Part 1: If a ball rolls down a ramp, 43cm in length raised 2.5cm off the table,
ID: 1682682 • Letter: P
Question
Part 1: If a ball rolls down a ramp, 43cm in length raised 2.5cm off the table, what is the final velocity of the ball when it rolls off the ramp onto the table?Part 2: If it were to then roll 5cm and fall off the table (94cm high) how far from the table would the ball land?
Explanation / Answer
a)using conservation of mechanical energy: potential energy depends on the vertical height and is independent of path followed in absence of friction. So assuming the ramp to be frictionless: mgh=0.5 mv2…………..(h=2.5 cm=0.025 m) =>v=(2gh)=(2x9.81x0.025)=0.7 m/s b) Assuming the table top to be frictionless the ball will continue to roll at the same velocity. When it will of the table top it will have a horizontal velocity of 0.7 m/s and no vertical velocity and behave as a projectile. Time taken to reach the ground can be found from: H=0.5gt2 H=94 cm=0.94 m,g=9.81m/s2 So t=0.4378 s Horizontal distance travelled during this period=0.7x0.4378=0.3064m=30.64 cm So the ball lands 30.64 cm from the table.