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?

A small bead of mass $m$ is constrained to slide without friction inside a circular vertical hoop of radius $r$ which rotates about a vertical axis (Fig. 5-58) at a frequency $f$. Find the angle $\theta$ where the bead will be in equilibrium within the hoop-that is, where it will have no tendency to move up or down along the hoop.

force $\vec{F}=12 \mathrm{~N} i$ is applied to the $3-\mathrm{kg}$ ball . What is the acceleration of the center of mass?

A 1500-kg car is moving westward with a speed of $20.0 \mathrm{~m} / \mathrm{s}$, and a $3000-\mathrm{kg}$ truck is traveling east with a speed of $16.0 \mathrm{~m} / \mathrm{s}$. Find the velocity of the center of mass of the car-truck system.

A35.0-kg traffic light is supported by two wires as in Figure 4-36.

$(b)$ Verify your answer by applying Newton’s laws and solving for the two tensions.

A35.0-kg traffic light is supported by two wires as in Figure 4-36.

$(b)$ Verify your answer by applying Newton’s laws and solving for the two tensions.

A35.0-kg traffic light is supported by two wires as in Figure 4-36.

$(a)$ Draw the light’s free-body diagram and use it to answer the following question qualitatively: Is the tension in wire 2 greater than or less than the tension in wire 1?

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 large box whose mass is $20.0 \mathrm{~kg}$ rests on a frictionless floor. A mover pushes on the box with a force of $250 \mathrm{~N}$ at an angle $35.0^{\circ}$ below the horizontal. Draw the box's free-body diagram and use it to determine the acceleration of the box.

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) $209 \mathrm{~N},(b) 418 \mathrm{~N},(c) 570 \mathrm{~N},(d) 360 \mathrm{~N},(e) 730 \mathrm{~N}$.

A100-g coin sits on a horizontally rotating turntable. The turntable makes exactly 1.00 revolution each second. The coin is located 10 cm from the axis of rotation of the turntable.

$(a)$ What is the frictional force acting on the coin?

You are swinging your younger sister in a circle of radius $0.75 \mathrm{~m}$, as shown in Figure 5-74. If her mass is $25 \mathrm{~kg}$ and you arrange it so she makes one revolution every $1.5 \mathrm{~s}$(b)$ What is the magnitude and direction of the force she exerts on you?

You are swinging your younger sister in a circle of radius $0.75 \mathrm{~m}$, as shown in Figure 5-74. If her mass is $25 \mathrm{~kg}$ and you arrange it so she makes one revolution every $1.5 \mathrm{~s}$(a)$ what is the magnitude and direction of the force that must be exerted by you on her? (Model her as a point particle.)

An automobile is going up a 15 degree grade at a speed of 30 m/s. The coefficient of static friction between the tires and the road is 0.70. What minimum distance would it take to stop if the car were going down the grade?