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A Level Further Mechanics Centre of Mass Q

hiya, i'm having a lot of trouble with this question. i managed to find the CoM in part i but i can't seem to work out how to find out whether it topples. i know i need to take moments of sorts but i'm confused as to how to draw my diagram (aka what forces i need to put). any help asap would be very much appreciated!






here is the question:


CoM Q.PNG




A mobile tower consists of the main vertical section (mass M tonnes), housing the engine, winding gear and controls, and the boom. The centre of mass of the main section is on the centre line. The boom, which has negligible mass, supports the load (L tonnes) and the counterweight (C tonnes). The main section stands on supports at P and Q, distance 2d apart. The counterweight is held at a fixed distance a m from the centre line of the main section and the load at a variable distance l (lower case L) m.

1) In the case when C = 3, M = 10, L = 7, a = 8, d = 2, l = 13, find the horizontal position of the centre of mass and say what happens.

2) Show that for these values of C, M, a, d and l the crane will not fall over when it has no load and find the maximum safe load that it can carry.

3) Formulate two inequalities in terms of C, M, L, a, d and l that must hold if the crane is to be safe loaded or unloaded.

4) Find in terms of M, a, d, l, the maximum load that the crane can carry.
(edited 2 months ago)
Reply 1
Original post by aditi_idk
hiya, i'm having a lot of trouble with this question. i managed to find the CoM in part i but i can't seem to work out how to find out whether it topples. i know i need to take moments of sorts but i'm confused as to how to draw my diagram (aka what forces i need to put). any help asap would be very much appreciated!






here is the question:


CoM Q.PNG




A mobile tower consists of the main vertical section (mass M tonnes), housing the engine, winding gear and controls, and the boom. The centre of mass of the main section is on the centre line. The boom, which has negligible mass, supports the load (L tonnes) and the counterweight (C tonnes). The main section stands on supports at P and Q, distance 2d apart. The counterweight is held at a fixed distance a m from the centre line of the main section and the load at a variable distance l (lower case L) m.

1) In the case when C = 3, M = 10, L = 7, a = 8, d = 2, l = 13, find the horizontal position of the centre of mass and say what happens.

2) Show that for these values of C, M, a, d and l the crane will not fall over when it has no load and find the maximum safe load that it can carry.

3) Formulate two inequalities in terms of C, M, L, a, d and l that must hold if the crane is to be safe loaded or unloaded.

4) Find in terms of M, a, d, l, the maximum load that the crane can carry.
Assuming youve worked out the COM in part 1 correctly, then youve just got to state whehter it lies in the footprint (base) of the tower or not as that will determine whether its stable or whether it topples.

The COM calculation involves force*distance calculations so youve already taken moments to determine its position.
(edited 2 months ago)
Reply 2
Original post by mqb2766
Assuming youve worked out the COM in part 1 correctly, then youve just got to state whehter it lies in the footprint (base) of the tower or not as that will determine whether its stable or whether it topples.

The COM calculation involves force*distance calculations so youve already taken moments to determine its position.
ahh thanks. i think i just didn't clock that the CoM lying in the base was the indication of whether the object would topple or not.

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