• Interpret and edit the code of a computer model of a block sliding down a ramp
• Use vectors to describe the motion of a block on a ramp and the forces acting upon it
• Apply Newton's 2nd Law to relate the acceleration of a block on a ramp to the forces acting on it

• 2-Dimensional kinematics
• Newton's 2nd Law
• Friction
  • Coefficient of friction $\mu$

• Interpretation of preexisting code
• Changing values of given code
• Creation of new lines of code

Part 1

1. What is the angle of the ramp?
2. What else can you change about the ramp?
3. What is the distance along the ramp that the block will travel?
4. What is the while loop used for?
5. What are the components of the net force vector?
6. What are the components of the acceleration vector for the block? Where does the acceleration of the block show up within the code?

Part 2

1. What happens to the net force as the block slides down the ramp? How do you know?
2. What happens if you increase the angle of the ramp? Why does that happen?
3. What happens to the motion of the block if you increase the mass? How can you be sure?

Part 3

1. Modify the code so that the ramp now has a coefficient of friction equal to 0.3
2. Create and label an arrow to represent the frictional force acting on the block

Link

GlowScript 2.7 VPython
#Call the library for Motion Map
get_library('https://rawgit.com/perlatmsu/physutil/master/js/physutil.js')
 
#Window setup
scene.range = 15
scene.background = vector(1, 1, 0.8)
 
 
#the values below can be adjusted to change the properties of the ramp
ramp_angle = 23 * pi/180
ramp_depth = 6
ramp_width = 30
ramp_position = vec(-15, -10, 0)
 
#the code below draws the ramp (lines 17 - 45)
ramp_color = color.gray(0.3)
edge_thickness = 0.05
edge_color = color.black
 
a = vertex(pos=vec(0, 0, 0)+ramp_position, color=ramp_color, opacity=.5)
b = vertex(pos=vec(0, 0, ramp_depth)+ramp_position, color=ramp_color, opacity=.5)
c = vertex(pos=vec(ramp_width, 0, 0)+ramp_position, color=ramp_color, opacity=.5)
d = vertex(pos=vec(ramp_width, 0, ramp_depth)+ramp_position, color=ramp_color, opacity=.5)
e = vertex(pos=vec(0, ramp_width * tan(ramp_angle), 0)+ramp_position, color=ramp_color, opacity=.5)
f = vertex(pos=vec(0, ramp_width * tan(ramp_angle), ramp_depth)+ramp_position, color=ramp_color, opacity=.5)
 
ramp_base = quad(v0=a, v1=b, v2=d, v3=c)
ramp_surface = quad(v0=e, v1=f, v2=d, v3=c)
ramp_back = quad(v0=e, v1=f, v2=b, v3=a)
ramp_side_near = triangle(vs=[a, c, e])
ramp_side_far = triangle(vs=[b, d, f])
 
def edge(v1, v2, r):
    cylinder(pos = v1.pos, axis = v2.pos-v1.pos, radius = r, color = edge_color)
 
ab = edge(a, b, edge_thickness)
ac = edge(a, c, edge_thickness)
bd = edge(b, d, edge_thickness)
cd = edge(c, d, edge_thickness)
ae = edge(a, e, edge_thickness)
bf = edge(b, f, edge_thickness)
ef = edge(e, f, edge_thickness)
df = edge(d, f, edge_thickness)
ec = edge(e, c, edge_thickness)
 
 
#The values below can be changed to modify the dimensions of the block
block_width = 3
block_height = 3
block_depth = 3
 
#Create the block on the ramp
block = box( pos=vector(0.5*(block_width**2+block_height**2)**0.5 * cos(atan(block_height/block_width) - ramp_angle), ramp_width * tan(ramp_angle) + 0.5*(block_width**2+block_height**2)**0.5 * sin(atan(block_height/block_width) - ramp_angle), 0.5*ramp_depth) + ramp_position, 
            axis=vector(ramp_width, -ramp_width * tan(ramp_angle), 0), 
            size=vector(block_width,block_height,block_depth),
            color = vector(0.65, 0.15, 0.15),
            texture = textures.wood_old,
            opacity = 0.7)
 
 
#Set up the physical properties like the mass and velocity of the block, the acceleration due to gravity, and time.
mblock = 50
vblock = vector(0, 0, 0)
g = vector(0,-9.8,0)
t = 0
tf = 5
dt = .001
 
#Define the force vectors acting on the block
Fgrav = mblock * g
Fnorm = vector(mag(Fgrav) * cos(ramp_angle)*sin(ramp_angle), mag(Fgrav)*cos(ramp_angle)*cos(ramp_angle), 0)
Fnet = Fgrav + Fnorm
 
#Create arrows to show the forces with labels
FgravArrow = arrow(pos = block.pos, axis=Fgrav/mblock, shaftwidth=0.3, color = color.green)
FnormArrow = arrow(pos = block.pos, axis=Fnorm/mblock, shaftwidth=0.3, color = color.green)
FgravLabel = label(pos=FgravArrow.pos, text='Fg', xoffset=-20, yoffset=-50, space=30, height=16, border=4, font='sans', line=False, color = color.black)
FnormLabel = label(pos=FnormArrow.pos, text='Fn', xoffset=20, yoffset=50, space=30, height=16, border=4, font='sans', line=False, color = color.black)
 
#Slide the block down the ramp
while block.pos.y > ( ramp_position.y+ 0.5*(block_width**2+block_height**2)**0.5 * cos(atan(block_width/block_height) - ramp_angle) ):
    rate(500)
 
 
    block.pos = block.pos + vblock*dt + 0.5*(Fnet/mblock)*dt**2 
 
    FgravArrow.pos = FgravArrow.pos + vblock*dt + 0.5*(Fnet/mblock)*dt**2
    FnormArrow.pos = FnormArrow.pos + vblock*dt + 0.5*(Fnet/mblock)*dt**2
    FgravLabel.pos = FgravLabel.pos + vblock*dt + 0.5*(Fnet/mblock)*dt**2
    FnormLabel.pos = FnormLabel.pos + vblock*dt + 0.5*(Fnet/mblock)*dt**2
 
    vblock = vblock + (Fnet/mblock)*dt
    t = t + dt