This week we will discuss the following topics:
1. Rotational Dynamics : Angular displacement, Angular velocity, angular acceleration.
2. Rigid Body and Moment of Inertia
3. Angular Momentum, conservation of Angular Momentum and Torque with some examples of applications.
4. Mechanical Equilibrium and conditions of equilibrium
5. Elasticity, Plasticity and Hooke's Law
6. Parallel Forces and net torque
7. Coefficient of Elasticity, stress and strain.
In: Physics
The cable of the 1800 kg elevator cab in the figure snaps when the cab is at rest at the first floor, where the cab bottom is a distance d = 4.9 m above a spring of spring constant k = 0.33 MN/m. A safety device clamps the cab against guide rails so that a constant frictional force of 3.2 kN opposes the cab's motion. (a) Find the speed of the cab just before it hits the spring. (b) Find the maximum distance x that the spring is compressed (the frictional force still acts during this compression). (c) Find the distance (above the point of maximum compression) that the cab will bounce back up the shaft. (d) Using conservation of energy, find the approximate total distance that the cab will move before coming to rest.
(Assume that the frictional force on the cab is negligible when the cab is stationary.)
In: Physics
A 0.320 kg puck at rest on a horizontal frictionless surface is struck by a 0.220 kg puck moving in the positive x direction with a speed of 4.05 m/s. After the collision, the 0.220 kg puck has a speed of 1.29 m/s at an angle of ? = 60.0° counterclockwise from the positive x axis.
(a) Determine the velocity of the 0.320 kg puck after the collision. Express your answer in vector form.
vf = ___m/s
(b) Find the percent of kinetic energy lost in the collision.
100*?K/Ki = ___%
In: Physics
An object with a size r0 has a Reynolds number of 4 when it moves through a fluid at a speed v0. What is the Reynolds number for an object with a size 2r0 moving through the same fluid at a speed v0/2?
The answer is 4. Please explain why and what concepts were used to get to this answer!!!
In: Physics
Study Guide 1
1. A child sitting 1.70 m from the center of a merry-go-round moves with a speed of 1.85 m/s, Calculate the centripetal acceleration of the child and the net horizontal force exerted on the child. (mass m = 22.5 kg )
2. A horizontal force of 320 NN is exerted on a 2.0-kg ball as it rotates (at arm's length) uniformly in a horizontal circle of radius 0.90 m, Calculate the speed of the ball.
3. Two objects attract each other gravitationally with a force of 2.3×10−10 N when they are 0.65 mm apart. Their total mass is 4.6 kg, Find their individual masses.
4. Calculate the speed of a satellite moving in a stable circular orbit about the Earth at a height of 4840 km
5. A satellite of mass 5430 kg orbits the Earth and has a period of 6570 s . Determine the radius of its circular orbit, the magnitude of the Earth's gravitational force on the satellite, and the altitude of the satellite.
All answers with units included
In: Physics
Using the minimal action principle obtain the equation of motion of the free particle from the relativistic Lagrangian.
In: Physics
(i) Define in words the strength of an electric field at a given point in space.
(ii) An electron experiences an acceleration of magnitude 2.0 × 1013 ms−2 in the positive x-direction, due to a uniform electric field. Calculate the magnitude and direction of the electric field.
In: Physics
Helium has a mass of 4 atomic mass units and is the second lightest element after hydrogen.
(i) Calculate the most probable speed of a helium atom in a gas at 295K.
(ii) Sketch the Maxwell speed distributions of a helium gas and an argon gas at the same temperature.
In: Physics
(a) A helium lamp is used for an experiment to study the photoelectric effect. The visible part of the spectrum emitted from the lamp is split into its components using a glass prism, which reveals a yellow spectral line at 587nm and a blue spectral line at 447nm.
(i) Explain briefly the origin of the distinct lines of different colour.
(ii) Has blue or yellow light higher energy (per photon)? Justify your answer.
(iii) The refractive index of the glass prism is larger for blue light than for yellow. Will the direction of blue or yellow light change by a larger angle compared to the incident light? Justify your answer.
(iv) Has blue or yellow light higher velocity within the glass prism? Justify your answer.
(b) The yellow light and blue light from part (a) hit a piece of potassium with work function 2.29 eV.
(i) Calculate the energy of the emitted photoelectrons.
(ii) Electrons are fermions. State the difference between fermions and bosons in terms of their spin quantum number.
(iii) Briefly explain the meaning of the Pauli exclusion principle.
(iv) A helium ion with total charge −e has 3 electrons. Show that there are four different combinations of spin magnetic quantum number that these electrons can have. Justify your answer on the basis of the aufbau principle.
In: Physics
Show that the affine connection is not a true tensor (general relativity/cosmology)
In: Physics
A square membrane has all four sides (length a) tightly clamped. Some of its vibrational modes are also dampened by a clamp placed at the center of the membrane. Find the first four distinct vibrational frequencies of this "square drum."
In: Physics
1 The equation of a transverse wave on a string is ? = (2.0 ?) sin(20? − 600?). What is the wave speed of the wave and the linear density of the string if it has a tension of 15 ??
2 A block is in simple harmonic motion on the end of a spring with its position given by ?(?) = ? cos(?? + ?). If ? = ?/5 ???, then at ? = 0 ? what percentage of the total mechanical energy is potential energy?
In: Physics
The speed of the two planes is 52.7 m/s, with the first plane travelling at this velocity in the y-direction and the second plane travelling with this speed in the x-direction. The initial separation of the planes is 30.5 m. Find the time at which the separation of the planes is at its minimum.
In: Physics
A person is driving his car on some road and suddenly a police car stops him for speeding, the police-detected radar gun emits a wave whose frequency is 8.0 × 109 ??.
1. How do you think the mechanism by which you know how fast a moving car can go works?
2. Does it depend on the speed of the police car? Does it depend on the speed of the person's car?
3. Does it depend on the two speeds?
4. What role does frequency play?
5. What function does the wave velocity fulfill?
In: Physics
Two low-friction physics demo carts collide on a horizontal track. The first cart, with a mass of 0.154 kg , is moving to the right with a speed of 0.810 m/s . The second cart, with a mass of 0.299 kg , is moving to the left with a speed of 2.21 m/s . The carts collide in an elastic collision, such that the total kinetic energy after the collsion is equal to the total kinetic energy before the collision.
1. What is the final speed of the 0.154 kg cart?
2. What is the direction of the final velocity of the 0.154 kg cart?
3. What is the final speed of the 0.299 kg cart?
4. What is the direction of the final velocity of the 0.299 kg cart?
In: Physics