When a slice of buttered toast is accidentally pushed over the edge of a counter, it rotates as it falls. If the distance to the
floor is 52 cm and for rotation less than 1 rev, what are the (a) smallest and (b) largest angular speeds that cause the toast to hit and then topple to be butter-side down
1 answer:
Answer: 4.83rad/s and 14.50 rad/s
Explanation:
The distance from the center to the floor d = 52cm = 0.52m
Rotation is less than 1 rev
The toast rotates at a constant angular speed
Using kinematic d = Vit + 1/2gt^2
d = 0+1/2gt^2
t = (2d/g) square root
t = square root of 2× 0.52/ 9.8
t = 0.325s
The toast is accidentally pushed over the edge of the centre with butter side up, then the toast rotates as it falls . If the toast hits the ground and topples, the smallest angle will be less than 1/4 rev with correspondence to the smallest angular speed
Wmin = change in tetha/ change in time
= 0.25 rev/ change in t
= 0.25×2pii / change in t
= 0.5pii/0.325
= 0.5×3.142/0.325
= 4.83 rad/s
The toast is accidentally pushed over the edge of the centre with butter side up, then the toast rotates as it falls . If the toast hits the ground and topples, the maximum angle will be less than 3/4 rev with correspondence to the maximum angular speed
Wmax = change in tetha/ change in time
= 0.75 rev/ Change in time
= 0.75 ×2pii/change in tetha
= 1.5pii/0.325
= 1.5 ×3.142/0.325
= 14.50 rad/s
Note the following
Vi is the initial speed of the toast which is zero because it was initially at rest
t is the time taken for the toast to hit the floor
g is the gravitational acceleration
d is the distance between the counter and the floor. There is an attachment for you as well.
Thanks
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