2. [1pt] A crane of mass M has a wheelbase, E, and its centre of mass midway bet

Question

2. [1pt] A crane of mass M has a wheelbase, E, 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 6 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. b) when the crane tips over, as a function of m and Answer True or False to each of the statements below, e if the first We will be considering two aspects: a) the force of the rear wheels on the ground, and statement is true and the rest, false, enter TFFFF. You only have 5 tries i·The crane is in static equilibnum t is most convenient to calculate torques about the point where the front wheel touches the ground. ii. If the crane tips due to the mass m, the front wheel would remain in contact with the ground. iii. As shown, the force of the rear wheel on the ground is less than Mg/2. V. For all

Explanation / Answer

crame mass = M

wheel base = l

boom length = L

angle = theta

mass = m

i) it will be convinent to calculate torque balance about the front wheel, hence true

ii) the rear whell will lift up first so true

iii) let normal forces on the rear wheel be R and on the front wheel be N

then from force balance

Mg + mg = R + N

also

tensin in the stirn g= T = mg

so force in boom = F

Fcos(theta) = mg*(l + Lcos(theta))/sqroot((l + Lcos(theta))^2 + (Lsin(theta))^2)

Fsin(theta) = mg + mg*Lsin(theta)/sqroot((l + Lcos(theta))^2 + (Lsin(theta))^2)

from torque balance

we can find out that

R < Mg/2

hence true

iv) true, the crane will trip fir theta < 90 deg if m is large enough

v) the weight of the cane leads to a counter clockwise torque about the front axle

hence false

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