To determine the location of his center of mass, a physics student lies on a lightweight plank supported by two scales L = 2.40 m apart If the left scale reads 278 N, and the right scale reads 116 N, calculate the student's mass.
Calculate the distance from the student's head to his center of mass.
Hmmmm. sum moments about the Left end.
116*2.4-(116+278)x=0
find x, the distance of the cg from the left end.
I'm still confused on how the find the center of the student's mass though????
To determine the student's mass and the distance from their head to their center of mass, we need to use the principle of moments.
1. Calculate the total weight of the student:
The total weight of the student is the sum of the readings on the left and right scales. In this case, the left scale reads 278 N and the right scale reads 116 N. Therefore, the total weight is: 278 N + 116 N = 394 N.
2. Calculate the distance between each scale and the center of mass:
Since the plank is supported at two points, the center of mass of the student lies directly between these two points. Thus, the distance between each scale and the center of mass is equal. In this case, the distance between the scales is given as L = 2.40 m.
3. Calculate the mass of the student:
To find the mass, we need to use the equation: weight = mass × acceleration due to gravity. Rearranging the equation gives the formula: mass = weight / acceleration due to gravity.
The acceleration due to gravity is approximately 9.8 m/s^2. Therefore, the mass of the student can be calculated as: mass = 394 N / 9.8 m/s^2 = 40.2 kg.
4. Calculate the distance from the student's head to their center of mass:
Since we know that the distance between each scale and the center of mass is equal (L = 2.40 m), with some basic geometry, we can determine that the distance from the head to the center of mass is half of L.
Therefore, the distance from the student's head to their center of mass is: 2.40 m / 2 = 1.20 m.
So, the student's mass is 40.2 kg, and the distance from their head to their center of mass is 1.20 m.
Hmmmmmmm
The student's weight is equal to the summation of the two reactions or 394N which is equal to 40.2 kg force.