A vertical force $\vec{T}$ is exerted on a 5-kg object near the surface of the earth, as shown in Figure 4-36. Find the acceleration of the object if (a) $T=5 N$, (b) $T=10 \mathrm{~N}$, and $(c) T=100 \mathrm{~N}$.

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) $360 \mathrm{~kg}$.

A $4.0-\mathrm{kg}$ object is subjected to two constant forces, $\vec{F}_1=(2.0 \mathrm{~N}) \hat{i}+(-3.0 \mathrm{~N}) \hat{j}$ and $\vec{F}_2=(4.0 \mathrm{~N}) \hat{i}-(11 \mathrm{~N}) \hat{j}$. The object is at rest at the origin at time $t=0$.

$(c)$ Where is the object at time $t=3.0 \mathrm{~s}$ ?

A $4.0-\mathrm{kg}$ object is subjected to two constant forces, $\vec{F}_1=(2.0 \mathrm{~N}) \hat{i}+(-3.0 \mathrm{~N}) \hat{j}$ and $\vec{F}_2=(4.0 \mathrm{~N}) \hat{i}-(11 \mathrm{~N}) \hat{j}$. The object is at rest at the origin at time $t=0$.

$(b)$ What is its velocity at time $t=3.0 \mathrm{~s}$ ?

A $4.0-\mathrm{kg}$ object is subjected to two constant forces, $\vec{F}_1=(2.0 \mathrm{~N}) \hat{i}+(-3.0 \mathrm{~N}) \hat{j}$ and $\vec{F}_2=(4.0 \mathrm{~N}) \hat{i}-(11 \mathrm{~N}) \hat{j}$. The object is at rest at the origin at time $t=0$.

$(a)$ What is the object's acceleration?