A gymnast with mass m 1 = 48 kg is on a balance beam that sits on (but is not at

Question

A gymnast with mass m1 = 48 kg is on a balance beam that sits on (but is not attached to) two supports. The beam has a mass m2 = 116 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.

1)

What is the force the left support exerts on the beam?

N

2)

What is the force the right support exerts on the beam?

N

3)

How much extra mass could the gymnast hold before the beam begins to tip?

kg

4)

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?

N

5)

What is the force the right support exerts on the beam?

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? N 5) What is the force the right support exerts on the beam? A gymnast with mass m1 = 48 kg is on a balance beam that sits on (but is not attached to) two supports. The beam has a mass m2 = 116 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. 1) What is the force the left support exerts on the beam? N 2) What is the force the right support exerts on the beam? N 3) How much extra mass could the gymnast hold before the beam begins to tip? kg 4)

Explanation / Answer

From Free body diagram

N1 + N2 = (m1 + m2 ) g = 164g

Taking moment about centre of mass;

m1gL/2 -N1(L/6) + N2 (L/6) = 0;

N1 - N2 = 144 g

N1 = 154 g; N2 = 10g

If the beam tips; then N2 = 0;

Then N1(L/6) = (48 + X)g L/2

N1 = 144 g+ 3gX

N1 = 164g +Xg

X = 10 kg

If the gymnast walks from left extreme to right extreme;

N1 will become 10 g and N2 will become 154 g

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