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

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

P251 ©Marasinghe

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 your work. This will be your equati

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 your work. This will be your equation (2).

y y

S

F ma m

m L

? ?

? ?

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

x x Sx xN W F ma? ? ?

P251 ©Marasinghe

 

 

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.”