6. Intro to Forces (Dynamics)

A chandelier is supported from the ceiling by 2 chains. Both chains make a 30° angle with the vertical. The tension in each chain is the same because of symmetry:T₁=T₂=50 N. What is the mass of the chandelier?

A sphere hangs suspended by a light string, resting against a vertical wall. The sphere has a mass of 2 kg and the string makes an 80° angle with the horizontal. What is the force from the wall against the ball?

A mobile at the art museum has a 2.0 kg steel cat and a 4.0 kg steel dog suspended from a lightweight cable, as shown in FIGURE EX7.21. It is found that ${\theta }_1$ = 20 degrees when the center rope is adjusted to be perfectly horizontal. What are the tension and the angle of rope 3?

A home mechanic wants to raise the 310-kg engine out of a car. The plan is to stretch a rope vertically from the engine to a branch of a tree 6.0 m above, and back to the bumper (Fig. 12–96). When the mechanic climbs up a stepladder and pulls horizontally on the rope at its midpoint, the engine rises out of the car. 

(a) How much force must the mechanic exert to hold the engine 0.50 m above its normal position?

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(II) The two trees in Fig. 12–54 are 6.2 m apart. A backpacker is trying to lift his pack out of the reach of bears. Calculate the magnitude of the force F→ that he must exert downward to hold a 19-kg backpack so that the rope sags at its midpoint by 

(a) 1.5 m.

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(I) Three forces are applied to a tree sapling, as shown in Fig. 12–49, to stabilize it. If F→_A = 385 N and F→_B = 515 N , find F→_C in magnitude and direction.

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(II) The two trees in Fig. 12–54 are 6.2 m apart. A backpacker is trying to lift his pack out of the reach of bears. Calculate the magnitude of the force F→ that he must exert downward to hold a 19-kg backpack so that the rope sags at its midpoint by

(b) 0.15 m.

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When a mass of 25 kg is hung from the middle of a fixed straight aluminum wire, the wire sags to make an angle of 12° with the horizontal as shown in Fig. 12–90. Determine the radius of the wire.

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