Socola and Brooke are balanced on a teeter-totter plank as shown below. Socola has a mass of 7.7 kg, and Brooke’s mass is 53 kg. Brooke is located 1.0 m from the pivot. Assume the plank is massless, and calculate how far Socola is from the pivot (x).
7.7•x = 53• 1
x=53/7.7 =6.88 m
To solve this problem, we can use the concept of torque, which is the rotational equivalent of force. The total torque on the teeter-totter must be zero for it to be in balance.
The torque exerted by an object is equal to its weight multiplied by the perpendicular distance from the pivot point. We know the mass of each person, so we can calculate their weights using the formula:
Weight = mass * gravitational acceleration
Given:
Mass of Socola (Ms) = 7.7 kg
Mass of Brooke (Mb) = 53 kg
Distance of Brooke from the pivot (D) = 1.0 m
Let's calculate the weight of each person:
Weight of Socola (Ws) = Ms * gravitational acceleration = 7.7 kg * 9.8 m/s^2
Weight of Brooke (Wb) = Mb * gravitational acceleration = 53 kg * 9.8 m/s^2
Now, let's calculate the torques exerted by Socola and Brooke:
Torque exerted by Socola (Ts) = Ws * x (distance of Socola from the pivot)
Torque exerted by Brooke (Tb) = Wb * D (distance of Brooke from the pivot)
Since the teeter-totter is balanced, the total torque is zero:
Ts + Tb = 0
Ws * x + Wb * D = 0
Substituting the values we calculated above:
7.7 kg * 9.8 m/s^2 * x + 53 kg * 9.8 m/s^2 * 1.0 m = 0
Rearranging the equation, we can solve for x:
7.7 kg * 9.8 m/s^2 * x = -53 kg * 9.8 m/s^2 * 1.0 m
x = (-53 kg * 9.8 m/s^2 * 1.0 m) / (7.7 kg * 9.8 m/s^2)
Simplifying the equation:
x = -53 / 7.7
x ≈ -6.88 m
Since the distance cannot be negative, we take the absolute value of x:
x ≈ 6.88 m
Therefore, Socola is approximately 6.88 meters from the pivot.
To solve this problem, we can use the principle of moments. According to the principle of moments, the sum of the clockwise moments is equal to the sum of the anticlockwise moments about any point in equilibrium.
In this case, the point of equilibrium will be the pivot. Let's assume that Socola is located at a distance of x meters from the pivot.
Now, let's calculate the moments of each person about the pivot:
Moment of Socola = Mass of Socola × Distance from pivot = 7.7 kg × x
Moment of Brooke = Mass of Brooke × Distance from pivot = 53 kg × 1.0 m
Since the system is in equilibrium, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments:
7.7 kg × x = 53 kg × 1.0 m
Now, we can solve for x:
x = (53 kg × 1.0 m) / 7.7 kg
x ≈ 6.88 m
Therefore, Socola is located approximately 6.88 meters from the pivot.