Physics 40S WS Zanzibar - Review Questions

The rate at which velocity changes over time. It's a vector quantity, meaning it has both magnitude (speed) and direction.

The product of an object's mass and its velocity. It measures the object's inertia in motion.

The force that acts on an object moving in a circular path, directed towards the center of the circle. It keeps the object from moving in a straight line.

The work done by a force to move an object over a certain distance. It's a scalar quantity, measured in Joules.

The ability to do work. It's a scalar quantity, measured in Joules.

The force of attraction between two objects with mass. The strength of the force depends on their masses and the distance between them.

The property of a material that resists the motion of an object sliding across its surface.

The force exerted by a magnetic field on a moving electric charge. It's a fundamental force of nature.

The force on a current-carrying wire in a magnetic field is given by the equation F = BILsin(theta), where F is the force, B is the magnetic field strength, I is the current, L is the length of the wire, and theta is the angle between the wire and the magnetic field. In this case, we have B = 0.7 Tesla, I = 3 Ampere, L = 9 cm = 0.09 m, and theta = 41 degrees. Plugging these values into the equation, we get F = 0.7 * 3 * 0.09 * sin(41) = 0.12 Newtons. Therefore, the magnitude of the force felt by the wire is 0.12 Newtons.

The spring constant (k) is a measure of the stiffness of a spring. It is defined as the force required to stretch or compress the spring by one unit of length. In this case, the spring constant is 200 N/m, which means that it takes 200 Newtons of force to stretch or compress the spring by 1 meter. The force required to 'load' the spring bumper is equal to the force exerted by the spring when it is compressed by a certain distance. This force can be calculated using Hooke's Law: F = -kx, where F is the force, k is the spring constant, and x is the displacement from the equilibrium position. In this case, the displacement is 40 cm = 0.4 m. Plugging these values into Hooke's Law, we get F = -200 * 0.4 = -80 Newtons. The negative sign indicates that the force is in the opposite direction to the displacement (i.e., the force is pushing back on the mass).

The work done in 'loading' a spring is equal to the energy stored in the spring when it is compressed or stretched. This energy is known as elastic potential energy. It can be calculated using the equation PE = (1/2)kx^2, where PE is the elastic potential energy, k is the spring constant, and x is the displacement from the equilibrium position. In this case, the displacement is 40 cm = 0.4 m. Plugging these values into the equation, we get PE = (1/2) * 200 * (0.4)^2 = 16 Joules. Hence, the work done in 'loading' the spring is 16 Joules.

The maximum speed of the mass can be calculated using the conservation of energy. The total mechanical energy of the system is conserved, meaning that the sum of kinetic energy (KE) and potential energy (PE) remains constant. Initially, the mass is at rest and the spring is compressed, so the total energy is equal to the potential energy of the spring. When the mass is released, the potential energy of the spring is converted into kinetic energy of the mass. At the moment the mass reaches its maximum speed, all the potential energy is converted into kinetic energy. Therefore, we can equate the initial potential energy of the spring to the final kinetic energy of the mass. The kinetic energy of an object is given by the equation KE = (1/2)mv^2, where m is the mass and v is the speed. Plugging in the values we have, we get 16 = (1/2) * 4 * v^2, which results in v = 2 m/s. Therefore, the maximum speed of the mass is 2 m/s.

The magnetic field strength inside a long solenoid is given by the equation B = μ₀nI, where B is the magnetic field strength, μ₀ is the permeability of free space (4π × 10^-7 T·m/A), n is the turn density (number of turns per unit length), and I is the current. In this case, the solenoid has 40 turns over a length of 20 cm = 0.2 m, so the turn density is n = 40 / 0.2 = 200 turns/m. The current flowing through the solenoid is 5 mA = 5 × 10^-3 A. Plugging these values into the equation, we get B = (4π × 10^-7) * 200 * (5 × 10^-3) = 1.26 × 10^-3 Tesla. Therefore, the magnitude of the magnetic field at the center of the solenoid is 1.26 × 10^-3 Tesla.

The turn density (η) of a solenoid is defined as the number of turns per unit length. It is a measure of how tightly the coils of the solenoid are wound. In this case, the solenoid has 40 turns over a length of 20 cm = 0.2 m, so the turn density is η = 40 / 0.2 = 200 turns/m.

The speed of a satellite in orbit around a planet can be calculated using the equation v = √(GM/r), where v is the speed, G is the gravitational constant (6.67 × 10^-11 N·m^2/kg^2), M is the mass of the planet, and r is the distance from the center of the planet to the satellite. In this case, the mass of the Earth is M = 6.0 × 10^24 kg, and the altitude of the satellite is 22 km, which means that the distance from the center of the Earth to the satellite is r = 6400 km + 22 km = 6422 km = 6.422 × 10^6 m. Plugging these values into the equation, we get v = √((6.67 × 10^-11) * (6.0 × 10^24) / (6.422 × 10^6)) = 7894 m/s. Therefore, the speed of the satellite is 7894 m/s. The period of orbit is the time it takes for the satellite to complete one orbit around the Earth. It can be calculated using the equation T = 2πr/v, where T is the period, r is the radius of the orbit, and v is the speed. Plugging in the values we know, we get T = 2π(6.422 × 10^6) / 7894 = 5108 seconds which is about 1.42 hours.

The electric field at a point due to a point charge is given by the equation E = kQ/r^2, where E is the electric field strength, k is Coulomb's constant (8.99 × 10^9 N·m^2/C^2), Q is the charge, and r is the distance from the charge. In this case, the charge at point A is 4 µC = 4 × 10^-6 C, and the distance to point B is 30 cm = 0.3 m. Plugging these values into the equation, we get E = (8.99 × 10^9) * (4 × 10^-6) / (0.3)^2 = 3.99 × 10^5 N/C. The electric field is directed from the positive charge at point A towards the negative charge at point B. Therefore, the electric field at point B is 3.99 × 10^5 N/C directed from A to B.