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 $\vec{F}_3$.

The distance, in feet, a moving object has traveled after t seconds is given by $s(t)=4 t^2 /(t+1)$. Find the speed and acceleration of the object after 3 seconds.

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?

What is one power of the federal government?

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 team of eight dogs pulls a sled with waxed wood runners on wet snow (mush!). The dogs have average masses of 19.0 kg, and the loaded sled with its rider has a mass of 210 kg. (a) Calculate the acceleration of the dogs starting from rest if each dog exerts an average force of 185 N backward on the snow. (b) Calculate the force in the coupling between the dogs and the sled.

A semi is traveling down the highway at a velocity of $v = 26\, \mathrm{\dfrac{m}{s}}$. The driver observes a wreck ahead, locks his brakes, and begins to slide. The truck has mass $m$ and a coefficient of kinetic friction between the tires and the road of $\mu_{k} = 0.26$. Write an expression for the sum of the forces in the $x$-direction for the truck while braking.

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.

A gymnast jumps straight up, with her center of mass moving at 2.80 m/s as she leaves the ground. How high above this point is her center of mass (a) 0.100 s, (b) 0.200 s, (c) 0.300 s, and (d) 0.500 s thereafter?