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Rectilinear Motion
1. Small objects are delivered to the 2 m inclined chute by a conveyor belt A
which moves at a speed v1=0.4 m/s. If the conveyor belt B has a speed
v2=0.9 m/s and the objects are delivered to this belt with no slipping,
calculate the coefficient of friction mk between the objects and the chute.
Rectilinear Motion
2. A force P is applied to the initially stationary cart. Determine the velocity
and displacement at time t=5 s for each of the force histories P1 and P2.
Neglect friction.
Rectilinear Motion
3. The sliders A and B are connected by a light rigid bar and move with
negligible friction in the slots, both of which lie in a horizontal plane. For the
position shown, the velocity of A is 0.4 m/s to the right. Determine the
acceleration of each slider and the force in the bar at this instant.
Rectilinear Motion
4. The collar slides down the rod. The
coefficient of friction is mk = 0.35. The
tension in the cable attached to the
collar is constant as 80 N and the angle
between the cable and the horizontal
remains the same as a throughout the
motion. The weight of the collar is 60
N. If the collar stops after 10 seconds it
starts sliding down the rod with an
initial velocity of 5 m/s, what should a
be?
Curvilinear Motion
5. The pin P is forced to move in the fixed parabolic slot by the moving
vertical guide. The centerline of the slot is described by y = 0.015x2 [mm].
When x = 40 mm, the speed v of the guide is 100 mm/s and is not changing at
this instant. Determine the magnitudes N and R of the forces which the guide
and the vertical plate, respectively, exert on the 50 g pin.
Curvilinear Motion
6. A 0.8-kg slider is propelled upward at A along the fixed curved bar which
lies in a vertical plane. If the slider is observed to have a speed of 4 m/s as it
passes position B, determine, (a) the magnitude N of the force exerted by the
fixed rod on the slider and (b) the rate at which the speed of the slider is
increasing. Assume that friction is negligible.
Curvilinear Motion
7. The small object is placed on the inner surface of the conical dish at the
radius shown. If the coefficient of static friction between the object and the
conical surface is 0.30, for what range of angular velocities w about the
vertical axis will the block remain on the dish without slipping? Assume that
speed changes are made slowly so that any angular acceleration may be
neglected.
Curvilinear Motion
8. The 1 kg collar slides along the smooth parabolic rod in the vertical plane
toward point O. The spring whose stiffness is k=600 N/m has an
unstretched length of 1 m. If, at the position shown in the figure, velocity of
the collar is 3.5 m/s, determine the force acting on the collar by the
parabolic rod for this instant. Neglect the friction.
Curvilinear Motion
9. The horizontal platform is rotating
with a constant angular velocity of
w=5 rad/s. Two identical blocks, each
with a mass of 2 kg are held in the
smooth slot within the platform by a
pair of springs each with a stiffness
of k=250 N/m. If the unstretched
length of each spring is lo= 0.18 m,
what should angle q be for steady
state position? Springs are attached
to the platform at point A.
(Consider only one block for the
solution of the problem.)
Curvilinear Motion
10. The slotted arm revolves in the horizontal plane about the fixed vertical
axis through point O. The 2 kg slider C is drawn toward O at the constant rate of
50 mm/s by pulling the cord S. At the instant for which r=225 mm, the arm has
a counterclockwise angular velocity w=6 rad/s and is slowing down at the rate
of 2 rad/s2. For this instant, determine the tension T in the cord and the
magnitude N of the force exerted on the slider by the sides of the smooth radial
slot. Indicate which side, A or B, of the slot contacts the slider.
Curvilinear Motion
11. The 1.5 kg cylinder C travels along the path described by r =(0.6sin q )
[meter]. If arm OA rotates counter clockwise with a constant angular velocity of
q =3 rad/s, determine the force exerted by the smooth slot in arm OA on the
cylinder at the instant q = 60°. The spring has a stiffness of 100 N/m and is
unstretched when q =30°. Motion occurs in the vertical plane.
Curvilinear Motion
12. The 1 kg ball A, which slides in a
slot in the rotating arm OB, is kept in
r=0.1(2+cos q) m
y
contact with the stationary cam C by a
B
spring. The spring has a stiffness of
1000 N/m and is unstretched when
r
0.2 m
the arm OB is in position OP. If the
arm rotates with the constant angular
velocity q =20 rad/s (ccw), calculate
A
q
P
Q
C
the normal force N which the cam
exerts on A and also the force R
exerted on A by the sides of the slot
when q=30o. All surfaces are smooth.
The problem occurs in vertical plane.
0.1 m
0.3 m
x
Curvilinear Motion
13. The slotted arm is used to move the
smooth 0.5 kg particle P around the
vertical path in the shape of a limaçon with
r = 0.3 (2 + cosq ) m. The spring with a
stiffness of k = 8 N/m in the slot ensures
that the particle P does not lose contact
with the path. The spring is unstretched
when q is equal to 90°. If q =
(0.5t2)
rad,
where t is in seconds, determine the forces
N and F which the rod and the slotted arm,
respectively, exerts on the particle at the
instant t = 1.5 s.
0.6 m
q
q
0.9 m