A force of 4.8 N acts on a 14 kg body initially at rest. Compute the work done by the force in (a) the first, (b) the second, and (c) the third seconds and (d) the instantaneous power due to the force at the end of the third second.
In the figure, two skaters, each of mass 50.8 kg, approach each other along parallel paths separated by 3.82 m. They have opposite velocities of 1.92 m/s each. One skater carries one end of a long pole of negligible mass, and the other skater grabs the other end as she passes. The skaters then rotate about the center of the pole. Assume that the friction between skates and ice is negligible. What are (a) the radius of the circle, (b) the angular speed of the skaters, and (c) the kinetic energy of the two-skater system? Next, the skaters each pull along the pole until they are separated by 2.73 m. What then are (d) their angular speed and (e) the kinetic energy of the system? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units
What's your normal body temperature? It may not be 98.6∘F, the oft-quoted average that was determined in the nineteenth century. A more recent study has reported an average temperature of 98.2∘F. What is the difference between these averages, expressed in Celsius degrees? Number Units
In unit-vector notation, what is the torque about the origin on a particle located at coordinates (0, -3.54 m, 8.58 m) due to (a) force F→1 with components F1x = 9.69 N and F1y = F1z = 0, and (b) force F→2 with components F2x = 0, F2y = 9.60 N, F2z = 9.72 N?
In the arrangement of the first figure, we gradually pull the block from x = 0 to x = +3.0 cm, where it is stationary. The second figure gives the work that our force does on the block. The scale of the figure's vertical axis is set by W5 = 3.0 J. We then pull the block out to x = +7.0 cm and release it from rest. How much work does the spring do on the block when the block moves from xi = +7.0 cm to (a) x = +3.0 cm, (b) x = −1.0 cm, and (c) x = −7.0 cm? (a) (b) (c)
A yo-yo has a rotational inertia of 793 g⋅cm2 and a mass of 85.6 g. Its axle radius is 2.54 mm, and its string is 107 cm long. The yo-yo rolls from rest down to the end of the string. (a) What is the magnitude of its linear acceleration? (b) How long does it take to reach the end of the string? As it reaches the end of the string, what are its (c) linear speed, (d) translational kinetic energy, (e) rotational kinetic energy, and (f) angular speed? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units Number Units
In the figure, what magnitude of force F→ applied horizontally at the axle of the wheel is necessary to raise the wheel over an obstacle of height h = 0.217 m? The wheel's radius is r = 0.627 m and its mass is m = 1.92 kg.
The figure shows two closed paths wrapped around two conducting loops carrying currents i1 = 8.8 A and i2 = 3.2 A. What is the value of the integral ∮B→ds→ for (a) path 1 and (b) path 2? (a) Number Units (b) Number Units
A cyclotron with dee radius 50.3 cm is operated at an oscillator frequency of 12.4 MHz to accelerate protons. (a) What magnitude B of magnetic field is required to achieve resonance? (b) At that field magnitude, what is the kinetic energy of a proton emerging from the cyclotron? Suppose, instead, that B = 1.81 T. (c) What oscillator frequency is required to achieve resonance now? (d) At that frequency, what is the kinetic energy of an emerging proton? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
The current density inside a long, solid, cylindrical wire of radius a = 4.2 mm is in the direction of the central axis and its magnitude varies linearly with radial distance r from the axis according to J = J0r/a, where J0 = 290 A/m2. Find the magnitude of the magnetic field at a distance (a) r = 0, (b) r = 3.3 mm and (c) r = 4.2 mm from the center. (a) Number Units (b) Number Units (c) Number Units
A certain commercial mass spectrometer is used to separate uranium ions of mass 3.92×10−25 kg and charge 3.20×10−19 C from related species. The ions are accelerated through a potential difference of 136 kV and then pass into a uniform magnetic field, where they are bent in a path of radius 1.43 m. After traveling through 180∘ and passing through a slit of width 0.846 mm and height 0.777 cm, they are collected in a cup. (a) What is the magnitude of the (perpendicular) magnetic field in the separator? If the machine is used to separate out 0.832 mg of material per hour, calculate (b) the current of the desired ions in the machine and (c) the thermal energy produced in the cup in 1.06 h. (a) Number Units (b) Number Units
A simple harmonic oscillator consists of a block of mass 1.20 kg attached to a spring of spring constant 410 N/m. When t = 0.780 s, the position and velocity of the block are x = 0.177 m and v = 2.930 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s? (a) Number Units (b) Number Units (c) Number Units
In Figure (a), a rectangular block is gradually pushed face-down into a liquid. The block has height d; on the bottom and top the face area is A = 5.50 cm2. Figure (b) gives the apparent weight Wapp of the block as a function of the depth h of its lower face. The scale on the vertical axis is set by Ws = 0.160 N. What is the density (in g/cm3) of the liquid? (a) (b)
Q1: (a) A mechanic pushes a 2.50×103 Kg car from rest to a speed of v, doing 5.00×103 J of work in the process. During this time, the car moves 25.0 m. Neglecting friction between car and road, find i. The velocity v, and ii. The horizontal force exerted on the car (b) A ball of mass m = 1.80 Kg is released from rest at a height h = 65.0 cm above a light vertical spring of force constant k as in the figure 1−a. The ball strikes the top of the spring and compresses it a distance d = 9.00 cm as in figure 1−b. Neglecting any energy losses during the collision, find: i. The speed of the ball as it touches the spring, and ii. the force constant of the spring Figure 1: Problem 1b Total points = 25 points Instructions: Write your answers in the space provided.
The figure shows capacitor 1 (C1 = 6.21 μF), capacitor 2 (C2 = 7.92 μF), and capacitor 3 (C3 = 8.14 μF) connected to a 13.7 V battery. When switch S is closed so as to connect uncharged capacitor 4 (C4 = 7.45 μF), (a) how much charge passes through point P from the battery and (b) how much charge shows up on capacitor 4? (a) Number Units (b) Number Units