The drawing shows identical springs that are attached to a box in two different ways. Initially, the springs are unstrained. The box (m = 3 kg) is then pulled to the right and released. In each case the initial displacement of the box is the same. The force constant k is 800 N/m. Find ω (rad/s) of the spring systems. The answer must be rounded to one decimal place. Don't put any unit in the blank.
When the displacement in SHM is equal to 1/7 of the amplitude xm, what fraction of the total energy is (a) kinetic energy and (b) potential energy? (c) At what displacement, in terms of the amplitude, is the energy of the system half kinetic energy and half potential energy? (Give the ratio of the answer to the amplitude) (a) Number Units (b) Number Units (c) Number Units *amplitude
An object has a charge of −1.9 μC. How many electrons must be removed so that the charge becomes +3.6 μC? Number Units
An object carries a charge of −6.3 μC, while another carries a charge of −2.0 μC. How many electrons must be transferred from the first to the second object so that both objects have the same charge? Number of electrons = Number Units
Question 3 (6 pts): The 100−g bullet traveling at 600 m/s strikes the 4−kg block centrally and is embedded within it. If the block slides on a smooth horizontal plane with a velocity of 12 m/s in the direction shown prior to impact, determine the velocity v2 of the block and embedded bullet immediately after impact.
The figure above shows a bullet of mass 200 g traveling horizontally towards the east with a speed of 400 m/s, which strikes a block of mass 1.5 kg that is initially at rest on a frictionless table. After striking the block, the bullet is embedded in the block and the block and the bullet move together as one unit. What is the magnitude and direction of the block/bullet combination immediately after impact? 25 m/s east 36 m/s west 47 m/s east 58 m/s west
A bullet is fired horizontally at a stationary 7.0 kg target. The target sits on a frictionless horizontal surface and is connected to a spring on the backside of the target. The spring has a spring constant of 5000 N/m. The 11.0 g bullet is traveling horizontally at 675 m/s the moment before it strikes the target. After 1 ms, the bullet is embedded into the target and begins to oscillate. Ignore air resistance. (a) Determine the speed of the block immediately after the collision. Hint: what quantity is conserved during the collision? (b) Find the period and amplitude of the resulting simple harmonic motion. (c) Find the initial phase of the resulting simple harmonic motion. Hint: note that the block is at its equilibrium position x = 0 at t = 0. (d) On three separate graphs, plot the position vs. time, velocity vs. time, and acceleration vs. time for the system starting when the bullet is fully embedded into the target. Be sure to clearly label your axes and the scale of each graph. (e) On a single graph, plot the potential energy, kinetic energy, and total mechanical energy as a function of time for the system starting when the bullet is fully embedded into the target. Be sure to clearly label your axes and the scale of your graph.
A ball is launched up a semicircular chute in such a way that at the top of the chute, just before it goes into free fall, the ball has a centripetal acceleration of magnitude 2 g. (Figure 1) figure 1 of 1 Part A How far from the bottom of the chute does the ball land? Your answer for the distance the ball travels from the end of the chute should contain R. View Available Hint(s) D =
The 80-g bullet is fired with velocity 720 m/s through a 5 kg box placed on the floor. The bullet then exits the box with velocity 500 m/s and the box is observed to slide a distance 3.5 m before coming to rest. Find the coefficient of kinetic friction between the box and the floor.
