Compute the flux of the vector field F→ = 6xi→ + yj→ + zk→ through the surface S, where S is the part of the surface z = −7x − 14y + 1, oriented upward, with (x, y) in the triangle R with vertices (0, 0), (0, 12), (3, 0). Enter an exact answer. ∫SF→⋅dA→ =
The figure shows two 24.8 kg ice sleds that are placed a short distance apart, one directly behind the other. A 3.96 kg cat initially standing on one sled jumps to the other one and then back to the first. Both jumps are made at a speed of 2.77 m/s relative to the ice. What are the final speeds of (a) the first sled and (b) the other sled?
Three uniform spheres of masses m1 = 2.50 kg, m2 = 4.00 kg, and m3 = 5.50 kg are placed at the corners of a right triangle (see figure below). Calculate the resultant gravitational force on the object of mass m2, assuming the spheres are isolated from the rest of the Universe. 10−11 N
A torque of 35.3 N⋅m is applied to an initially motionless wheel which rotates around a fixed axis. This torque is the result of a directed force combined with a friction force. As a result of the applied torque the angular speed of the wheel increases from 0 to 10.5 rad/s. After 6.10 s the directed force is removed, and the wheel comes to rest 60.6 s later. (a) What is the wheel's moment of inertia (in kg⋅m2)? kg⋅m2 (b) What is the magnitude of the torque caused by friction (in N⋅m)? N⋅m (c) From the time the directed force is initially applied, how many revolutions does the wheel go through? revolutions
A 45.2-kg girl is standing on a 149-kg plank. Both originally at rest on a frozen lake that constitutes a frictionless, flat surface. The girl begins to walk along the plank at a constant velocity of 1.54î m/s relative to the plank. (a) What is the velocity of the plank relative to the ice surface? î m/s (b) What is the girl's velocity relative to the ice surface? î m/s
An ∠C circuit like the one in the figure below contains an 60.0 mH inductor and a 18.0 μF capacitor that initially carries a 175 μC charge. The switch is open for t < 0 and is then thrown closed at t = 0. (a) Find the frequency (in hertz) of the resulting oscillations. Hz (b) At t = 1.00 ms, find the charge on the capacitor. μC (c) At t = 1.00 ms, find the current in the circuit. mA (d) What If? What are the first three times (in ms), after t = 0, when the capacitor is fully charged again? smallest value ms ms largest value ms
A block of mass m1 = 1.85 kg and a block of mass m2 = 6.20 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed wedge-shaped ramp makes an angle of θ = 30.0° as shown in the figure. The coefficient of kinetic friction is 0.360 for both blocks. (a) Draw force diagrams of both blocks and of the pulley. No file chosen (b) Determine the acceleration of the two blocks. (Enter the magnitude of the acceleration.) m/s2 (c) Determine the tensions in the string on both sides of the pulley. left of the pulley N right of the pulley
The figure shows a circular region of radius R = 2.50 cm in which a uniform electric flux is directed out of the plane of the page. The total electric flux through the region is given by ΦE = (4.00 mV⋅m/s)t, where t is in seconds. What is the magnitude of the magnetic field that is induced at radial distances (a) 1.50 cm and (b) 5.00 cm?
In the figure below, block 1 has mass m1 = 440 g, block 2 has mass m2 = 512 g, and the pulley, which is mounted on a horizontal axle with negligible friction, has radius R = 5.50 cm. When released from rest, block 2 falls 70.9 cm in 5.23 s without the cord slipping on the pulley. What is its rotational inertia of the pulley? Specify your answer in SI units up to 4 decimal places. Do not include units.
In the figure, a string, tied to a sinusoidal oscillator at P and running over a support at Q, is stretched by a block of mass m. Separation L = 0.8 m, linear density μ = 1.4 g/m, and the oscillator frequency f = 200 Hz. The amplitude of the motion at P is small enough for that point to be considered a node. A node also exists at Q. (a) What mass m allows the oscillator to set up the fourth harmonic on the string? (b) What standing wave mode, if any, can be set up if m = 3 kg (Give 0 if the mass cannot set up a standing wave)? (a) Number Units (b) Number Units
The figure shows a rigid structure consisting of a circular hoop of radius R and mass m, and a square made of four thin bars, each of length R and mass m. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of 3.3 s. If R = 1.1 m and m = 2.5 kg, calculate the angular momentum about that axis.
A flat uniform circular disk has a mass of 2.74 kg and a radius of 93.4 cm. It is suspended in a horizontal plane by a vertical wire attached to its center. If the disk is rotated 2.19 rad about the wire, a torque of 0.0215 N⋅m is required to maintain that orientation. Calculate (a) the rotational inertia of the disk about the wire, (b) the torsion constant, and (c) the angular frequency of this torsion pendulum when it is set oscillating. (a) Number Units (b) Number Units (c) Number Units
Samples A and B are at different initial temperatures when they are placed in a thermally insulated container and allowed to come to thermal equilibrium. Figure (a) gives their temperatures T versus time t. Sample A has a mass of 4.73 kg; sample B has a mass of 1.28 kg. Figure (b) is a general plot for the material of sample B. It shows the temperature change ΔT that the material undergoes when energy is transferred to it as heat Q. The change ΔT is plotted versus the energy Q per unit mass of the material, and the scale of the vertical axis is set by ΔTs = 4.20∘C. What is the specific heat of sample A? (a) (b) Number Units