Name: Date:
Subject and Section: Permit No.:
Student No.:
Problem Set P3 | Dynamics of Rigid Bodies
Instructions: Answer the following questions in an organized, neat and complete manner. Keep final answer in
three decimal places, units included and enclosed in a rectangle. Avoid erasures. Wrong/missing/incomplete
solution is wrong. Cheating is a sin.
Situation 1 (B12.13)The two blocks shown are originally at rest. Neglecting the masses of the pulleys and the
effect of friction in the pulleys and between block A and the incline, determine:
_________________1. the acceleration of each block.
_________________2. the tension in the cable.
Situation 2 (B12.16) Boxes A and B are at rest on a conveyor belt that is initially at rest. The belt is suddenly
started in an upward direction so that slipping occurs between the belt and the boxes. Knowing that the
coefficients of kinetic friction between the belt and the boxes are (𝜇 ) = 0.30 and (𝜇 ) = 0.32.
_________________3. determine the initial acceleration of Box A.
_________________4. determine the initial acceleration of Box B.
Situation 3 (B12.31) A 10-lb block B rests as shown on a 20-lb bracket A. The coefficients of friction are 𝜇 =
0.30 and 𝜇 = 0.25 between block B and bracket A, and there is no friction in the pulley or between the bracket
and the horizontal surface.
_________________5. Determine the maximum weight of block C if block B is not to slide on bracket A.
_________________6. If the weight of block C is 10% larger than the answer found in #5 determine the
accelerations of A.
_________________7. If the weight of block C is 10% larger than the answer found in #5 determine the
accelerations of B.
_________________8. If the weight of block C is 10% larger than the answer found in #5 determine the
accelerations of C.
Situation 4 (B12.37) During a hammer thrower’s practice swings, the 7.1-kg head A of the hammer revolves at
a constant speed 𝑣 in a horizontal circle as shown. If 𝜌 = 0.93 𝑚 and 𝜃 = 60° , determine
_________________9. the tension in wire BC.
_________________10. the speed of the hammer’s head.
Situation 5 (H 13-69) The 0.8-Mg car travels over the hill having the shape of a parabola. When the car is at
point A, it is traveling at 9 𝑚/𝑠 and increasing its speed at 3 𝑚/𝑠 . Determine:
_________________11. The resultant normal force that all the wheels of the car exert on the road at this instant.
_________________12. The resultant frictional force that all the wheels of the car exert on the road at this
instant.
Situation 6 (H – 13.82) The 8-kg sack slides down the smooth ramp. If it has a speed of 1.5 𝑚/𝑠 when 𝑦 = 0.2 𝑚
, determine:
_________________13. the normal reaction the ramp exerts on the sack
_________________14. the rate of increase in the speed of the sack at this instant.
Situation 7 (B13.9) A package is projected up a 15° incline at A with an initial velocity of 8 m/s. Knowing that
the coefficient of kinetic friction between the package and the incline is 0.12, determine:
_________________15. The maximum distance 𝑑 that the package will move up the incline
_________________16. The velocity of the package as it returns to its original position.
Situation 8 (B13.12) Packages are thrown down an incline at A with a velocity of 1 m/s. The packages slide
along the surface ABC to a conveyor belt which moves with a velocity of 2 m/s. Knowing that 𝑑 = 7.5 𝑚 and
𝜇 = 0.25 between the packages and all surfaces, determine:
_________________17. the speed of the package at C.
_________________18. The distance a package will slide on the conveyor belt before it comes to rest relative
to the belt.
Situation 9 (B13.20) The system shown is at rest when a constant 30 lb force is applied to collar B.
_________________19. If the force acts through the entire motion, determine the speed of collar B as it strikes
the support at C.
_________________20. After what distance d should the 30 lb force be removed if the collar is to reach support
C with zero velocity?
Situation 10 (H 14-35) When the 150-lb skier is at point A he has a speed of 5 𝑓𝑡/𝑠. Point B has the slope
follows the cosine curve shown. Neglect friction and air resistance.
_________________21. Determine his speed when he reaches point B on the smooth slope.
_________________22. What is the normal force on his skis at B and his rate of increase in speed?
_________________23. The 10-lb block is pressed against the spring so as to compress it 2 𝑓𝑡 when it is at A.
If the plane is smooth, determine the distance 𝑑, measured from the wall, to where the block strikes the
ground. Neglect the size of the block. (H 14-33)
Situation 11 (H 14-37) If the track is to be designed so that the passengers of the roller coaster do not
experience a normal force equal to zero or more than 4 times their weight, determine the limiting heights and
so that this does not occur. The roller coaster starts from rest at position A. Neglect friction.
_________________24. ℎ .
_________________25. ℎ
