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 child rolls a $0.600 \mathrm{~kg}$ basketball up a long ramp. The basketball can be considered a thin-walled, hollow sphere. When the child releases the basketball at the bottom of the ramp, it has a speed of $8.0 \mathrm{~m} / \mathrm{s}$. When the ball returns to her after rolling up the ramp and then rolling back down, it has a speed of $4.0 \mathrm{~m} / \mathrm{s}$. Assume the work done by friction on the basketball is the same when the ball moves up or down the ramp and that the basketball rolls without slipping. Find the maximum vertical height increase of the ball as it rolls up the ramp.

Two cannons are pointed directly toward each other, as shown in Figure 3-32. When fired, the cannonballs will follow the trajectories shown—P is the point where the trajectories cross each other. If we want the cannonballs to hit each other, should the gun crews fire cannon A first, cannon B first, or should they fire simultaneously? Ignore any effects due to air resistance.

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?

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.

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?

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?

It is the year 2075 and space travel is common. A physics professor brings his favorite teaching demonstration with him to the moon. The apparatus consists of a very smooth (frictionless) horizontal table and an object to slide on it. On Earth, when the professor attaches a spring (force constant $50 \mathrm{~N} / \mathrm{m}$ ) to the object and pulls horizontally so the spring stretches $2.0 \mathrm{~cm}$, the object accelerates at $1.5 \mathrm{~m} / \mathrm{s}^2$.

$(b)$ What would the object's acceleration be under identical conditions on the moon?

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?

It is the year 2075 and space travel is common. A physics professor brings his favorite teaching demonstration with him to the moon. The apparatus consists of a very smooth (frictionless) horizontal table and an object to slide on it. On Earth, when the professor attaches a spring (force constant $50 \mathrm{~N} / \mathrm{m}$ ) to the object and pulls horizontally so the spring stretches $2.0 \mathrm{~cm}$, the object accelerates at $1.5 \mathrm{~m} / \mathrm{s}^2$.

$(a)$ Draw the free-body diagram of the object and use it and Newton's laws to determine the object's mass.

(a) If a person can jump a maximum horizontal distance (by using a $45 ^ { \circ }$ projection angle) of 3.0 m on Earth, what would be his maximum range on the Moon, where the free-fall acceleration is g/6 and g = 9.80 m/s$^2$? (b) Repeat for Mars, where the acceleration due to gravity is 0.38g.

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?

To train astronauts to work on the moon, where the free-fall acceleration is only about 1/6 of that on Earth, NASA submerges them in a tank of water. If an astronaut who is carrying a backpack, air conditioning unit, oxygen supply, and other equipment, has a total mass of $250 \mathrm{~kg}$, determine the following quantities.

$(b)$ her weight on the moon.