#4 Please answer the question neatly with steps and show all units, for good rat

Question

#4 Please answer the question neatly with steps and show all units, for good rating!

L fa An old trick is to go over your head in a vertical circle with a bucket of water without getting wet. If the radius of the circle is 1.2m, bow fast would the bucket of water have to be moving at the top the circle to be successful e, to keep the water in the bucket)? lf complete a fall vertical circle with the same radius and same speed asin part what the the bottom of the water be at the would from of has 3,5kg? (s) What would the required normal be at an angle of 40p as measured from the bottom of the circle? A 3.0kg box starts from rest and slides 10m down a 37 inclined (ramp) e with the coefficient ofkinetic friction-w 0.50. Determine the work done by each of the following forces acting on the box the force of the nonmal force, and the force of gravity. What friction, moving at the end of is the total or net work done by all forces on the box. fs) How finst is the box the 10m slide? Do by work energy methods) Continued on next page.

Explanation / Answer

force of gravity = mg * sin(theta)

work done = force * distance

work done by gravity = mg * sin(theta) * distance

work done by gravity = 3 * 9.8 * sin(37) * 10

work done by gravity = 176.93 J

normal force = mg * cos(theta)

work done by normal force = mg * cos(theta) * distance

work done by normal force = 3 * 9.8 * cos(37) * 10

work done by normal force = 234.798 J

friction force = k * normal force

work done by friction force = k * normal force * distance

work done by friction force = 0.5 * 234.798

work done by friction force = 117.399 J

total work done = total force * distance

total work done = (mg * sin(theta) - k * mg * cos(theta)) * distance

total work done = 176.93 - 117.399

total work done = 59.531 J

by conservation of energy

initial energy = final energy

mgh = total work done + 0.5 * mv^2

3 * 9.8 * 10 * sin(37) = 59.531 + 0.5 * 3 * v^2

v = 8.85 m/s

speed at bottom = 8.85 m/s

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