# Physics

A child's toy consists of a small wedge that has an acute angle θ. The

sloping side of the wedge is rough with a coefficient of static friction of

μS. A puck of mass m on the wedge remains at constant height such that

the distance from the bottom of the wedge to the puck remains at L as the

wedge spins at a constant speed as shown at right. The wedge is spun by

rotating, as an axis, a vertical rod that is firmly attached to the wedge at

the bottom end.

Assignment: __GCA-CH06A-021518_(100 pts)_ Pg1/3

Table:______ Station:______ Name:______________________________

Absent from Group:___________________________________________

S 

Carefully review and understand the figure given below at left. xz plane is horizontal. z-axis is

tangential to the track of the puck.

a). What is the direction of puck’s velocity? _______________________

b). If the speed of rotation is constant, what is the direction of puck’s acceleration? ______________

c). If the speed of rotation is increasing, what is the approximate direction of puck’s acceleration?

d). Give the radius of the puck’s track in terms of known quantities. __________________________

e). Assume that the speed is constant and it is so HIGH that the puck is at the verge of sliding “out.”

On the figure given below at left, draw all the forces acting on the puck. Then draw a clear and

complete FBD on the coordinate system given below at right. Verify that your FBD is accurate

before moving to part (f).

x

y

θ

h). At this limiting condition (puck about to slide), what is the relationship between magnitudes of

normal and friction forces? This your equation (3).

f). Apply to and develop

a relationship between unknown quantities

, magnitudes of normal and friction forces,

and given quantities , , , and . Show

x x

Max

S

F ma m

v

m L

 

 

on (1).

Now you will derive an expression for the maximum constant speed, vMax, the puck can have before it

starts to slide “out.” To do this, you will have to apply Newton’s 2nd Law to the puck in x and y

directions and also relate the magnitudes of normal and frictional forces acting on the puck to each

other using μS. Note that there are three unknown quantities, vMax and magnitudes of normal and

friction forces. Hence, we need three equations to solve for vMax.

Assignment: __CA-CH06A_(100 pts)__ Pg2/3

Table:______ Station:______ Name:______________________________

g). Apply to and develop

a relationship between unknown quantities

magnitudes of normal & friction forces,

and given quantities , , , and . Show

y y

S

F ma m

m L

 

 

i). Using equations (1), (2), and (3), derive an expression for vMax. Comment on your result.

Nx Wx  FSx  max

Assignment: __CA-CH06A_(100 pts)__ Pg3/3

Table:______ Station:______ Name:______________________________

j). Now assume that the speed is constant and it is so LOW that the puck is at the verge of sliding “in.”

On the figure given below at left, draw all the forces acting on the puck. Then draw a clear and

complete FBD on the coordinate system given below at right. Verify that your FBD is accurate before

moving to part (k).

x

y

θ

k). Utilizing the techniques you used for parts (f) through (i), derive an expression for the minimum

constant speed, vMin, the puck can have before it starts to slide “in.”