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Jupyter notebook E.ipynb

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Kernel: Anaconda (Python 3)

Physics Chapter 4

Practice E

Overcoming Friction

1. A student pulls on a rope attached to a box of books and moves the box down the hall. The student pulls with a force of 185 N at an angle of 25.0° above the horizontal. The box has a mass of 35.0 kg, and μk between the box and the floor is 0.27. Find the acceleration of the box.

import numpy
import math

Fapplied = 185
O = 25.0

m = 35.0
uK = 0.27
g = 9.81

Fappliedx = Fapplied*math.cos(O)
Fappliedy = Fapplied*math.sin(O)
Fg = m*g
Fn = (0 - Fappliedy) + Fg
Fk = uK*Fn
a = (Fappliedx - Fk)/m

print ("The acceleration is", a)
The acceleration is 2.4016300079245383

2. The student in item 1 moves the box up a ramp inclined at 12° with the horizontal. If the box starts from rest at the bottom of the ramp and is pulled at an angle of 25.0° with respect to the incline and with the same 184 N force, what is the acceleration up the ramp? Assume that μk= 0.27.

import numpy
import math

Fapplied = 185
O = 25.0
m = 35.0
uK = 0.27
g = 9.81

Fappliedx = Fapplied*math.cos(O)
Fappliedy = Fapplied*math.sin(O)
Fg = m*g
Fn = (0 - Fappliedy) + Fg
Fk = uK*Fn
a = (Fk - Fappliedx)/m

print ("The acceleration is", a)
The acceleration is -2.4016300079245383

3. A 75 kg box slides down a 25.0° ramp with an acceleration of 3.60 m/s².

a. Find μk between the box and the ramp

import numpy
import math

m = 75
O = 25.0
a = 3.60
g = 9.81

Fk = (m*g*math.sin(O)) - (m*a)
Fn = (m*g*math.cos(O))
uK = Fk/Fn

print ("The μk is", uK)
The μk is -0.5037558622571474 
b. What acceleration would a 175 kg box have on this ramp?

import numpy
import math

m = 175
O = 25.0
g = 9.81
am = 3.60
mt = 75


Fn = (mt*g*math.cos(O))
Fk = (mt*g*math.sin(O)) - (mt*am)
uK = Fk/Fn
a = ((m*g*math.sin(O)) - (uK*m*g*math.cos(O)))/m

print ("The acceleration is", a)
The acceleration is 3.6

4. A box of books weighing 325 N moves at a constant velocity across the floor when the box is pushed with a force of 425 N exerted downward at an angle of 35.2° below the horizontal. Find μk between the box and the floor.

import numpy
import math

Fg = 325
Fapplied = 425

O = 0 - 35.2

Fappliedy = Fapplied*math.sin(O)
Fappliedx = Fapplied*math.cos(O)
Fk = Fappliedx
Fn = Fg - Fappliedy
uK = Fk/Fn

print ("The μk is", uK)
The μk is -4.836877680430392