A uniform cylinder of radius 30 cm and mass 12 kg is mounted so as to rotate freely about a horizontal axis that is parallel to and 14 cm from the central longitudinal axis of the cylinder. (a) What is the rotational inertia of the cylinder about the axis of rotation? (b) If the cylinder is released from rest with its central longitudinal axis at the same height as the axis about which the cylinder rotates, what is the angular speed of the cylinder as it passes through its lowest position? (a) Number Units (b) Number Units
Suppose 6.07 mol of an ideal diatomic gas, with molecular rotation but not oscillation, experienced a temperature increase of 76.4 K under constant-pressure conditions. What are (a) the energy transferred as heat Q, (b) the change ΔEint in internal energy of the gas (c) the work done by the gas and (d) the change ΔK in the total translational kinetic energy of the gas? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
Three point charges are located on a circular arc as shown in the figure below. (Take r = 4.16 cm. Let to the right be the +x direction and up along the screen be the +y (a) What is the total electric field at P, the center of the arc? E→ = î N/C + ј N/C (b) Find the electric force that would be exerted on a −4.98−nC point charge placed at P. F→ = i^ N + j^ N
Multiple-Concept Example 7 deals with the concepts that are important in this problem. A penny is placed at the outer edge of a disk (radius = 0.159 m) that rotates about an axis perpendicular to the plane of the disk at its center. The period of the rotation is 1.90 s). Find the minimum coefficient of friction necessary to allow the penny to rotate along with the disk. μs = Number Units
A circular wire loop of radius 19.2 cm carries a current of 2.25 A. It is placed so that the normal to its plane makes an angle of 42.0∘ with a uniform magnetic field of magnitude 9.61 T. (a) Calculate the magnitude of the magnetic dipole moment of the loop in amperes-square meters. (b) What is the magnitude of the torque acting on the loop? (a) Number Units (b) Number Units
Two blocks are free to slide along the frictionless wooden track shown below. The block of mass m1 = 4.97 kg is released from the position shown, at height h = 5.00 m above the flat part of the track. Protruding from its front end is the north pole of a strong magnet, which repels the north pole of an identical magnet embedded in the back end of the block of mass m2 = 9.20 kg, initially at rest. The two blocks never touch. Calculate the maximum height to which m1 rises after the elastic collision. m
A photon having energy 0.850 MeV is scattered by a free electron initially at rest such that the scattering angle of the scattered electron is equal to that of the scattered photon as shown in the figure (a) Determine the scattering angle of the photon and the electron. photon electron (b) Determine the energy and momentum of the scattered photon. energy MeV momentum kg⋅m/s (c) Determine the kinetic energy and momentum of the scattered electron. kinetic energy MeV momentum kg⋅m/s
The 6 kg object in Figure 7-18 is released from rest at a height of 5 m on a curved frictionless ramp. At the foot of the ramp is a spring of force constant k = 350 N/m. The object slides down the ramp and into the spring, compressing it a distance x before coming momentarily to rest. Figure 7-18 Find x.
Consider the blocks on the curved ramp as seen in the figure. The blocks have masses m1 = 2.00 kg and m2 = 3.90 kg, and are initially at rest. The blocks are allowed to slide down the ramp and they then undergo a head-on, elastic collision on the flat portion. Determine the heights (in m) to which m1 and m2 rise on the curved portion of the ramp after the collision. Assume the ramp is frictionless, and h = 4.10 m. hm1 = m hm2 = m
It is generally a good idea to gain an understanding of the "size" of units. Consider the objects listed and calculate the magnitude of their momentum in SI units. A ladybug weighing 37.30 mg flies by your head at 2.33 mi/h momentum of ladybug: kg⋅m/s A 67.50 lb boy walks at 2.53 mi/h. momentum of boy: kg⋅m/s A car weighing 2.370×103 lb is moving at a speed of 25.30 mi/h momentum of car: kg⋅m/s Based on your answers, which of the scenarios likely describe an object possessing a momentum of 1 kg⋅m/s? a beetle walking across a jungle floor a mosquito flying through a swamp an elephant running across a field
A certain cylindrical wire carries current. We draw a circle of radius r around its central axis in Figure (a) to determine the current i within the circle. Figure (b) shows current i as a function of r2. The vertical scale is set by is = 4.9 mA, and the horizontal scale is set by rs2 = 5.0 mm2. (a) Is the current density uniform? (b) If so, what is its magnitude? (a) (b) Number Units
In the figure, block 1 has mass m1 = 440 g, block 2 has mass m2 = 560 g, and the pulley is on a frictionless horizontal axle and has radius R = 5.1 cm. When released from rest, block 2 falls 73 cm in 4.7 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
A beam of nuclei is used for cancer therapy. Each nucleus has an energy of 129 MeV, and the relative biological effectiveness (RBE) of this type of radiation is 16. The beam is directed onto a 0.180−kg tumor, which receives a biologically equivalent dose of 163 rem. How many nuclei are in the beam? Number Units
A torque of 37.1 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 5.80 s the directed force is removed, and the wheel comes to rest 61.0 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
In the figure, a small 0.458 kg block slides down a frictionless surface through height h = 1.22 m and then sticks to a uniform vertical rod of mass M = 0.916 kg and length d = 2.28 m. The rod pivots about point O through angle θ before momentarily stopping. Find θ. Number Units
Two identical point charges (q = +7.80×10−6 C) are fixed at opposite corners of a square whose sides have a length of 0.680 m. A test charge (q0 = −8.40×10−8 C), with a mass of 7.40×10−8 kg, is released from rest at one of the corners of the square. Determine the speed of the test charge when it reaches the center of the square.
At the instant of the figure, a 2.30 kg particle P has a position vector r→ of magnitude 7.10 m and angle θ1 = 46.0∘ and a velocity vector v→ of magnitude 4.70 m/s and angle θ2 = 30.0∘. Force F→, of magnitude 9.10 N and angle θ3 = 30.0∘ acts on P. All three vectors lie in the xy plane. About the origin, what are the magnitude of (a) the angular momentum of the particle and (b) the torque acting on the particle? (a) Number Units (b) Number Units
14 kg bicycle has 1.2m-diameter wheels, each with a mass of 3.0 kg. The mass of the rider is 38 kg . Estimate the fraction of the total kinetic energy (KE) of the rider-bicycle system that is associated with the rotation of the wheels. (Hint: find the ratio of the KE associated with the rotation of the wheels to that associated with the total KE of the bicycle and rider). 50% 40% 10% 20%