A bullet (W1 = 2.0 oz) with a is fired horizontally with a velocity v1 = 1780 ft/sec into the block (W2 = 6.3 lb) of soft wood initially at rest on the horizontal surface. The bullet emerges from the block with the velocity v2 = 1265 ft/sec, and the block is observed to slide a distance of d = 9.6 ft before coming to rest. Determine the coefficient of kinetic friction μk between the block and the supporting surface. Answer: μk =
Suppose that 2 J of work is needed to stretch a spring from its natural length of 32 cm to a length of 49 cm. (a) How much work (in J) is needed to stretch the spring from 36 cm to 41 cm? (Round your answer to two decimal places.) J (b) How far beyond its natural length (in cm) will a force of 10 N keep the spring stretched? (Round your answer one decimal place.) cm
After striking the block, the bullet is embedded in the block and the block and the bullet move together as one unit. (a) What are the magnitude (in m/s) and direction of the velocity of the block/bullet combination immediately after the impact? magnitude m/s direction (b) What are the magnitude (in N⋅s) and direction of the impulse by the block on the bullet? magnitude N⋅s direction (c) What are the magnitude (in N⋅s) and direction of the impulse from the bullet on the block? magnitude N⋅s direction N
A 4.41-g bullet is moving horizontally with a velocity of +354 m/s, where the sign + indicates that it is moving to the right (see part a of the drawing). The bullet is approaching two blocks resting on a horizontal frictionless surface. Air resistance is negligible. The bullet passes completely through the first block (an inelastic collision) and embeds itself in the second one, as indicated in part b. Note that both blocks are moving after the collision with the bullet. The mass of the first block is 1199 g, and its velocity is +0.644 m/s after the bullet passes through it. The mass of the second block is 1576 g . (a) What is the velocity of the second block after the bullet imbeds itself? (b) Find the ratio of the total kinetic energy after the collision to that before the collision. (a) Before collision (b) After collision (a) vblock2 = Number Units (b) KEafter/KEbefore = Number Units
Mary is at a gathering where there is a clarinet player in the background. The clarinets is a pipe open on one end, and has a length L = 35 cm. The clarinet emits sound waves with the oscillation pattern shown in the figure. The speed of sound in air is vs = 343 m/s, and the density of air is ρ = 1.293 kg/m3. (a) (5 pts) What is the frequency of this pattern in Hertz? What is the angular frequency? (b) (5 pts) When Mary is at a distance of r = 3 m, as shown in the figure, the sound level she hears is 67 dB , what is the intensity of the sound at that distance? (c) (5 pts) What is the displacement amplitude of the wave at 5 m , where Mary is standing in part (b)?
As shown in the figure below, a bullet is fired at and passes through a piece of target paper suspended by a massless string. The bullet has a mass m, a speed v before the collision with the target, and a speed (0.536)v after passing through the target. (a) Before collision (b) After collision The collision is inelastic and during the collision, the amount of energy lost is equal to a fraction [(0.443)KEb BC ] of the kinetic energy of the bullet before the collision. Determine the mass M of the target and the speed V of the target the instant after the collision in terms of the mass m of the bullet and speed v of the bullet before the collision. (Express your answers to at least 3 decimals.) V = v M = m
The figure below shows the velocity, v, of an object (in meters /sec). Estimate the total distance the object traveled between t = 0 and t = 18. The total distance traveled is approximately meters.
The figure shows an approximate plot of force magnitude F versus time t during the collision of a 61 g Superball with a wall. The initial velocity of the ball is 37 m/s perpendicular to the wall, in the negative direction of an x axis. It rebounds directly back with approximately the same speed, also perpendicular to the wall. What is Fmax , the maximum magnitude of the force on the ball from the wall during the collision? Number Units
In Figure (1), a 3.50 g bullet is fired horizontally at two blocks at rest on a frictionless table. The bullet passes through block 1 (mass 1.44 kg) and embeds itself in block 2 (mass 1.97 kg). The blocks end up with speeds v1 = 0.610 m/s and v2 = 1.38 m/s (see Figure (2)). Neglecting the material removed from block 1 by the bullet, find the speed of the bullet as it (a) leaves and (b) enters block 1. (1) (2) (a) Number Units (b) Number Units
The figure gives the lateral magnification m of an object versus the object distance p from a spherical mirror as the object is moved along the mirror's central axis through a range of values for p. The horizontal scale is set by ps = 15.0 cm. What is the magnification of the object when the object is 24 cm from the mirror? Number Units
In the figure, two particles, each with mass m = 0.90 kg, are fastened to each other, and to a rotation axis at O, by two thin rods, each with length d = 6.0 cm and mass M = 1.3 kg. The combination rotates around the rotation axis with angular speed ω = 0.32 rad/s. Measured about O, what is the combination's (a) rotational inertia and (b) kinetic energy? (a) Number Units (b) Number Units
