A vaulter holds a 34.1 N pole in equilibrium by exerting an upward force U with her leading hand and a downward force D with her trailing hand. Point C is the center of gravity of the pole. Given d1 = 1.100 m, d2 = 1.65 m, and d3 = 2.75 m, what are the magnitudes of U and D?
i am not sure of what formula to use for mag, pls help!!
A figure or better description is needed to explain the orientation of the pole and the meaning of d1, d2, and d3.
It sounds like you are describing the situation in which the vaulter is running towards the bar while holding the pole horizontal. The trailing hand holds the bar near one end, pushing down, while the leading hand, about 2 meters ahead, pushes up.
What you need to do is write a moment equilibrium equation (total moment = 0) , with the weight of the pole acting at the center of gravity. Take moments about the location of one hand and you can solve directly for the force on the other hand.
2.75 m sounds short for a pole vaulter's pole, except perhaps for beginners. 3.5 meters is more typical
http://www.everythingtrackandfield.com/mfpbCat1PlusLanding.aspx_Q_CategoryID_E_194
sum of M_A=0
U(d_1)-F_y(d_1+d_2)=0
F_y=34.1 N
solve for U and plug in numbers.
sum of F_y=0
-D+U-F_y=0
solve for D, plug in numbers
To find the magnitudes of U and D, we can use the principle of moments. The principle of moments states that the sum of the clockwise moments about any point is equal to the sum of the counterclockwise moments about the same point.
In this case, we can choose point C as the point about which we calculate the moments. Since the pole is in equilibrium, the sum of the clockwise moments must equal the sum of the counterclockwise moments.
Let's assume the upward force U is positive and the downward force D is negative. The moments caused by U and D can be calculated by multiplying the force magnitude by the distance from the point C.
Clockwise moments:
Moment of U = magnitude of U × d1
Counterclockwise moments:
Moment of D = magnitude of D × d3
Given that the pole is in equilibrium, the two moments will be equal:
Moment of U = Moment of D
Therefore, we can set up the equation:
magnitude of U × d1 = magnitude of D × d3
Solving this equation will give us the magnitudes of U and D.
To make it easier to solve, we can rearrange the equation:
magnitude of U = magnitude of D × d3 / d1
Now we can substitute the given values into the equation:
magnitude of U = 34.1 N × 2.75 m / 1.1 m
After performing the calculation, we find that the magnitude of U is approximately 85.25 N.
To find the magnitude of D, we can substitute the value of U into the rearranged equation:
magnitude of D = magnitude of U × d1 / d3
magnitude of D = 85.25 N × 1.1 m / 2.75 m
After performing the calculation, we find that the magnitude of D is approximately 34.1 N.
Therefore, the magnitudes of U and D are approximately 85.25 N and 34.1 N, respectively.