Mechanics: Forces, Motion, and Orbits
A drone is hovering perfectly still in the air. Suddenly, the operator pushes the throttle, and the drone accelerates straight upward. Compare the upward force of lift to the downward force of gravity in both scenarios.
When hovering perfectly still, the upward force of lift is exactly equal to the downward force of gravity (net force is zero). When accelerating straight upward, the upward force of lift is greater than the downward force of gravity.
Two ice skaters of equal mass are skating toward each other at the exact same speed. They collide and hold onto each other. What is their final velocity immediately after the collision, and what physics principle explains this?
Their final velocity is 0 m/s (they stop completely). This is explained by the Law of Conservation of Momentum (their initial momentums were equal and opposite, cancelling out to zero).
A skateboarder drops into a frictionless half-pipe. At what point is their gravitational potential energy the lowest, and what happens to their kinetic energy at that exact point?
Their gravitational potential energy is lowest at the very bottom of the half-pipe. At this exact point, their kinetic energy is at its maximum (they are moving the fastest).
What is the fundamental difference between the diffraction of a wave and the refraction of a wave?
Diffraction is the bending of a wave around an obstacle or through an opening. Refraction is the bending of a wave as it passes through a boundary from one medium to another (caused by a change in speed).
The double-slit experiment produces a pattern of bright and dark bands on a screen, while the photoelectric effect shows light knocking electrons off a metal plate. Which model of light (wave or particle) does each experiment support?
The double-slit experiment supports the wave model of light (showing interference patterns). The photoelectric effect supports the particle model of light (showing individual photons knocking electrons loose).
The magnitude of the centripetal force acting on an object traveling in a horizontal, circular path will decrease if the
radius of the path is increased.
To figure out how to decrease the centripetal force (Fc), we need to look at where the variables are located in the fraction:
Variables in the numerator (m and v) have a direct relationship with force. If you increase mass or speed, the force increases.
The variable in the denominator (r) has an inverse relationship with force. If you increase the radius, you are dividing by a larger number, which makes the overall force decrease.
A woman with horizontal velocity v1 jumps off a dock into a stationary boat. After landing in the boat, the woman and the boat move with velocity v2 . Compared to velocity v1 , velocity v2 has
smaller magnitude and the same direction.
This scenario is an example of a perfectly inelastic collision, which is governed by the Law of Conservation of Momentum. The total momentum of the system before the woman lands in the boat must equal the total momentum of the system after she lands.
A boat weighing 900 newtons requires a horizontal force of 600 newtons to move it across the water at 15 meters per second. The boat’s engine must provide energy at the rate of 1. 2.5 × 10-2 J 2. 4.0 × 101 W 3. 7.5 × 103 J 4. 9.0 × 103 W
Equation - P = F x v
P = 9.0 x 103W
As a car approaches a pedestrian crossing the road, the driver blows the horn. Compared to the sound wave emitted by the horn, the sound wave detected by the pedestrian has a
higher frequency and a higher pitch
The Concept: This scenario is a classic example of the Doppler Effect . This principle describes how the frequency of a wave changes when the source and the observer are moving relative to one another.
The Physics: As the car moves toward the pedestrian, it is essentially "catching up" to the sound waves it is emitting from its horn. This compresses the physical space between the sound waves in front of the car, causing them to bunch up.
Frequency: Because the waves are bunched closer together, they reach the pedestrian's ear more frequently (more waves hit the ear per second). This translates to a higher frequency.
Pitch: In terms of human hearing, frequency directly determines pitch. Therefore, an increase in the sound wave's frequency is perceived by the pedestrian as a higher pitch.
The energy produced by the complete conversion of 2.0 × 10-5 kilogram of mass into energy is
Equation. - E= mc2
E = 1.8 TJ
E = 18.0 x 1011J
E = 1.8 x 1012J
A "Space Tug" is designed to capture satellite debris. Why does the tug need to maintain a specific, constant horizontal speed to stay in a stable circular orbit around Earth, rather than just firing its thrusters upward away from the planet?
To stay in a stable circular orbit, the tug must move horizontally fast enough so that as gravity pulls it downward, the surface of the Earth curves away at the exact same rate (it is in constant free-fall). If it just fired straight up, it would lose speed, stop, and fall straight back down to Earth.
Maritime engineers use massive rubber fendering systems on docks. Using the impulse-momentum theorem, explain exactly how these rubber fenders prevent a docking ship's hull from cracking compared to hitting a bare concrete dock.
The impulse-momentum theorem states that Impulse (F x t) equals the change in momentum. The rubber fenders compress, which increases the time (t) of the collision. By increasing the time it takes the ship to stop, the average impact force (F) is significantly decreased.
