A 2-kg picture is hung by two wires of equal length. Each makes an angle $\theta$ with the horizontal, as shown in Figure 4-37. (a) Find the general equation for the tension $T$, given $\theta$ and the weight $w$ for the picture. For what angle $\theta$ is $T$ the least? The greatest? $(b)$ If $\theta=30^{\circ}$, what is the tension in the wires?

A 10-kg object on a frictionless table is subjected to two horizontal forces, $\vec{F}_1$ and $\vec{F}_2$, with magnitudes $F_1=20 \mathrm{~N}$ and $F_2=30 \mathrm{~N}$, as shown in Figure 4-35. (a) Find the acceleration $\vec{a}$ of the object. (b) A third force $\vec{F}_3$ is applied so that the object is in static equilibrium. Find $\vec{F}_3$.

A ball weighing 100-N is shown suspended from a system of cords (Figure 4-39). What are the tensions in the horizontal and angled cords?

In Figure 4-38a, a 0.500-kg block is suspended at the midpoint of a 1.25-m-long string. The ends of the string are attached to the ceiling at points separated by 1.00 m.

$(c)$ The 0.500-kg block is removed and two 0.250-kg blocks are attached to the string such that the lengths of the three string segments are equal (Figure 4-38b). What is the tension in each segment of the string?

In Figure 4-38a, a 0.500-kg block is suspended at the midpoint of a 1.25-m-long string. The ends of the string are attached to the ceiling at points separated by 1.00 m.

$(b)$ What is the tension in the string?

In Figure 4-38a, a 0.500-kg block is suspended at the midpoint of a 1.25-m-long string. The ends of the string are attached to the ceiling at points separated by 1.00 m.

$(a)$ What angle does the string make with the ceiling?

A 42.6-kg lamp is hanging from wires as shown in Figure 4-37. The ring has negligible mass. The tension $T_1$ in the vertical wire is (a) $209 \mathrm{~N},(b) 418 \mathrm{~N},(c) 570 \mathrm{~N},(d) 360 \mathrm{~N},(e) 730 \mathrm{~N}$.

A traffic light is supported by two wires as in Figure 4-31. Is the tension in the wire that is more nearly vertical greater than or less than the tension in the other wire?

A 6-kg box on a frictionless horizontal surface is attached to a horizontal spring with a force constant of $800 \mathrm{~N} / \mathrm{m}$. If the spring is stretched $4 \mathrm{~cm}$ from its equilibrium length, what is the acceleration of the box?

A vertical spring of force constant $600 \mathrm{~N} / \mathrm{m}$ has one end attached to the ceiling and the other to a $12-\mathrm{kg}$ block resting on a horizontal surface so that the spring exerts an upward force on the block. The spring stretches by $10 \mathrm{~cm}$. (a) What force does the spring exert on the block? (b) What is the force that the surface exerts on the block?

Find the mass of a 165-lb engineer in kilograms.

If only a single nonzero force acts on an object, must the object have an acceleration relative to any inertial reference frame? Can it ever have zero velocity?

A placekicker must kick a football from a point 36.0 m (about 40 yards) from the goal. Half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 20.0 m/s at an angle of 53.08 to the horizontal. (a) By how much does the ball clear or fall short of clearing the crossbar? (b) Does the ball approach the crossbar while still rising or while falling?

Find the weight of a 54-kg student in $(a)$ newtons, and $(b)$ pounds.