An object with mass $m=1.0 \mathrm{~g}$ and charge $q$ is placed at point $A$, which is $0.05 \mathrm{~m}$ above an infinitely large, uniformly charged, nonconducting sheet $\left(\sigma=-3.5 \cdot 10^{-5} \mathrm{C} / \mathrm{m}^2\right)$. Gravity is acting downward $\left(g=9.81 \mathrm{~m} / \mathrm{s}^2\right)$. Determine the number, $N$, of electrons that must be added to or removed from the object for the object to remain motionless above the charged plane.

Given that at time $t_i$, the kinetic energy of a particle is $30.0 \mathrm{~J}$ and the potential energy of the system to which it belongs is $10.0 \mathrm{~J}$. At some later time $t_f$, the kinetic energy of the particle is $18.0 \mathrm{~J}$. If the potential energy of the system at time $t_f$ is $5.00 \mathrm{~J}$, are there any nonconservative forces acting on the particle? Explain.

A teacher says the following in a lesson: "The Earth has two tides per day, not just one. Tides are caused by the gravity of the Moon acting on the oceans. The Moon, however, only passes overhead once per day. That explains the tide on the side of the planet facing the Moon. What explains the fact that there is another tide on the side facing away from the Moon?
Choose the most appropriate notes you might take
A. Earth has tides.
B. Earth, tides, there are 2 per day
C. Earth, tides, caused by Moon's gravity, 2 per day, why 2?
D. The Earth has two tides per day, not just one. Tides are caused by the gravity of the Moon acting on the oceans. The Moon, however, only passes overhead once per day. That explains the tide on the side of the planet facing the Moon. What explains the fact that there is another tide on the side facing away from the Moon?

A person of mass $M$ lies on the floor doing leg raises. His leg is $95 \mathrm{~cm}$ long and pivots at the hip. Treat his legs (including feet) as uniform cylinders, with both legs comprising $34.5 \%$ of body mass, and the rest of his body as a uniform cylinder comprising the rest of his mass. He raises both legs $50.0^{\circ}$ above the horizontal. (c) Since the center of mass of his body rises, there must be an external force acting. Identify this force.

A platform is rotating at an angular speed of 2.2 rad/s. A block is resting on this platform at a distance of 0.30 m from the axis. The coefficient of static friction between the block and the platform is 0.75. Without any external torque acting on the system, the block is moved toward the axis. Ignore the moment of inertia of the platform and determine the smallest distance from the axis at which the block can be relocated and still remain in place as the platform rotates.

(1) Two external forces, $\langle 40,-70,0\rangle\ \mathrm{N}$ and $\langle 20,10,0\rangle\ \mathrm{N},$ act on a system. What is the net force acting on the system? (2) A hockey puck initially has momentum $\langle 0,2,0\rangle\ \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}.$ It slides along the ice, gradually slowing down, until it comes to a stop. (a) What was the impulse applied by the ice and the air to the hockey puck? (b) It took 3 seconds for the puck to come to a stop. During this time interval, what was the net force on the puck by the ice and the air (assuming that this force was constant)?

A long, straight wire containing a semicircular region of radius $0.95 \mathrm{~m}$ is placed in a uniform magnetic field of magnitude $2.20 \mathrm{~T}$. What is the net magnetic force acting on the wire when it carries a current of $3.40 \mathrm{~A}$? (what does symmetry tell you about the forces on the upper and lower halves of the semicircular region?)

According to the second law of thermodynamics, is the universe moving to a more ordered state or to a more disordered state?

A refrigerator moves heat from cold to warm. Why doesn't this violate the second law of thermodynamics?

The proportionality constant $k$ in Coulomb's law is huge in ordinary units, whereas the proportionality constant $G$ in Newton's law of gravitation is tiny. What does this indicate about the relative strengths of these two forces?

What does the inverse-square law tell you about the relationship between force and distance?

Why is charge usually transferred by electrons rather than by protons ?

A sled with a mass of $5.80 \mathrm{~kg}$ is pulled along the ground through a displacement given by $\overrightarrow{\mathbf{~d}}=(4.55 \mathrm{~m}) \hat{\mathbf{~x}}$. (Let the $x$ axis be horizontal and the $y$ axis be vertical.) How much work is done on the sled when the force acting on it is $\overrightarrow{\mathbf{~F}}=(2.89 \mathrm{~N}) \hat{\mathbf{x}}+$ $(0.131 \mathrm{~N}) \hat{\mathbf{y}}$ ?

Two plastic spheres, each carrying charge uniformly distributed throughout its interior, are initially placed in contact and then released. One sphere is 60.0 cm in diameter, has mass 50.0 g, and contains $-10.0 \mu C$ of charge. The other sphere is 40.0 cm in diameter, has mass 150.0 g, and contains $-30.0 \mu C$ of charge. Find the maximum acceleration and the maximum speed achieved by each sphere (relative to the fixed point of their initial location in space), assuming that no other forces are acting on them. (The uniformly distributed charges behave as though they were concentrated at the centers of the two spheres.)