6. Intro to Forces (Dynamics)

Which of the following is true when two vectors sum to $0$ in two-dimensional equilibrium?

Which of the following objects is in equilibrium in two dimensions?

Which of the following free-body diagrams represents a box in equilibrium in two dimensions?

Which of the following best describes a body in equilibrium in two dimensions?

Which type of equilibrium is observed when a ball is placed at the bottom of a hemispherical bowl?

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?

Find the tension in each cord in Fig. E$5.7$ if the weight of the suspended object is $w$.

A large wrecking ball is held in place by two light steel cables (Fig. E$5.6$). If the mass m of the wrecking ball is $3620$ kg, what are the (a) tension $T_B$ in the cable that makes an angle of $40°$ with the vertical and (b) the tension $T_A$ in the horizontal cable?

A $1130$-kg car is held in place by a light cable on a very smooth (frictionless) ramp (Fig. E$5.8$). The cable makes an angle of $31.0°$ above the surface of the ramp, and the ramp itself rises at $25.0°$ above the horizontal. Find the tension in the cable.

A picture frame hung against a wall is suspended by two wires attached to its upper corners. If the two wires make the same angle with the vertical, what must this angle be if the tension in each wire is equal to $0.75$ of the weight of the frame? (Ignore any friction between the wall and the picture frame.)

A football coach sits on a sled while two of his players build their strength by dragging the sled across the field with ropes. The friction force on the sled is 1000 N, the players have equal pulls, and the angle between the two ropes is 20°. How hard must each player pull to drag the coach at a steady 2.0 m/s?

In an electricity experiment, a 1.0 g plastic ball is suspended on a 60-cm-long string and given an electric charge. A charged rod brought near the ball exerts a horizontal electrical force F_electric on it, causing the ball to swing out to a 20° angle and remain there. What is the magnitude of F_electric?

An accident victim with a broken leg is being placed in traction. The patient wears a special boot with a pulley attached to the sole. The foot and boot together have a mass of 4.0 kg, and the doctor has decided to hang a 6.0 kg mass from the rope. The boot is held suspended by the ropes, as shown in FIGURE P6.40, and does not touch the bed. Determine the amount of tension in the rope by using Newton's laws to analyze the hanging mass. Hint: If the pulleys are frictionless, which we will assume, the tension in the rope is constant from one end to the other.

The three ropes in FIGURE EX6.1 are tied to a small, very light ring. Two of these ropes are anchored to walls at right angles with the tensions shown in the figure. What are the magnitude and direction of the tension T3 in the third rope?