Question

Did anyone get this? I've tired everyway I could think of and I still keep getting it wrong!!

HRW5 12-8E A solid sphere of weight 2.84 kg rolls up an incline with an inclination angle of 42.5°. At the bottom of the incline the center of mass of the sphere has a translational speed of 5.09 m/s.
(a) What is the kinetic energy of the sphere at the bottom of the incline?
J
(b) How far does the sphere travel along the incline before coming to rest?
m

Answer 1

radius of sphere given?

Answer 2

K = mv^2 = 2.84*5.09^2
The sphere will continue moving if there are no forces that stoped it.

Answer 3

there are plenty of other forces coming into play. it is only because of FRICTIONAL FORCE opposing motion that the ROLLING MOTION of sphere is possible
without radius this sum cant be done

Answer 4

Im still confused as what to do. Are teacher doesn't explain things well to us. So I very confused on this problem. Let me try the formula. Thank you so very much!!

Answer 5

At the bottom of the incline the sphere has two types of mechanical energy:
- translational kinetic energy, the good old \( \frac{1}{2}mv^2 \)
- and also rotational kinetic energy, \( \frac{1}{2}I\omega^2 \) where \( I \) is the moment of inertia of the sphere and \( \omega \) is the angular velocity

Now Salini is right. To calculate \( I \) and \( \omega \) we need the radius. For example, \( I = \frac{2}{5}mr^2 \) and therefore depends critically on the radius \( r \) of the sphere and it not sufficient to have only the mass \( m \).

Answer 6

But that is the problem. No radius is given.

Answer 7

In which case, the problem wants you to ignore rotational kinetic energy.

Answer 8

Let me post the practice problem with anwsers. It might help you. I didn't do much for me

Answer 9

oh......

Answer 10

HRW5 12-8E A solid sphere of weight 3.30 kg rolls up an incline with an inclination angle of 19.5°. At the bottom of the incline the center of mass of the sphere has a translational speed of 3.03 m/s.
(a) What is the kinetic energy of the sphere at the bottom of the incline?

21.2
J
(b) How far does the sphere travel along the incline before coming to rest?

1.96
m

Answer 11

Hence do this: calculate the kinetic energy at the bottom. At the top where the sphere stops, all of that energy is gravitational potential energy. Set the expressions for these two equal and solve for the distance.

Answer 12

gottcha!!!!

Answer 13

then what produces torque which cause the rolling of the sphere?
it is only the component of friction that creates a torque right?

Answer 14

Yes, and of course I agree that in a complete analysis of this situation we need to include rotational motion. In its absence, it seems that this question is at a very elementary level of kinematics and is just considering translational motion.