechanical bathroom scale placed on an inclined plane that makes the angle α = 21.3° with the horizontal. What is the reading on the scale?
i've tried m*g*sin(21.3) and it still says I'm wrong
To find the reading on the scale, you need to consider the components of the person's weight along the incline and perpendicular to the incline.
1. Find the component of the person's weight parallel to the incline:
F_parallel = m*g*sin(α)
= 86.0 kg * 9.8 m/s^2 * sin(21.3°)
≈ 348.3 N
2. Find the component of the person's weight perpendicular to the incline:
F_perpendicular = m*g*cos(α)
= 86.0 kg * 9.8 m/s^2 * cos(21.3°)
≈ 804.9 N
3. The reading on the scale is equal to the perpendicular component of the person's weight (F_perpendicular):
Reading on the scale = 804.9 N
So, the reading on the scale is approximately 804.9 N.
To find the reading on the scale, we need to consider the forces acting on the person on the inclined plane.
First, let's draw a free-body diagram for the person on the inclined plane.
The weight of the person can be broken down into two components: the force perpendicular to the inclined plane (mgcos(α)) and the force parallel to the inclined plane (mgsin(α)). The normal force (N) from the surface of the inclined plane will balance out the perpendicular component of the weight.
The reading on the scale will be equal to the normal force (N).
Now, let's calculate the normal force using the given information.
Normal force (N) = mgcos(α)
Plugging in the values:
m = 86.0 kg
g = 9.8 m/s² (acceleration due to gravity)
α = 21.3°
N = 86.0 kg * 9.8 m/s² * cos(21.3°)
Using a scientific calculator, evaluate N to find the reading on the scale.