Modern electric vehicles (EVs) use "regenerative braking". When the driver takes their foot off the accelerator, the car slows down, and the battery charges. Explain this process using the Law of Conservation of Energy.
Energy cannot be created or destroyed, only transformed. Instead of converting the car's kinetic energy into wasted heat via friction brakes, the electric motor acts as a generator, converting the kinetic energy into electrical energy, which is then stored as chemical potential energy in the battery.
A city is installing 5G cell towers. They use 24 GHz waves for incredibly fast data transfer in open areas, but use 600 MHz waves to ensure people deep inside concrete apartment buildings still get a signal. Why is the 600 MHz wave better at reaching inside the buildings?
600 MHz waves have a much longer wavelength (and lower frequency) than 24 GHz waves. Longer wavelengths are much better at diffracting around obstacles and penetrating solid materials like concrete without being absorbed or reflected.
Why is UV-C radiation frequently used in hospital sterilization tools to kill bacteria, whereas the microwaves used to heat up your lunch are harmless to your cellular DNA?
UV-C radiation has a much higher frequency, meaning its individual photons carry much more energy (E=hf). UV-C photons have enough energy to break chemical bonds and damage DNA (ionizing). Microwave photons have very low energy and can only make molecules vibrate/heat up.
A baby and a stroller have a total mass of 20 kilograms. A force of 36 newtons keeps the stroller moving in a circular path with a radius of 5.0 meters. Calculate the speed at which the stroller moves around the curve. [Show all work, including the equation and substitution with units.]
Equation Fc = mv2/r
v = 3.0 m/s
A 1.0-kilogram laboratory cart moving with a velocity of 0.50 meter per second due east collides with and sticks to a similar cart initially at rest. After the collision, the two carts move off together with a velocity of 0.25 meter per second due east. The total momentum of this frictionless system is 1. zero before the collision 2. zero after the collision 3. the same before and after the collision 4. greater before the collision than after the collision.
Same before and after the collision
This question is testing the Law of Conservation of Momentum. This law states that in a closed, isolated system (like the "frictionless system" mentioned in the problem), the total momentum before a collision must exactly equal the total momentum after the collision.
The amount of work done against friction to slide a box in a straight line across a uniform, horizontal floor depends most on the 1. time taken to move the box 2. distance the box is moved 3. speed of the box 4. direction of the box’s motion
Distance the box is moved
In this scenario, the force doing the work is friction. Because the floor is uniform and horizontal, and the mass of the box isn't changing, the force of friction remains constant the entire time the box is sliding. Since the force (F) is a constant number, the total amount of Work (W) done depends entirely on the distance (d) the box is pushed. The further you push it, the more work you have to do against friction.
A 512-hertz sound wave travels 100 meters to an observer through air at STP. What is the wavelength of this sound wave?
Equation - v = f x lambda
lamba = 0.646 m
After a uranium nucleus emits an alpha particle, the total mass of the new nucleus and the alpha particle is less than the mass of the original uranium nucleus. Explain what happens to the missing mass.
Converted into Energy
the Law of Conservation of Mass-Energy dictates that this missing mass wasn't destroyed or lost. Instead, it was completely transformed into energy. his newly created energy is released during the decay. It primarily manifests as the kinetic energy of the products (causing the alpha particle to shoot outward at extremely high speeds and the new nucleus to recoil) and sometimes as high-energy electromagnetic radiation (gamma rays).
Two small asteroids, Asteroid A ( 4 x 105 kg) and Asteroid B (2 x 105kg), are separated by a distance of 1,000 m. Calculate the magnitude of the gravitational force of attraction between them. (G=6.67 x 10-11Nm/kg2)
Equation - Fg=Gm1m2/r2
Fg= 5.34 x 10-6N
A 1,200 kg car traveling at 15 m/s crashes into a barrier and is brought to rest in 0.2 seconds. Calculate the average impact force exerted on the car during the crash.
Equation - F(delta t) = m(delta v)
F = -90,000 Newtons.
A crane lifts a 500 kg steel beam vertically upward a distance of 20 m at a constant speed in 40 seconds. Calculate the mechanical power generated by the crane. (Use g= 9.81 m/s2)
W = F x d
P = W/t
P = 2,452.5 Watts
A sonar signal traveling through seawater has a frequency of 50,000 Hz and a wavelength of 0.03 m. Calculate the speed of the sonar wave in the seawater.
v = f x lambda
v = 1,500 m/s
An atom emits a photon of light with an energy of 4.5 x 10-19J. Calculate the frequency of this photon. (h=6.63 x 10-34Js)
Equation - E=hf
E = 6.79 x 1014Hz