PROBLEM 13.67
Cornhole is a game that requires you to toss beanbags
through a hole in a wooden board. People with limited
arm mobility often have difficulty enjoying this favorite
tailgating activity. An adapted launching device attaches
to a wheelchair so that points O and A are fixed. The
device mimics an underhand throw by utilizing an elastic
band to power the arm OC, which rotates about pin O.
The elastic cord has an unstretched length of 1 ft and is
attached to fixed point A and to point B on the arm. The
combined weight of the beanbag and holder at C is 4 lbs,
and you can neglect the weight of the rod OB. Knowing
that the starting position is 30 degrees from the
horizontal as shown in the figure, determine the spring
constant if the velocity of the bean bag is 31 ft/s when
the bag is released at an angle of θ = 45 degrees.
PROBLEM 13.67 (Continued)
PROBLEM 13.68
A spring is used to stop a 50–kg package which is moving down a 20º
incline. The spring has a constant
30 kN/mk=
and is held by cables so
that it is initially compressed 50 mm. Knowing that the velocity of the
package is 2 m/s when it is 8 m from the spring and neglecting friction,
determine the maximum additional deformation of the spring in
bringing the package to rest.
PROBLEM 13.69
Solve Problem 13.68 assuming the kinetic coefficient of friction between
the package and the incline is 0.2.
PROBLEM 13.68 A spring is used to stop a 50–kg package which is
moving down a 20° incline. The spring has a constant
30 kN/mk=
and is held by cables so that it is initially compressed 50 mm. Knowing
that the velocity of the package is 2 m/s when it is 8 m from the spring
and neglecting friction, determine the maximum additional deformation
of the spring in bringing the package to rest.
PROBLEM 13.69 (Continued)
PROBLEM 13.70
A section of track for a roller coaster consists of two circular
arcs AB and CD joined by a straight portion BC. The radius
of AB is 27 m and the radius of CD is 72 m. The car and its
occupants, of total mass 250 kg, reach Point A with
practically no velocity and then drop freely along the track.
Determine the normal force exerted by the track on the car as
the car reaches point B. Ignore air resistance and rolling
resistance.
PROBLEM 13.70 (Continued)
50 : cos40
nn n
F ma N mg ma°Σ = − ° = −
cos40 ( cos40 )
nn
N mg ma m g a= °− = °−
PROBLEM 13.71
A section of track for a roller coaster consists of two circular
arcs AB and CD joined by a straight portion BC. The radius of
AB is 27 m and the radius of CD is 72 m. The car and its
occupants, of total mass 250 kg, reach Point A with
practically no velocity and then drop freely along the track.
Determine the maximum and minimum values of the normal
force exerted by the track on the car as the car travels from A
to D. Ignore air resistance and rolling resistance.
PROBLEM 13.71 (Continued)
PROBLEM 13.72
A 1–lb collar is attached to a spring and slides without friction
along a circular rod in a vertical plane. The spring has an
undeformed length of 5 in. and a constant
10 lb/ft.k=
Knowing that the collar is released from being held at A
determine the speed of the collar and the normal force between
the collar and the rod as the collar passes through B.