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Balancing force components

Mathematics · Mechanics · ages 17-18

Name ______________________ Date ____________

Only two forces act on a particle: 9 N east and 9 N north. Sam says their equal magnitudes put the particle in equilibrium. Is Sam's statement true?
Circle one: True False
Take east and north as positive. Three forces have components (east, north), in N: (9, 4), (-5, 3) and (-4, k). What signed value of k gives equilibrium?
Answer: ______________
A 6 N force pulls east and an 8 N force pulls north on a small ring. What is the magnitude, in N, of the third force needed to put the ring in equilibrium?
Answer: ______________
A book rests on a level table with no other applied forces. Ignore air forces. Which pair lists the forces acting on the book?
- Earth's downward pull and the book's downward push on the table
- The table's upward normal force and the table's own downward weight
- Earth's downward pull and the table's upward normal force
A 12 kg particle rests on taut strings sloping up left at 30° and up right at 60° above the horizontal. Use g = 10 N/kg, sin30° = cos60° = 1/2 and cos30° = sin60° = √3/2. Which tensions balance it?
- Left 60√3 N; right 60 N
- Left 60 N; right 60√3 N
- Left 120 N; right 120 N
- Left 120 N; right 120√3 N
Forces of 7 N east, 3 N west and 2 N north act on a ring. Which components must one extra force have to put it in equilibrium?
- 4 N west and 2 N south
- 4 N east and 2 N north
- 10 N west and 2 N south
A 6 kg mass hangs at rest from two vertical strings sharing the load equally. Take g = 10 N/kg. What is the tension in each string, in N?
Answer: ______________
A 4 kg particle rests on two taut strings sloping up on opposite sides, each at 30° above the horizontal. Take g = 10 N/kg and sin30° = 1/2. What is each tension, in N?
Answer: ______________
A ball reaches the highest point of a vertical throw. Ignore air resistance. Lee says it is in equilibrium because its velocity is zero at that instant. Which statement checks Lee's claim?
- Its upward throwing force still balances its downward weight.
- Its weight acts downward, so its resultant force is nonzero.
- Its weight becomes zero until its downward motion has begun.
A book rests on a level table with no other applied forces. Its weight and the table's normal force are equal and opposite. They are therefore an action-reaction pair. Is this statement true?
Circle one: True False

Answer key

For grown-ups. Fold this page away before handing over the rest.

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False · Equal magnitudes do not cancel unless the two directions are opposite. Here the horizontal total is 9 N east and the vertical total is 9 N north.
-7 · The horizontal total is 9 - 5 - 4 = 0. The vertical equation is 4 + 3 + k = 0, giving k = -7 N.
10 · The first two forces have a 10 N resultant, so the balancing force must be 10 N in the opposite direction.
Earth's downward pull and the table's upward normal force · Earth pulls the book downward, and the table pushes it upward. Forces acting on the table do not belong in the book's force list.
Left 60 N; right 60√3 N · Horizontal balance gives T_R = √3 T_L. Vertical balance gives T_L/2 + 3T_L/2 = 120. Thus T_L = 60 N and T_R = 60√3 N.
4 N west and 2 N south · The existing totals are 4 N east and 2 N north. One force with components 4 N west and 2 N south cancels both totals.
30 · The weight is 60 N, so each string carries half: 30 N.
40 · Horizontal balance gives equal tensions T. The weight is 40 N, so vertical balance gives T/2 + T/2 = 40. Each tension is 40 N.
Its weight acts downward, so its resultant force is nonzero. · At the highest point, the velocity is briefly zero but gravity still acts downward. A nonzero resultant means the ball is not in equilibrium.
False · Both forces act on the book. An action-reaction pair acts on two different bodies, so the book's weight and normal force are not such a pair.