Speed of Objects Rolling and Sliding Down a Hill

In summary, the problem involves a solid marble and a block of ice with the same mass starting from rest at the same height and moving down a hill. The marble rolls without slipping while the ice slides without friction. Using the equation 1/m v^2 = mgh, the speed of the ice can be found to be the square root of 2gh. For the marble, the equation 1/2 mv^2 = mgh + 1/2 I ω^2 is used, and after solving for v, the correct answer is the square root of 10gh/7. The student initially made a mistake by including an "m" in the equation for the marble and using the incorrect fraction of 2
  • #1
valeriex0x
43
0

Homework Statement



A solid uniform marble and a block of ice, each with the same mass, start from rest at the same height H above the bottom of a hill and move down it. The marble rolls without slipping, but the ice slides without friction.

Find the speed of each of these objects when it reaches the bottom of the hill.
Vice:?
Vmarble:?

Homework Equations



1/m v^2 = mgh

The Attempt at a Solution



Ice:
1/2 mv^2=mgh

v= squareroot 2gh

Marble:
mgh=1/2 mv^2 + 1/2 I ω^2

=1/2 mv^2 +1/2(2/5 mr^2) (v/r)^2

The answers i entered in were marked incorrect by masteringphysics.

Please advise! : (
 
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  • #2
Hi valerie! x0x :smile:

Your v for the block of ice is correct.
And your equation for the marble is correct too.

The only thing missing is that you didn't give v of the marble.
Did you solve your equation for v?
 
  • #3
well i got stuck... and i don't know why its marking me wrong. for the marble i got v: squareroot 2/4 mgh


anythoughts?
 
  • #4
valeriex0x said:
well i got stuck... and i don't know why its marking me wrong. for the marble i got v: squareroot 2/4 mghanythoughts?

I'm afraid that in that case you did not solve your own equation correctly.

For starters, there should not be an "m" in there.
There isn't an "m" for the block of ice either!

But your fraction of 2/4 is wrong too.

How did you arrive at your solution for v?
Can you show some (major) steps?
 
  • #5
oh never mind ... this stupid mastering physics wanted a capital H instead of h.

aughhhhhh! the marble was squareroot 10 gh/7
 
  • #6
thanks for your help! i caught that at the last min!
 
  • #7
Congrats with your right answer! :smile:
 

FAQ: Speed of Objects Rolling and Sliding Down a Hill

What is rotational motion?

Rotational motion is the movement of an object around an axis or center point. This type of motion is commonly seen in objects such as wheels, planets, and marbles.

What factors affect the rotational motion of a marble?

The factors that affect the rotational motion of a marble include its mass, shape, surface texture, and the force applied to it.

How does rotational motion differ from linear motion?

Rotational motion involves movement around a fixed point or axis, while linear motion involves movement in a straight line. Additionally, rotational motion is described by concepts such as angular velocity and torque, while linear motion is described by concepts such as velocity and acceleration.

What is the relationship between rotational motion and energy?

In rotational motion, kinetic energy is transferred through rotation, as opposed to linear motion where kinetic energy is transferred through translation. The amount of energy in rotational motion depends on the speed of rotation and the moment of inertia of the object.

How is rotational motion used in everyday life?

Rotational motion is used in many everyday objects, such as wheels on cars and bicycles, ceiling fans, and rotating doors. It is also used in sports, such as throwing a ball or swinging a tennis racket.

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