A person whose mass is m = 60.5 kg steps on a mechanical bathroom scale placed on an inclined plane that makes the angle α = 31.7° with the horizontal. What is the reading on the scale?
For this question I used the formula FN=mgcostetha= 60.5x9.8xcos31.7 but the answer is wrong.
Please help
Fp = mg*sin31.7 = Force parallel to the
Inclined plane = Scale reading.
Fn = mg*Cos31.7 = Normal = Force perpendicular to the inclined plane.
Well, sounds like someone's having a weighty problem! Let's see if I can help lighten the mood and solve this puzzling question for you, shall we?
So, to find the reading on the scale, we need to resolve the gravitational force acting on the person into two components: one perpendicular to the inclined plane (called the normal force) and one parallel to the inclined plane (called the force due to gravity).
First, let's find the force due to gravity acting parallel to the inclined plane. We can calculate it using the formula F_parallel = mg * sin(α), where α is the angle of the inclined plane. Plugging in the given values, we have F_parallel = 60.5 kg * 9.8 m/s^2 * sin(31.7°).
Next, let's find the normal force, which is acting perpendicular to the inclined plane. We can calculate it using the formula F_normal = mg * cos(α). Plugging in the given values, we have F_normal = 60.5 kg * 9.8 m/s^2 * cos(31.7°).
Now, the reading on the scale is equal to the normal force, since the scale measures the force acting perpendicular to it. So, the reading on the scale would be F_normal = 60.5 kg * 9.8 m/s^2 * cos(31.7°).
Now, grab your calculator and crunch those numbers! And remember, even if the answer doesn't make you laugh, life is all about the ups and downs, just like this inclined plane. Good luck!
To find the reading on the scale, we need to consider the forces acting on the person on the inclined plane.
There are two forces acting on the person:
1. The gravitational force acting vertically downward, given by mg, where m is the person's mass (60.5 kg) and g is the acceleration due to gravity (approximately 9.8 m/s²).
2. The normal force acting perpendicular to the inclined plane.
In this case, we need to resolve the weight vector into two components: one parallel to the inclined plane and one perpendicular to it.
The weight component perpendicular to the inclined plane is given by:
F_perpendicular = mg * cos(α)
The weight component parallel to the inclined plane is given by:
F_parallel = mg * sin(α)
The normal force (F_N) is equal in magnitude and opposite in direction to the weight component perpendicular to the inclined plane (F_perpendicular).
Therefore, the reading on the scale is equal to the magnitude of the normal force, which is F_N = F_perpendicular.
Using the given values, we can calculate the reading on the scale as follows:
F_perpendicular = mg * cos(α)
= 60.5 kg * 9.8 m/s² * cos(31.7°)
Calculating the above expression gives us:
F_perpendicular ≈ 521.209 N
Therefore, the reading on the scale will be approximately 521.209 N.
To find the reading on the scale, we need to consider the forces acting on the person on an inclined plane.
First, we need to resolve the gravitational force, mg, into components parallel and perpendicular to the inclined plane. The component of the weight perpendicular to the inclined plane is given by:
F_perpendicular = mg * cos(α)
In this case, α is the angle between the inclined plane and the horizontal, so cos(α) = cos(31.7°).
Next, we need to compare the normal force, FN, acting on the person with the magnitude of the force perpendicular to the inclined plane, F_perpendicular.
Since the person is in equilibrium (not accelerating up or down the inclined plane), the normal force must be equal in magnitude to the force perpendicular to the inclined plane.
Therefore, the reading on the scale is given by the magnitude of the normal force:
Reading on the scale (FN) = F_perpendicular = mg * cos(α)
In this case, the mass (m) is given as 60.5 kg and the angle α is given as 31.7°, so the correct calculation is:
Reading on the scale (FN) = 60.5 kg * 9.8 m/s² * cos(31.7°)
Please double-check your calculations to ensure you are entering the correct values into your calculator or formula.