Question

-A smug little kitten pounces about on the top of a skyscraper. In his excessive confidence, he slips and tumbles over the edge. Don't worry...he manages to cling to a pipe that extends out horizontally from the top of the building and is safe...for now. (Use g=9.80 m/s^2 for the acceleration of gravity for the entire problem.) If kitten has a mass of (m1=2.9 kg) and hangs at rest from the pipe, with what magnitude of force must he cling to the pipe to prevent from falling?

-A child looks out his window and sees the cat hanging from the pipe above, so she decides to act. The child opens the window and flings a lasso at the cat, successfully ensnaring his tail with the rope. If the cat's tail is located (x=1.59 m) from the wall (in the horizontal direction) and (y=3.67 m) from the window (in the vertical direction), what angle does the rope make with the wall? (Give your answer to 3 sig figs. and give the angle in units of degrees [deg]

-Seeing that she has snagged the cat by the tail, she attempts to pull the cat free from the pipe by pulling the rope with a constant force of (F1=26.8 N). What is the magnitude of the upward force that kitten must apply to the pipe to keep from falling? (Give your answer to 3 sig figs.)

-What is the magnitude of the horizontal force that kitten must apply to the pipe to keep from falling? (Give your answer to 3 sig figs.)

-Finally, the rope snaps, disorienting kitten. This causes him to lose his grip, plummeting to the ground below (don't worry...I won't let him die). At this very moment, a group of physics students who have been analzing the situation from directly below, band together to construct a large, pillowy pile of trash bags from a nearby dumpster for the cat to land on. Assuming kitten falls from rest, how fast is he going when he arrives at the cozy trash bag landing pad (h=80.7 m) below? (Give your answer to 3 sig figs.)

Answer 1

F = mg

F = 2.9*9.80

F = 28.42 N (force needed to prevent from falling)

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Here we have a triangle with perpendicular length as 1.59 and base as 3.67

use trigonometry function

tan = 1.59 / 3.67

= arctan (1.59 / 3.67)

= 23.4 degree

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Here, the total force is weight of kitten + the vertical component of force applied on rope

vertical component = 26.8 * sin 66.6 = 24.59 N

how I got 66.6 ?

we found out the angle between rope and wall as 23.4 , the other angle is 90 ( stright pipe), so the angle with rope makes at the other end of pipe where kitten is ( 180 - 90 - 23.4 = 66.6)

so, total force needed = 24.59 + 28.42 = 53 N

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d) horizontal force = 26.8 * cos 66.6 = 10.6 N

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e) using kinematics

v² - u² = 2ah

v² = 2ah

v = sqrt (2ah)

v = sqrt (2*9.8*80.7)

v = 39.8 m/s