How Do You Calculate the Center of Mass and Kinetic Energy in Physics Problems?

[physixnot4me]

HELP PLEASE! :)
(2)Compute the x and y coordinates of the centre of mass of the piece.

=> I'm not sure what steps are to computing coordinates. I have a cartesian plane with a block shaped 'C'... Do i just break it down into geometric shapes (i.e. rectangles/squares) and compute the CM of each one, then what do i do to get the CM of the total block?

(3) A 40 kg box initally at rest is pushed 5.00m along a rough, horizontal floor
with a constant, applied horizontal force of 130 N. If the coefficient of
friction between box and floor is 0.300, find:

(a) the work done by the applied force
(b) increase in internal energy in the box-floor system due to friction

=> I know w=u*Fn*d to find work due to friction, how do i go by finding the INCREASE in internal energy?... kinetic energy = 1/2mv^2?

(c) the work done by normal force

(d) the work done by gravitational force

=> for Wg=mgdcos(theta)... is thetha perpendicular (90 degrees) to horizontal?

(e) the change in kinetic energy of the box

=>change in kinetic energy of box, equals Ek after - Ek before... how can i solve for this if i don't know the final velocity?

(f) the final speed of the box

=> conservation of kinetic energy is used?

 

[whozum]

(2) If its a C block that is uniform, then symmetry will help you find either the x or y coordinate, depending on how the C is standing. You will most likely need to integrate to find the other coordinate. If you find the CM of polygonal shapes, then the CM of the CM's will be the total CM, if that makes sense.

(3) Work done is given by the dot product of force and distance.
(b) Uhm, energy lost to friction dissipates as heat I think.
(c,d) refer to the definition of work, yes its 90 deg
(e) You can find the final velocity using one of the kinematic equations (the one that doesn't involve time)
(f) Similar to (e).

 

[Doc Al]

(2)Compute the x and y coordinates of the centre of mass of the piece.

=> I'm not sure what steps are to computing coordinates. I have a cartesian plane with a block shaped 'C'... Do i just break it down into geometric shapes (i.e. rectangles/squares) and compute the CM of each one, then what do i do to get the CM of the total block?

You have the right idea. Once you have the CM of each piece, you can treat each piece as a point mass located at its CM. To find the CM of the total, use the definition of CM: $(m_1 x_1 + m_2 x_2 + ...)/M_{total}$

(3) A 40 kg box initally at rest is pushed 5.00m along a rough, horizontal floor
with a constant, applied horizontal force of 130 N. If the coefficient of
friction between box and floor is 0.300, find:

(a) the work done by the applied force
(b) increase in internal energy in the box-floor system due to friction

=> I know w=u*Fn*d to find work due to friction, how do i go by finding the INCREASE in internal energy?... kinetic energy = 1/2mv^2?

The work done by friction is the increase in internal energy ("heat").

(c) the work done by normal force
(d) the work done by gravitational force

=> for Wg=mgdcos(theta)... is thetha perpendicular (90 degrees) to horizontal?

Right. So the work done by the gravity is?

(e) the change in kinetic energy of the box

=>change in kinetic energy of box, equals Ek after - Ek before... how can i solve for this if i don't know the final velocity?

You know the work done by the applied force, and the work done by friction, so you can determine the change in KE of the box.

(f) the final speed of the box

=> conservation of kinetic energy is used?

Once you figure out the KE of the box, use the definition of KE to find the speed.