2. Inside a delivery facility. a package (m kg) launched initial speed of 7.50 m

Question

2. Inside a delivery facility. a package (m kg) launched initial speed of 7.50 m/s at the bottom of a metal ramp (a 50'). The coefficient of fiction with an ramp is 0.200 a. (4 (Do NOT kinetic between the package an b. pts.) conservation of energy to solve any part of this problem your wor (2 pts.) How the magnitude and direction of the Show c. pts. much time does it for the package to come to rest? Show your work. sliding back down)? What maximum vertical height does the package (and possibly Show your work. reach before coming to rest d. (2 pts.) What is the minimum coefficient of static friction that would cause the package it reaches its greatest height? Show your work. to remain at rest when

Explanation / Answer

(a)

Fnet = -m*g*sintheta - fk

Fnet = -m*g*sintheta - uk*m*g*costheta

from newtons second law Fnet = m*a

ma = -m*g*sintheta - uk*m*g*costheta

a = -g*(sintheta + uk*costheta)

a = -9.8*(sin15 + (0.2*cos15))

a = -4.43 m/s^2

magnitde = 4.43 m/s^2

direction = down the ramp

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(b)

up the ramp

initial velocity vi = 7.5 m/s

acceleration a = -4.43 m/s^2

time = t = ?

final velocity vf = 0

vf = vi + a*t

0 = 7.5 -4.43*t

t = 1.69 s <<<----answer

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(c)

along the plane

d = vi*t + (1/2)*a*t^2

d = (7.5*1.69)-(0.5*4.43*1.69^2)

d = 6.35 m

sin15 = y/d

y = d*sin15

y = 6.35*sin15 = 1.643 m <<<<--------answer

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(d)

us = tan15 = 0.267 <<<-----answer

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