Effect of Friction on Ball Rolling Down a Ramp

​
time (sec)
0
height {m}
5
friction?
at height = 5 m
velocity = 0.000 m/sec
final velocity slip = 9.899 m/sec
This Demonstration shows the translational velocity of a ball, projected in 2D, as it moves down a ramp. There are two limiting cases, one with no friction and one with friction, so there is no slippage of the ball. With friction, there is both translational and rotational kinetic energy as the ball rolls down the ramp. When there is no slippage, the ball slides down the ramp with no rotation.

Details

Snapshot 1: the initial position of the ball; the velocity at this time is 0
Snapshot 2: after a time, and at a height, the ball has moved down to its current position
Snapshot 3: after the same time, and at the same height, the ball has moved down to its current position; this position is different from the position of snapshot 2
The final velocity of the sliding object is
2gh
, while the final velocity of the rolling object is
2mgh
2
r
/(m
2
r
+I)
, where
g
is the gravitational acceleration,
h
is the height of the ramp,
m
is the mass of the object,
r
is the radius of the object, and
I
is the moment of inertia of the ball,
(2/5)m
2
r
.
This Demonstration was written in Making Math.

External Links

Disk Sliding or Rolling in a Semicircular Well
Roller Coasters
Shooting a Ball from a Block Sliding Down a Ramp

Permanent Citation

Athena Hung, Caili Chen
​
​"Effect of Friction on Ball Rolling Down a Ramp"​
​http://demonstrations.wolfram.com/EffectOfFrictionOnBallRollingDownARamp/​
​Wolfram Demonstrations Project​
​Published: June 3, 2014