To work this problem, use the fact that the image formed by the first surface becomes the object for the second surface. The figure below shows a piece of glass with index of refraction n = 1.50 surrounded by air. The ends are hemispheres with radii R1 = 2.00 cm and R2 = 4.00 cm, and the centers of the hemispherical ends are separated by a distance of d = 8.10 cm. A point object is in air, a distance of p = 1.05 cm from the left end of the glass. (a) Locate the image of the object due to refraction at the two spherical surfaces. cm to the right of the second surface (b) Is the image real or virtual? real virtual
In the figure, block 1 has mass m1 = 467 g, block 2 has mass m2 = 540 g, and the pulley is on a frictionless horizontal axle and has radius R = 4.70 cm. When released from rest, block 2 falls 76.0 cm in 3.40 s without the cord slipping on the pulley. (a) What is the magnitude of the acceleration of the blocks? What are (b) tension T2 (the tension force on the block 2 ) and (c) tension T1 (the tension force on the block 1)? (d) What is the magnitude of the pulley's angular acceleration? (e) What is its rotational inertia? Caution: Try to avoid rounding off answers along the way to the solution. Use g = 9.81 m/s2. (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units
The uniform solid block in the figure has mass 24.6 kg and edge lengths a = 0.638 m, b = 1.97 m, and c = 0.133 m. Calculate its rotational inertia about an axis through one corner and perpendicular to the large faces. Number Units
The body in the figure is pivoted at O, and two forces act on it as shown. If r1 = 2.07 m, r2 = 3.06 m, F1 = 4.95 N, F2 = 5.08 N, θ1 = 79.0∘, and θ2 = 54.0∘, what is the net torque about the pivot? Number Units
A 44.7-kg skater is standing at rest in front of a wall. By pushing against the wall she propels herself backward with a velocity of −2.17 m/s. Her hands are in contact with the wall for 0.956 s. Ignore friction and wind resistance. Find the average force she exerts on the wall (which has the same magnitude, but opposite direction, as the force that the wall applies to her). Note that this force has direction, which you should indicate with the sign of your answer. Number Units
A spring with spring constant 24 N/m is compressed a distance 8.0 cm by a ball with a mass of 217.5 g (see figure below). The ball is then released and rolls without slipping along a horizontal surface, leaving the spring at point A. The process is repeated, using a block instead, with a mass identical to that of the ball. The block compresses the spring by 8.0 cm and is also released, leaving the spring at point A. Assume the ball rolls, but ignore other effects of friction. (Assume that the ball is a solid ball.) (a) What is the speed of the ball at point B? m/s (b) What is the speed of the block at point B? m/s
How much work must be done to increase the speed of an electron from rest to (a) 0.552c, (b) 0.901c, and (c) 0.9971c? (a) Number Units (b) Number Units (c) Number Units
How much work (in J) is done by the boy pulling his sister 27 m in a wagon as shown in the figure below? (i) Assume no friction acts on the wagon. (Assume d = 27 m and F = 44 N. Enter a number.) W = J
A lumberjack (mass = 107 kg) is standing at rest on one end of a floating log (mass = 214 kg) that is also at rest. The lumberjack runs to the other end of the log, attaining a velocity of +3.45 m/s relative to the shore, and then hops onto an identical floating log that is initially at rest. Neglect any friction and resistance between the logs and the water. (a) What is the velocity of the first log (again relative to the shore) just before the lumberjack jumps off? (b) Determine the velocity of the second log (again relative to the shore) if the lumberjack comes to rest relative to the second log. (a) Number Units (b) Number Units
In the figure, a 3.7 kg block is accelerated from rest by a compressed spring of spring constant 640 N/m. The block leaves the spring at the spring's relaxed length and then travels over a horizontal floor with a coefficient of kinetic friction μk = 0.234. The frictional force stops the block in distance D = 7.8 m. What are (a) the increase in the thermal energy of the block-floor system, (b) the maximum kinetic energy of the block, and (c) the original compression distance of the spring? (a) Number Units (b) Number Units (c) Number Units
An X-ray photon is scattered at an angle of θ = 180.0∘ from an electron that is initially at rest. After scattering, the electron has a speed of 5.60×106 m/s. Find the wavelength of the incident X-ray photon.
Switch S in in the figure is closed at time t = 0, to begin charging an initially uncharged capacitor of capacitance C = 15.1 μF through a resistor of resistance R = 21.2 Ω. At what time is the potential across the capacitor equal to that across the resistor? Number Units
The drawing shows a skateboarder moving at 7.10 m/s along a horizontal section of a track that is slanted upward by θ = 51.0∘ above the horizontal at its end, which is 0.710 m above the ground. When she leaves the track, she follows the characteristic path of projectile motion. Ignoring friction and air resistance, find the maximum height H to which she rises above the end of the track.
A car (mass = 1170 kg) is traveling at 33.0 m/s when it collides head-on with a sport utility vehicle (mass = 2690 kg) traveling in the opposite direction. In the collision, the two vehicles come to a halt. At what speed was the sport utility vehicle traveling? Before collision After collision Number Units
The three displacement vectors in the drawing have magnitudes of A = 4.06 m, B = 5.26 m, and C = 3.12 m. Find the resultant ((a) magnitude and (b) directional angle) of the three vectors by means of the component method. Express the directional angle as an angle above the positive or negative x axis. (a) Number Units (b) Number Units