Question

Consider a rigid steel beam of length L = 13 m and mass mb = 388 kg resting on two supports, one at each end. A worker of mass mw = 74 kg sits on the beam at a distance x from support A. Refer to the figure.

When the worker sits at a distance x = 7.5 m from support A, calculate the force, in newtons, that support B must exert on the beam in order for it to remain at rest. Use g with three significant figures.

Answer 1

Answer:

2321 N

Explanation:

Let g = 9.807 m/s2

Assume this is a uniform beam and the center of mass it at the geometric center, which is half way between the 2 ends, or h = 13/2 = 6.5 m from the left end (support A).

For the system to remain at rest, then the total moments around a point (let pick support A) must be 0. Moments created by each force is the product of the force magnitude and the moment arm, aka distance from the force to support A

$\sum M_A = 0$

$M_w + M_b + M_B = 0$

$F_wx + F_bh + F_BL = 0$

$m_wgx + m_bgh = -F_BL$

If we take upward direction be the positive direction, that means all the gravity acting downward are negative

$74*(-9.807)*7.5 + 388(-9.807)*6.5 = -F_B13$

$-13F_B = -30176.139$

$F_B = -30176.139/-13 = 2321 N$

So the force at support B has a magnitude of 2321 N acting upward

Answer 2

The force, in newtons, that support B must exert on the beam in order for it to remain at rest is 2321 N.

Calculation of the force:

here we assume g = 9.807 m/s^2

Also,

length L = 13 m and mass mb = 388 kg resting on two supports, one at each end. A worker of mass mw = 74 kg sits on the beam at a distance x from support A

Now

74*(-9.807) * 7.5 + 388 (-9.807) * 6.5 = -Fb13

-13Fb = -30176.139

fb = 2321 N

Learn more about force here: https://brainly.com/question/3398162