**Two thin beams are joined end-to-end as shown in the figure to make a single object. (The object is seen from the side.) The left beam is 11.3 kg and 1.00 m long and the right one is 41.0 kg and 2.00 m long.**

**How far from the left end of the left beam is the center of gravity of the object?**

**Known Variables:**

**x** = center of gravity

**m** = mass of each beam

**m1=** 11.3 kg

**m2**= 41.0 kg

**d =** distance from the left side to the middle. (center of gravity)

**left beam, d** = (1/2)(1.00 m) = 0.5 m

**right beam, d** = 1.00 m + (1/2)(2.00m) = 2.0 m

**x =** (Σmd) / (Σm)

**x =** [(11.3)(0.5) + (41.0)(2.0)] / (11.3 + 41.0)

**x=**(5.65 + 82)/52.3

**x =** 1.68m

**2) What is the gravitational torque on the object about an axis through its left end?**

**τ = **(m1 + m2)(g)(x)

***note gravity is s downward force, so it is negative**

τ = (11.3 kg + 41.0 kg)(-9.81 m/s²)(1.68 m)

**τ **= -859 N·m

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