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A ball, released from rest, takes 4.00s to roll down a straight, 12.0m long, ramp(inclined plane). What is the speed of the ball halfway down the ramp?

Question

A ball, released from rest, takes 4.00s to roll down a straight, 12.0m long, ramp(inclined plane). What is the speed of the ball halfway down the ramp?

check_circleAnswer
Step 1

Given,

Initial velocity u 0
Distance s AB 12.0 m
and, 6.0 m
2
Time taken to travel B to A-
t 4.00 s
sin
D
C
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Initial velocity u 0 Distance s AB 12.0 m and, 6.0 m 2 Time taken to travel B to A- t 4.00 s sin D C

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Step 2

Let the ball of mass m and the inclination angle is θ. Now, by the conservation of energy and take D as a reference point.

Initial Potential Energy
Initial Kinetic Energy
Final Potential Energy Final Kinetic Energy
mgl sine+0 0-mv
1
mglsine
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Initial Potential Energy Initial Kinetic Energy Final Potential Energy Final Kinetic Energy mgl sine+0 0-mv 1 mglsine

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Step 3

Initial Kinetic Energy is zero because initially ball was in the rest and f...

1
- mv
mgl sin 0
2
gl sin
2
6gsin 0v
2
V12g sin 0
v V117.6 sin 0 m/s
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1 - mv mgl sin 0 2 gl sin 2 6gsin 0v 2 V12g sin 0 v V117.6 sin 0 m/s

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