A 0.55-kg ball, attached to the end of a horizontal cord, is revolved in a circle of radius 1.3 m on a frictionless horizontal s
1 answer:
The tension of the cord is the centripetal force that keeps the ball in circular motion:
where T is the tension of the cord,
is the centripetal force, 
is the mass of the ball, v its speed and 
is the radius of the circle.
The maximum allowed tension is T=75 N, before the cord breaks. Using this value inside the formula, we can find which is the maximum allowed value fot the speed v:
where T is the tension of the cord,
The maximum allowed tension is T=75 N, before the cord breaks. Using this value inside the formula, we can find which is the maximum allowed value fot the speed v:
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Keeping in mind that:
- Distance is the length of the total path covered by the person, regardless of the directions of the different parts of motion
- Displacement is just the distance in a straight line between the final point and the initial point
Let's apply these concepts to solve the different parts of the problem:
1. 120 m, 80 m west
The total distance is the sum of the length of the different paths:
distance = 100 + 20 = 120 m
To find the displacement, we need to find the distance between the starting point and the ending point. Assuming the starting point as
x = 0
Michelle moved 100 m westward and 20 m eastward, so the ending point is at
ending point = 100 - 20 = 80 m (westward)
So, the displacement is
displacement = 80 - 0 = 80 m (west)
2. 6400 m, 0
The distance is equal to the length of the track multiplied by the number of laps, so:
The track is circular, and the runner completes exactly 4 laps: it means that at the end of the motion, the runner is at her starting point. So ending point and starting point coincide, and so the displacement
displacement = ending point - starting point = 0
3. 40 m; 10 m forward
The total distance is just the sum of the lengths of the different parts of the motion, so:
distance = 20 + 5 + 10 + 5 = 40 m
The find the displacement, we need to assign signs to every direction:
Forward --> positive along the forward-backward direction
Backard --> negative along the forward-backward direction
Right --> positive direction along the right-left direction
Left --> negative direction along the right-left direction
Along the forward-backward direction, the displacement is:
20 m forward and 10 m backward, so 20 - 10 = 10 (forward)
Along the left right direction, the displacement is:
5 m right and 5 m left, so 5 - 5 = 0
So the net displacement is 10 m (forward)
4. 16 km; 4 km south
Again, t total distance is the sum of the lengths of the different parts of the motion, so:
distance = 2 + 4 + 6 + 4 = 16 km
To find the displacement, we assign signs to every direction:
North --> positive along the north-south direction
south --> negative along the north-south direction
east --> positive direction along the east-west direction
west --> negative direction along the east-west direction
Along the north-south direction, the displacement is:
2 km north and 6 km south, so 2 - 6 = -4 km (4 km south)
Along the east-west direction, the displacement is:
4 km east and 4 km west, so 4 - 4 = 0
So the net displacement is 4 km south
5. 37.7 m; 24 m
The distance covered by the skater is the length of half circumference, so given the radius
r = 12 m
The distance is
The displacement is the distance in a straight line between the ending position and the starting position. Since the skater ends her motion halfway around the circle, the distance between the initial and final point is equal to the diameter of the circle (two times the radius). So,
Answer:
First product is FCH-OH chemically known as 2-[2-furyl(hydroxyl)methyl]-Second product is FCH i.e (2E)-2-[2-furyl-methylene]-cyclohexanone
Explanation:
Please see the attached image for complete chemical reaction of aldol condensation of cyclohexanone
Aldol Condensation is a form of electrophilic substitution reaction in which the alpha carbon in enols or enolate anions is substituted by an electrophile to form carbon-carbon bond. Cyclohexanone also known as the first ketone consists of two alpha-carbons and four potential substitutions i.e alpha-hydrogens but none of the hydrogen on the ring is substituted. Ketones such as cyclohexanone are much more acidic than their parent hydrocarbon.
First product is FCH-OH chemically known as 2-[2-furyl(hydroxyl)methyl]-cyclohexanone that further undergoes dehydration resulting into FCH i.e (2E)-2-[2-furyl-methylene]-cyclohexanone
Based on the explanations above, the compound formed is shown in the image.
