NEWTON’S THIRD LAW & ACTION-REACTION FORCES
MATH PROBLEMS
BASE PROBLEM
1. A force of 60 N [E] acts on a combination of two boxes that are adjacent to each other on a frictionless surface. The force acts directly on Box A which has a mass of 20 kg. Box B has a mass of 10 kg. Find:
a) the acceleration of the boxes (2.0 m/s2 [E])
b) the force exerted by box A on box B (20 N [E])
c) the force exerted by box B on box A (20 N [W])
BASE PROBLEM
2. Two toboggans are connected by a rope. The first toboggan has a mass of 60 kg and the second has a mass of 40 kg. The two toboggans are pulled by a rope connected to the first toboggan. If the force exerted on the tope is 250 N [E], and friction can be ignored, find:
a) the acceleration of the toboggans (2.5 m/s2 [E])
b) the tension in the rope connecting the toboggans (1.0 x 102 N)
BASE PROBLEM WITH CHALLENGE
3. Suppose a third toboggan of mass 25 kg is connected to the second toboggan in question Find:
a) the acceleration of the system of three toboggans (2.0 m/s2 [E])
b) the force exerted by toboggan one on toboggan two (1.3 x 102 N [E])
c) the force exerted by the second toboggan on the last one (50 N [E])
BASE PROBLEM
4. Two boys, one with a mass of 60 kg and the other with a mass of 90 kg, are standing side by side in the middle of an ice rink. One of them pushes the other with a force of 360 N for 0.10.s Assuming that the ice surface is frictionless:
a) what is the acceleration of each boy? (6.0 m/s2, 4.0 m/s2)
b) what speed will each boy reach after 0.10s? (0.60 m/s, 0.40 m/s)
c) does it matter which boy did the pushing?
WITH FRICTION
5. A dog team driven by a hunter pulls two toboggans. The dog team can apply a maximum force of 700 N. Each toboggan experiences a constant frictional force of 100 N and has a mass of 300 kg.
a) determine the acceleration of the two toboggans (0.833 m/s2 [forward])
b) what is the force of the rope joining the toboggans together? (350 N)
WITH FRICTION
6. Two boxes that are adjacent to one another. A man attaches a rope to the first Box and pulls horizontally. Box A is the first box and has a mass of 5 kg and box B has a mass of 10 kg. If the action-reaction force between the two boxes is 30 N and we assume a frictionless surface, find:
a) the acceleration of the boxes (3 m/s2 [horizontal])
b) the applied force on the first box (45 N or 5 X 101 N [horizontal])
WITH GRAVITY
7. Two cans of paint are suspended from a pulley on the ceiling. There is a rope between the two containers that attaches them together. The top can has a mass of 3 kg and the bottom can has a mass of 5 kg. The cans are moved upward by pulling on the first rope with a force of 500 N. Assume there is no air resistance.
a) what is the acceleration of the cans? (52.7 m/s2 or 5 X 101 m/s2 [up])
b) what is the tension in the rope between the two cans? (313 N or 3 X 102 N [up])
WITH GRAVITY
8. Two bales of hay are being pulled up the side of a silo by a rope. There is a rope attaching the bales of hay together. The top bail of hay has a mass of 50 kg and the bottom bail of hay has a mass of 65 kg. The tension in the rope that joins the two bales of hay together is 2500 N. Assume there is no air resistance.
a) what is the acceleration of the hay? (29 m/s2 [up])
b) what is the applied force in the top rope pulling the bales of hay up the silo? (4.5 X 103 N [up])