In a certain laboratory experiment a steel ball is released from rest near the t
ID: 2145388 • Letter: I
Question
In a certain laboratory experiment a steel ball is released from rest near the top of a 30 incline ramp from vertical height h above the end of the ramp. The ball rolls without slipping through a displacement of 14 m down the ramp to the edge of the table. The ball (moment of inertia I= (2/5) MR2) has a radius 0.06 m and mass of 0.50 kg. Using a clear diagram showing clear calculations
a) Determine the magnitude of the linear velocity of the center mass of the sphere at the bottom of the ramp.
b) If the ball rolls of the inclined ramp from the edge of the table and falls freely through a vertical distance of 0.80m to the lab floor. At what horizontal distance from the edge of the table does the ball first strike the floor?
Explanation / Answer
a) h = 14sin30 = 7 m
using energy conservation
mgh = mv^2 /2 + Iw^2 /2 and w = v/r
mg x 7 = m x v^2 /2 + (2mr^2 /5) x (v/r)^2 /2
v = 9.90 m/s
b) in vertical ,
h = ut + at^2 /2
0.80 = 9.90sin30 x t + 9.8t^2 /2
4.9t^2 + 4.95t - 0.80 = 0
t = 0.142 sec
d = 9.90cos30 x t = 1.22 m