1) 2) 3) 4) 5) 6) A gymnast with mass m1 = 45 kg is on a balance beam that sits

Question

1)

2)

3)

4)

5)

6)

A gymnast with mass m1 = 45 kg is on a balance beam that sits on (but is not attached to) two supports. The beam has a mass m2 = 113 kg and length L = 5 m. Each support is 1/3 of the way from each end. Initially the gymnast stands at the left end of the beam. What is the force the left support exerts on the beam? What is the force the right support exerts on the beam? How much extra mass could the gymnast hold before the beam begins to tip? Your submissions: Now the gymnast (not holding any additional mass) walks directly above the right support. What is the force the left support exerts on the beam? What is the force the right support exerts on the beam? At what location does the gymnast need to stand to maximize the force on the right support? at the center of the beam at the right support at the right edge of the beam

Explanation / Answer

forces upward = forces downward

(S1) + (S2) = (m1)(g) + (m2)(g)

(S1) + (S2) = (45 kg)(9.81 m/s) + (113 kg)(9.81 m/s)

(S1) + (S2) = 1550 N [1]

torques balance (using the right end as a reference):

(S1)(2/3)(L) + (S2)(1/3)(L) = (m1)(g)(L) + (m2)(g)(1/2)(L)

(S1)(2) + (S2) = 3[(m1)+ (m2)/2](g)

(S1)(2) + (S2) = 3[(45 kg)+ (113 kg)/2](9.81 m/s)

(S1)(2) + (S2) = 2987.145 N [2]

1)

[2] - [1]:

(S1) = 2987.145 - 1550 N

(S1) = 1437.145 N

2)

1437.145 N + (S2) = 1550 N

(S2) = 112.855 N

3)

Using the left support as the pivot,

(M)(g)(1/3)(L) = (m2)(g)(L/2 - L/3)

M = (m2)/2

M = (113 kg)/2

M = 56.5 kg

56.5 - 45 kg = 11.5 kg

beam weight = m2*9.81

(113 x 9.81) = beam weight of 1108.53 N.

With the gymnast right over the right support, only 1/2 the beam weight remains on the left support.

4) (1108.53/2) = 554.265 N.

5) The right is now supporting that plus (45 x 9.81) = 441.45 N.

6)

At what location does the gymnast need to stand to maximize the force on the right support?

ANSWER- at the right edge of the beam

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.