Need help with physics concept questions

Question

Thanks in advance for answering.

1. must there be necessarily be matter at the center of mass of an object? give an example

2. There must be equal amounts of matter on either side of the center of mass? true or false?

3.if the forces on an object balance, do the torques necessarily balance? b. if the torques on an object balance, do the forces necessarily balance?

4. In picking an axis about which to compute torques in rotational equilibrium, it is nearly always best to choose an axis through the center of mass of the object. True or false

5. why is it easier to hold a 10kg body in your hand at your side than to hold it with your arm extended horizontally?

6. Can a ladder remain stable if the floor were frictionless instead of the wall? why?

Answer 1

No, an empty bucket.

True.

No, no.

True.

Because holding the mass out you need to contract your muscles which prevents the flow of blood to them, and so they eventually tire out due to lactic acid build up. Holding the mass at your side is easier since the mass is held mainly by the tendons and bones in your arm, rather than your muscles.

No, because the floor exerts a horizontal force on the ladder which prevents it from slipping. Without that, the ladder would immediately fall down. This is why sometimes it is necessary to have someone hold the bottom of the ladder.

Answer 2

1.put a ring into a vacuum and then you don't have matter in the center i guess. that fits in the category of what u asked

2. more like equal amounts in every direction

3. depends on the length factor if you are thinking the seesaw picture with 2 kids each at one end (those fattys!) , force is a factor of torque and the forces can alter.

4.skip

5.it is harder to hold at horizontal because it really is harder! NOTHING TO DO WITH HUMAN BODY just physics. remember torque? well you know the equaton right? its the distance x force x sin(angle)

lets say the angle was 90degrees so sin 90 is 1 so lets take that out of question. so distance for arms down is small because your weights are not that much away from body. but if your arms are extended from your shoulders then the force seems more because then you have a bigger distance to multiply to the force. ALOT MORE

6. no cuzz theres no friction to keep the ladder in a certain spot. :P unless there was a giant amount of friction on the wall for example a nail wall which somehow stabbed ur wooden ladder and held it in place to the wall :D  

Answer 3

centre is british, center is american, centre is something i'm used to.

Like the person above said, no it's not necessary, for example a ring has it's centre of mass at the centre of the ring( ie the inner hollow).

This i believe to be false, as the centre of mass for a body is closer to the heavier masses for a system of masses. take a simple coordinate system. mass 1 5kg at x=1 and mass 2 15kg at x=10. if you work out the centre of mass it comes to 7.75 from origin. the masses on either side are different. BUT, the moment of the masses about the centre of gravity is 0. if you think of the formula used to calculate centre of mass it makes sense. For our body the femur is one heavy bone.

to the first No, to the second Yes.

but it needs a further explanantion. Torques unlike forces are dependent on the point of application as well as direction of rotation. imagine a metal plate held longitudinally with a pivot passing vertically through so that the pivot acts like a line of symmetry. now if we have 5Nm acting anticlockwise(ccw) on side A. to balance it we apply 5Nm acting clockwise(cw). Numerically this is zero. and if we apply 5Nm cw at A then the plate will not turn.( this covers question b). now if we apply 5Nm cw on the symmetrically opposite side to A, at B. then the forces are balanced but we now have a couple. and the plate turns( question a). For example opening or closing a tap. you can physically imagine this.

my moment of inertia is a little poor, but i think yes

when the weight is near your body you support only it's weight. mg downwards. as you move your arm out horizontally your creating a moment arm. which creates a moment of 10kgf x distance from shoulder( not exactly, it's to the line passing through our cg). so you have to support the weight as well as counter the moment or torque.

the ladder question is a good one. No it's not possible as if you draw a free body diagram of a ladder, you will realise that the mg components of the ladder is balanced by the frictional force between the floor and ladder. without this force placing the ladder will be impossible.

i hope i managed to answer the questions