The roller coaster in Figure Q2a starts at the point A from rest. The track is designed in a way such that the passengers should experience no more than 4 times their weights at point B and no less than zero weight at point C. Find the limits on the heights h1 and h2. Neglect friction. Figure Q2a
In the figure shown below, one end of a cord is attached to the floor and the other end is attached to a small set of essentially massless wheels through a slot in a track on which the wheels roll without friction. As a result of this arrangement, the upper end of the cord is essentially free. At equilibrium, the cord is vertical and motionless. When it carries a small amplitude wave, the cord is under a uniform tension of 1.20 N. The cord has a mass of 5.80 g and a length of 85.0 cm. (a) Find the speed (in m/s) of the transverse waves in the cord. m/s (b) The cord's vibration possibilities are a set of standing-wave states, each with a node at the fixed bottom end and an antinode at the free top end. Find the node-antinode distances (in m) for the first three harmonics. Enter your answers from the lowest to the highest harmonic. m m m (c) Find the frequency (in Hz) of each of these states. (Enter your answers from simplest to more complicated.) Hz Hz Hz (d) What If? The wheels get stuck on the track and are unable to move, hence making the cart stationary. Determine the node-antinode distance (in m) and frequency of vibration (in Hz) for the third harmonic. distance m frequency Hz
A sample of radium 88 224 Ra (atomic mass = 224.020186 u, T1/2 = 3.66 days) contains N0 = 1.83×1021 nuclei and undergoes a decay to produce radon 86 220 Rn (atomic mass = 220.011368 u). The atomic mass of an a particle is 4.002603 u . The latent heat of fusion for water is 33.5×104 J/kg. With the energy released in 3.66 days, how many kilograms of ice could be melted at 0∘C
According to Hooke's Law, the force required to hold the spring stretched xm beyond its natural length is given by f(x) = kx, where k is the spring constant. Suppose that 3 J of work is needed to stretch a spring from its natural length of 34 cm to a length of 49 cm. Find the exact value of k, in N/m. k = N/m (a) How much work (in J) is needed to stretch the spring from 42 cm to 44 cm ? (Round your answer to two decimal places.) (b) How far beyond its natural length (in cm) will a force of 25 N keep the spring stretched? (Round your answer one decimal place.) cm
A puck of mass m = 1.00 kg slides in a circle of radius r = 21.0 cm on a frictionless table while attached to a hanging cylinder of mass M = 3.80 kg by a cord through a hole in the table. What speed keeps the cylinder at rest? Number Units
In the figure above, block 1 of mass m1 slides from rest along a frictionless ramp from height h and then collides with stationary block 2, which has mass m2 = 3m1. After the collision, block 2 slides into a region where the coefficient of kinetic friction is μk and comes to a stop in distance d within that region. NOTE: Express your answer in terms of the variables given, and g. (a) What is the value of distance d if the collision is elastic? d = (b) What is the value of distance d if the collision is completely inelastic? d =
A wheel of radius 0.155 m, which is moving initially at 52.1 m/s, rolls to a stop in 206 m. Calculate the magnitudes of (a) its linear acceleration and (b) its angular acceleration. (c) The wheel's rotational inertia is 0.430 kg⋅m2 about its central axis. Calculate the magnitude of the torque about the central axis due to friction on the wheel. (a) Number Units (b) Number Units (c) Number Units
A track is mounted on a large wheel that is free to turn with negligible friction about a vertical axis (see the figure below). A toy train of mass m is placed on the track and, with the system initially at rest, the train's electrical power is turned on. The train reaches a steady speed of 0.136 m/s with respect to the track. What is the angular speed of the wheel if its mass is 2.82 m and its radius is 0.343 m? (Treat the wheel as a hoop, and neglect the mass of the spokes and hub.) Number Units
A person is on a playground swing, motionless at the highest point of their arc. a. What energy transformation takes place as they swing back down to the lowest point of their motion? b. On the diagram at right, please label: i. the places where each energy is at a maximum. ii. the place where the velocity of the person is at a maximum. iii. the places where the height of the person is at a maximum. c. If there is no friction in the system, is energy conserved perfectly along the person's swinging motion? d. What's the equation for kinetic energy? e. What's the equation for Ug in terms of m, g and h ? f. What's the equation for Ug in terms of m, g, L and θ? g. For m = 50 kg, L = 4.0 m and θ = 60∘, what is the maximum velocity of the person?
The mass of a string is 6.0×10−3 kg, and it is stretched so that the tension in it is 170 N. A transverse wave traveling on this string has a frequency of 370 Hz and a wavelength of 0.62 m. What is the length of the string? Number Units
(a) What is the angular speed ω about the polar axis of a point on Earth's surface at a latitude of 34∘N? (Earth rotates about that axis.) (b) What is the linear speed v of the point? What are (c) ω and (d) v for a point at the equator? (Note: Earth radius equals 6370 km and let one day be 24 hours) (a) Number Units (b) Number Units (c) Number Units (d) Number Units
10: The system shown in the figure is released from rest with the spring in unstretched position. a) Find the linear speed of the 4 kg mass and the angular speed of the pulley when the 20 kg block slid 10 cm down the incline. b) How far the 20 kg will slide until it stops? c) How many revolutions will the pulley rotate before it stops?
A block of mass 0.5 kg is placed on a rough horizontal plane. If a force P = 2 tN is acts on the block at an angle α (tanα = 3/4). The friction coefficient is 0.4 when static and 0.3 when moving. Find the time at which the block start moving. Find the friction force at t = 2 sec. Find the acceleration and velocity of the block at t = 2 sec.
The graph in the figure shows the emf produced by a generator as a function of time t. The coil for the generator has an area of A = 0.150 m2 and consists of N = 14 turns. The coil rotates in a field of magnitude 0.250 T. (a) Determine the period of the motion. (b) What is the angular frequency of the rotating coil? (c) Find the value of the emf when t = 1/4 T, where T denotes the period of the coil motion. (d) What is the emf when t = 0.025 s? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
A 0.001 kg bullet is fired from a gun and lodges inside a wooden block of mass 0.2 kg. The block and bullet then slide on a rough floor with a coefficient of kinetic friction μk = 0.4 before coming to rest after sliding a distance of 3 m. Compare KEi, the initial kinetic energy of the bullet, with Wf, the work done by the frictional force between the block and the floor in stopping the block. KEi > Wf KEi = Wf KEi < Wf