Two people are carrying a uniform 788.0 N log through the forest. Bubba is 2.0 m from one end of the log (x), and his partner is 1.1 m from the other end (y). The log is 6.2 m long (z). What weight is Bubba supporting?
508.4 N
[2(2.0m)/6.2m]x788.0N
To determine the weight that Bubba is supporting, we need to calculate the distribution of the weight along the log.
We can use the concept of torque, which is the measure of a force's tendency to rotate an object about an axis. Torque depends on two factors: the magnitude of the force and the distance from the axis of rotation.
In this case, the axis of rotation is the center of the log since the log is assumed to be balanced. The weight of the log is acting downward, so the torque created by the weight is counteracted by the torques created by Bubba and his partner.
The formula for torque is:
Torque = Force x Distance
Let's assign some variables to the given values:
- Force of the log's weight (W) = 788.0 N
- Distance of Bubba from the end of the log (x) = 2.0 m
- Distance of Bubba's partner from the other end of the log (y) = 1.1 m
- Length of the log (z) = 6.2 m
First, we need to determine the total torque created by the log's weight, which is the same regardless of the position of Bubba and his partner:
Total Torque = W x (z / 2)
Since the log is uniform, the center of the log is at the midpoint, z/2.
Total Torque = 788.0 N x (6.2 m / 2) = 2442.8 N.m
Next, we calculate the torques created by Bubba and his partner:
Torque created by Bubba = x x Fb
Torque created by his partner = y x Fp
Since the log is in equilibrium, the total torques created by Bubba and his partner should equal the total torque created by the log's weight:
x x Fb + y x Fp = Total Torque
Since the force is the same for both Bubba and his partner (Fb = Fp), we can rewrite the equation as:
x x Fb + y x Fb = Total Torque
Now, we can solve for the force that Bubba is supporting (Fb):
(Fb x x) + (Fb x y) = Total Torque
Fb(x + y) = Total Torque
Fb = Total Torque / (x + y)
Substituting the values:
Fb = 2442.8 N.m / (2.0 m + 1.1 m)
Fb ≈ 732.86 N
Therefore, Bubba is supporting approximately 732.86 N of the log's weight.
To determine the weight that Bubba is supporting, we need to divide the total weight of the log by the ratio of their distances from the center of the log.
First, let's calculate the ratio of their distances from the center of the log:
Ratio = x / z = 2.0 m / 6.2 m = 0.3226 (rounded to four decimal places)
Next, we divide the total weight of the log by the ratio to find the weight Bubba is supporting:
Weight supported by Bubba = Total weight of the log / Ratio
Weight supported by Bubba = 788.0 N / 0.3226 = 2440.71 N
Therefore, Bubba is supporting approximately 2440.71 N of weight.