A 1000-kg load is being moved by a crane. Find the tension in the cable that supports the load as $(a)$ it moves upward with a speed increasing by $2 \mathrm{~m} / \mathrm{s}$ each second, $(b)$ it is lifted at constant speed, and $(c)$ it moves upward with speed decreasing by $2 \mathrm{~m} / \mathrm{s}$ each second.

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?

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

On the moon, the acceleration due to the effect of gravity is only about $1 / 6$ of that on Earth. An astronaut whose weight on Earth is $600 \mathrm{~N}$ travels to the lunar surface. His mass, as measured on the moon, will be $(a) 600 \mathrm{~kg}$, (b) $100 \mathrm{~kg}$, $(c) 61.2 \mathrm{~kg}$, $(d) 9.81 \mathrm{~kg}$, (e) $360 \mathrm{~kg}$.