CTSE-2. A door is pushed on by two forces, a smaller force at the door knob AND a larger force nearer the hinge as shown. The door does not move.

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1 Page 1 of 6 Static Equilibrium Concept Tests CTSE-1. A mass m is hung from a clothesline stretched between two poles as shown. As a result, the clothesline sags very slightly as shown. The tension T in the clothesline has magnitude.. A) mg B) mg/2 C) slightly greater than mg/2 D) considerably greater than mg/2 E) considerably less than mg/2 Answer: considerably greater than mg/2 CTSE-2. A door is pushed on by two forces, a smaller force at the door knob AND a larger force nearer the hinge as shown. The door does not move. y hinge Big force x Small force. The force exerted on the door by the hinge... A) is zero B) points (along +y) C) points (along -y) D) points lower right E) points upper right Answer: points lower right Use net = 0.

2 Page 2 of 6 CTSE-3. A bar has four forces, all of the same magnitude, exerted on it, as shown. What is the sign of the net torque about the axis of rotation? Use the sign convention shown. axis + d d d d A) torque is zero B) positive (+) C) negative ( ) Answer: positive (+) CTSE-4. A light board of length 4d is stationary. our forces, all of the same magnitude, are being applied as shown. + d d d d If we choose the left end of the board as the axis of rotation, then the net torque about that axis is A) torque is zero B) positive (+) C) negative ( ) Answer: torque is zero (It must be, since the board is stationary.)

3 Page 3 of 6 CTSE-5. A mass M is placed on a very light board supported at the ends, as shown. The free-body diagram shows directions of the forces, but not their correct relative sizes. M L R (2/3)L L/3 Mg What is the ratio R L? (Hint: consider the torque about the mass M). A) 2/3 B) 1/3 C) 1/2 D) 2 E) none of these Answer: The ratio is 2. Suppose now the board has mass m, so the free-body diagram is now L R Compared to when the board had no mass, the force R is now.. A) greater B) less C) the same. mg Mg Answer: greater Consider the torques when the axis is at the left end of the board.

4 Page 4 of 6 CTSE-6. A ladder of weight W L leans against a wall. The ladder has rollers at the top so that the wall exerts a normal force only on the top of the ladder. A person of weight W P slowly climbs the ladder. A free-body diagram for the ladder is shown. Wall y W L x As the person ascends the ladder, the force from the wall ( wall ) A) increases B) decreases C) stays the same. (Hint: Consider the torque about the point where the ladder touches the ground.) Answer: increases. Part II. As the person ascends the ladder the force of friction x, between the ladder and the ground... A) increases B) decreases C) stays the same. Answer: increases. Part III. The ladder is more likely to slip when the person is... A) lower B) higher C) doesn't matter. Answer: higher Part IV. All during the time that the person ascends, but before the ladder slips, is it true that fric = s N? A) Yes B) No Answer: No. s N is the MAXIMUM possible value of the force of static friction. The force of static friction can be anything less than or equal to the maximum. W P (friction)

5 Page 5 of 6 CTSE-7. A sign of mass m s is hung from a uniform horizontal bar of mass m B as shown. y x T m B g m S g What is the sign of the x-component of the force exerted on the bar by the wall? A) Positive B) Negative C) WX = 0. Answer: Positive Use x = 0 What is the sign of the y-component of the force exerted on the bar by the wall? A) Positive B) Negative C) WY = 0. (HINT: consider the torques about the right end of the bar.) Answer: Positive

6 Page 6 of 6 CTSE-8. A box of mass M is sitting at the edge of a diving board of the same mass M, total length L. The board has two supports: one in the middle, one on the end, as shown. What is the y-component of the force on the board Y from the right support? (Hint: consider the torque about the C.M. of the board.) M M y x L/2 L/2 A) Mg B) Mg C) 2Mg D) 2Mg E) None of these Answer: Mg (The diving board must be nailed to the right support.) CTSE-9. A mass M is supported by two threads as shown. The free-body diagram correctly shows the directions of the forces but does not correctly show their magnitudes. T 1 T 1 T 2 m T 2 mg Which tension is larger: T 1 or T 2? A) T 1 B) T 2 C) Both have the same magnitude. Answer: T 1 must be larger, since T 1x = T 2