4. [1pt] A crane of mass M has a wheelbase, , and its centre of mass midway betw

Question

4. [1pt]
A crane of mass M has a wheelbase, , and its centre of mass midway between the wheels (the mass of the boom is negligible). The boom has length L and makes an angle with the horizontal. The crane is in contact with the ground only at its front and rear tires. The diagram shows the crane, supporting a mass m in front.

We will be considering two aspects: (a) the force of the rear wheels on the ground, and (b) when the crane tips over, as a function of m and . Answer True or False to each of the statements below; e.g., if the first statement is true and the rest, false, enter TFFFF. You only have 5 tries!

As shown, the force of the rear wheel on the ground is less than Mg/2.

The crane is in static equilibrium. It is most convenient to calculate torques about the point where the front wheel touches the ground.

As shown, the crane would never tip, regardless of the size of m

For all < 90°, the crane will tip if m is large enough.

As shown, the weight of the crane leads to a clockwise torque about the rear axle.

2)If the crane does not tip, which of the equations gives the force of the rear wheels on the ground?

N = g((M+2m)/2(mLcos)/)

N = g(M/2(mLcos)/)

N = g((M+m)/2(mcos)/L)

N = g((M+m)/2(mLcos)/)

N = g(m(1/2(mLcos)/))

N = g((M+2m)/2(mLsin)/)

N = g(M/2(mLsin)/)

N = g((M+m)/2(mLsin)/)

None of these

3)

he angle is adjusted so that the crane could tip. What is the maximum value of m before the crane will tip at that angle?

4)What is the maximum load the crane can lift if =0°? Assume M = 2.70×104 kg, = 5.40 m, and L = 23 m.

A) m = M/(2Lsin2) B) m = ML/(2sin2L) C) m = M/(2Lcos) D) m = ML/(2cos2L) E) m = M/(2Lsin) F) m = M/(2Lcos2) G) m = M/(2Lcos) H) None of these

Explanation / Answer

the force of the rear wheel on the ground is less than Mg/2. False

The crane is in static equilibrium. It is most convenient to calculate torques about the point where the front wheel touches the ground.   True

As shown, the crane would never tip, regardless of the size of m. False

For all < 90°, the crane will tip if m is large enough. True

As shown, the weight of the crane leads to a clockwise torque about the rear axle. True

2) If the crane does not tip, which of the equations gives the force of the rear wheels on the ground?

N = g(M/2(mLcos)/)

3)G) m = M/(2Lcos)

4) m = Ml/2L = 3163.565 kg

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