物理讨论专区

vick5821

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help pls..thanks

数学系

不知为什么，看不到你上传的图片。

vick5821

nvm..that one i will upload soon..help me with this..

A solid sphere of radius 15.0 cm and mass 10.0kg rolls down an inclined plane make an angle of 25 degree to the horizontal. If the sphere rolls without slipping from rest to the distance of 75.0 cm and the inclined surface is smooth, calculate
a) the total kinetic energy of the sphere
b) the linear speed of the sphere
c)the angular speed about the centre of mass.
(Given the moment of inertia of solid sphere is Icm = 2/5mR^2 and g = 9,81)

I get the answer as
a) 43.76J
b) 2.5 ms-1
c) 16.67

but the teacher said is wrong wor..can help?? thanks

数学系

回复 383# vick5821


Okay, I just wrote up my solution without calculation. This is your job to complete those calculation.
a) The gain of "total" kinetic energy is equal to the loss of potential energy, that is

Total kinetic energy = mgh, where h = ???

b) Total kinetic energy = 0.5 mv^2 + 0.5I(omega)^2 = 0.5mv^2 + 0.5(0.4mR^2)(v/R)^2, where omega = v/R. Thus, v = ???

c) omega = v/R = ???

数学系

Another thing to remind you: You have to put the unit for your angular speed.

vick5821

but for a, the total kinetic energy isnt that need to add rotational KE and translation KE??

数学系

Recall the principle of conservation of energy, which you had learned since your PMR.

vick5821

but then I understand that..but total KE for the sphere suppose to have translation and rotation??

数学系

回复 388# vick5821


   Yes.

vick5821

but then I understand that..but total KE for the sphere suppose to have translation and rotation??

vick5821

Then suppose should get what I get??? if i use conservation of energy then get diff ans wor

vick5821

but then I understand that..but total KE for the sphere suppose to have translation and rotation??why use conservation of energy..if use conservation energy then the KE found is the combination of both??

数学系

You have to get through it yourself; I have gave my explanation clearly.

vick5821

when the body rools down got linear acceleration and angular acceleration rite??

数学系

“the sphere rolls without slipping from rest”

vick5821

this is my working..you see can I do it like this or not..see whether I understand correct or not
a) K(total) = K(translation) + K ( rotational)
                =1/2mv^2 + 1/2 Iw^2              v calculated ffrom the linear motion equation and get 2.5 ms-1 so w= v/r =16.67

then i sub into the formula and get 43.76 J .Can I do it like this???

数学系

Your v cannot be computed from linear motion equation, I can guarantee that. Your potential energy does not be converted entirely to kinetic energy.

vick5821

you mean in my working the PE is not all converted to KE?and why v cannot be clculated from linear equation?

数学系

Sorry, what I mean "kinetic energy" refer to "translational" kinetic energy.

数学系

If you want to apply linear motion equation, you have to make sure that all the potential energy is converted entirely to "translational" kinetic energy. (I thought you know people would implicitly mean "kinetic energy" as "translational kinetic energy", "total kinetic energy" as "rotational + translational".)