A 62kg person lies flat on uniform plank of mass 15kg.The plank, with the person lying on it,is placed on a brick at the head and a bathroom scale at the foot,both under the plank.The persons toe to head dist is 1.56m.The length of the plank is also 1.56m.
a)the reading on the bathroom scale is 30kg.Use this information to determine how far the centre of gravity of the person is from the toes.
0.994m
Let X be the distance of the brick from the center of mass of the person.
Set the total moment about the brick equal to zero and solve for the unknown X.
30kg*1.56 m - 15kg*0.78 m - X*62kg = 0
(0.78 m is the location of the center of mass of the uniform board)
Well, clearly this person has quite the balancing act going on!
To start, we need to find the weight of the plank and the person combined. The weight reading on the bathroom scale is 30kg. Since the scale is measuring both the person and the plank together, we need to subtract the weight of just the plank from this reading.
Given that the mass of the plank is 15kg, we can convert this to weight by multiplying it by the acceleration due to gravity (9.8 m/s^2). So, the weight of the plank is 15kg * 9.8 m/s^2 = 147 N.
To find the weight of the person, we can subtract the weight of the plank from the total reading on the bathroom scale. 30kg - 15kg = 15kg. So, the weight of the person is 15kg * 9.8 m/s^2 = 147N.
Now that we have the weight of the person, we can find the distance between the centre of gravity of the person and their toes. This can be done using the concept of a lever arm.
Since the plank and person are lying flat, the centre of gravity will be at the midpoint of the length of the plank. So, the distance between the centre of gravity and the toes is half of the total length of the plank, which is 1.56m / 2 = 0.78m.
Therefore, the centre of gravity of the person is 0.78m away from their toes.
I hope this helps! Keep walking the tightrope of physics!
To determine the distance of the center of gravity of the person from the toes, we can consider the balance of moments.
First, let's calculate the gravitational force acting on the person:
Gravitational force on the person = mass of the person x acceleration due to gravity
= 62 kg x 9.8 m/s^2
= 607.6 N
Next, let's analyze the forces acting on the plank. Since the system is in equilibrium, the sum of the vertical forces in the y-direction must be zero:
Sum of vertical forces = Normal force from the brick + Normal force from the bathroom scale - Gravitational force on the person
= (mass of the plank x acceleration due to gravity) + Bathroom scale reading x acceleration due to gravity - 607.6 N
Given that the bathroom scale reading is 30 kg, we can substitute this value:
(15 kg x 9.8 m/s^2) + (30 kg x 9.8 m/s^2) - 607.6 N = 0
Simplifying this equation, we can solve for the mass of the plank:
147 N + 294 N - 607.6 N = 0
441 N - 607.6 N = 0
-166.6 N = 0
Since -166.6 N is not equal to zero, it means that the equilibrium condition is not satisfied, which implies there might be an error in the given information.
Please double-check the provided values and their accuracy to correct any mistakes and obtain the correct solution.