A block (mass = 2.0 kg) is hanging from a massless cord that is wrapped around a pulley (moment of inertia = 1.1×10−3 kg⋅m2), as the drawing shows. Initially the pulley is prevented from rotating and the block is stationary. Then, the pulley is allowed to rotate as the block falls. The cord does not slip relative to the pulley as the block falls. Assume that the radius of the cord around the pulley remains constant at a value of 0.040 m during the block's descent. (a) Draw the free-body diagram showing the forces that act on the pulley. (b) Draw the free-body diagram showing the forces that act on the block. Find (c) the angular acceleration of the pulley and (d) the tension in the cord.
Refer to the figure. Let the mass of the block be 1.40 kg and the angle θ be 36.0∘. Find (a) the tension in the cord and (b) the normal force acting on the block. (c) If the cord is cut, find the magnitude of the block's acceleration. (a) Number i Units (b) Number Units (c) Number Units
A person pushing a horizontal, uniformly loaded, 27.80 kg wheelbarrow of length L is attempting to get it over a step of height h = 0.390R, where R is the wheel's radius. The center of gravity of the wheelbarrow is in the center of the wheelbarrow. What is the horizontal component Px of the minimum force P→ necessary to push the wheelbarrow over the step? The gravitational acceleration is g = 9.81 m/s2. Px =
A 2.09 kg hockey puck slides on a horizontal, frictionless surface at 1.7 m/s when it is struck by a 0.21 kg bullet traveling perpendicularly to the puck at 107 m/s. The bullet becomes wedged inside the puck. The sketch shows the view from above. J of kinetic energy was lost in the collision. (Enter a positive number)
An object is moving along a straight line, and the uncertainty in its position is 2.40 m. (a) Find the minimum uncertainty in the momentum of the object. Find the minimum uncertainty in the object's velocity, assuming that the object is (b) a golf ball (mass = 0.0450 kg) and (c) an electron. (a) Number Units (b) Number Units (c) Number Units
In exercising, a weight lifter loses 0.231 kg of water through evaporation, the heat required to evaporate the water coming from the weight lifter's body. The work done in lifting weights is 1.66×105 J. (a) Assuming that the latent heat of vaporization of perspiration is 2.42×106 J/kg, find the change in the internal energy of the weight lifter. (b) Determine the minimum number of nutritional Calories of food that must be consumed to replace the loss of internal energy (1 nutritional Calorie = 4186 J). (a) Number Units (b) Number Units
The water level in a vertical glass tube 1.00 m long can be adjusted to any position in the tube. A tuning fork vibrating at 675 Hz is held just over the open top end of the tube, to set up a standing wave of sound in the air-filled top portion of the tube. (That air-filled top portion acts as a tube with one end closed and the other end open.) Take the speed of sound to be 343 m/s. (a) For how many different positions of the water level will sound from the fork set up resonance in the tube's air-filled portion? What are the (b) least and (c) second least water heights in the tube for resonance to occur? (a) (b) Number Units (c) Number Units
At its highest temperature, a space heater has a resistance of 49.5 Ω when it is plugged into a wall outlet that supplies a peak voltage of 169.7 V sinusoidally at 60 Hz. What is the average power output P¯ of the space heater? P¯ = W
Two spheres are each rotating at an angular speed of 22.0 rad/s about axes that pass through their centers. Each has a radius of 0.520 m and a mass of 1.57 kg. However, as the figure shows, one is solid and the other is a thin-walled spherical shell. Suddenly, a net external torque due to friction (magnitude = 0.340 N⋅m) begins to act on each sphere and slows the motion down. How long does it take (a) the solid sphere and (b) the thin-walled sphere to come to a halt? Solid sphere Thin-walled spherical shell (a) Number Units (b) Number Units
A long solenoid has 130 turns/cm and carries current i. An electron moves within the solenoid in a circle of radius 2.59 cm perpendicular to the solenoid axis. The speed of the electron is 0.0667 c(c = speed of light, equal to 2.998×108 m/s). Find the current i in the solenoid. Number Units
What multiple of the time constant τ gives the time taken by an initially uncharged capacitor in an RC series circuit to be charged to 87.6% of its final charge? Number Units
The figure gives the path of a squirrel moving about on level ground, from point A (at time t = 0), to points B (at t = 5 min), C (at t = 10 min), and finally D (at t = 15 min). Consider the average velocities of the squirrel from point A to each of the other three points. Of them, what are the (a) magnitude and (b) angle of the one with the least magnitude and (c) the magnitude and (d) angle of the one with the greatest magnitude? Give the angles in the range (−180∘, 180∘] (a) Number Units (b) Number Units (c) Number Units (d) Number Units
Two vectors, r→ and s→ lie in the xy plane. Their magnitudes are 3.01 and 6.72 units, respectively, and their directions are 332∘ and 48.0∘, respectively, as measured counterclockwise from the positive x axis. What are the values of (a) r→⋅s→ and (b) |r→×s→|? (a) Number Units (b) Number Units
The switch in the figure is closed on a at time t = 0. What is the ratio EL/E (a) just after t = 0 and (b) at t = 2.10TL? (c) At what multiple of TL will EL/E = 0.500?
The figure below shows a capacitor, with capacitance C = 4.97 μF, and a resistor, with resistance R = 6.23 MΩ, connected in series to a battery, with E = 32.0 V. The circuit has a switch, which is initially open. (a) What is the circuit's time constant (in seconds)? s (b) What is the maximum charge (in μC) on the capacitor after the switch is closed? μC (c) What is the current (in μA) through the resistor 10.0 s after the switch is closed? μA
Two charged particles A and B carry a charge of +2q and −q respectively. (i) What is the electric potential, V, at a distance x from the origin on the x-axis? (ii) A third charged particle, C, carrying a charge of +q is placed at the x = 0 Calculate the potential energy in the system, given that l = 0.2 m and q = 12 nC. (iii) Determine the work done by the electric force when C is brought from infinity to the origin.
Three particles are listed in the table. The mass and speed of each particle are given as multiples of the variables m and v, which have the values m = 1.71×10−8 kg and v = 0.200c. The speed of light in a vacuum is c = 3.00×108 m/s. Determine the momentum for each particle according to special relativity.
The 2-kg block is released from rest at A and slides down along the cylindrical surface. If the attached spring has a stiffness k = 20 N/m, determine its unstretched length so that it does not allow the block to leave the surface until θ = 70∘. Assume friction is μk = 0.1.
A +5.2 μC point charge is located on the x-axis at x = +6.6 cm, and a −2.9 μC point charge is located on the y-axis at y = +4.7 cm. Determine the direction of electric field at the origin. Give your answer in units of degrees between 0∘ to 360∘ as measured from the x-axis to the y-axis. Type your answer...
Use Lenz's law to answer the following questions concerning the direction of induced currents. a b (a) What is the direction of the induced current in the resistor R in Figure a when the bar magnet is moved to the left? a to b b to a The magnitude is zero. (b) What is the direction of the current induced in the resistor R immediately after the switch S in Figure b is closed? a to b b to a The magnitude is zero. (c) What is the direction of the induced current in the resistor R when the current I in Figure c decreases rapidly to zero? a to b b to a The magnitude is zero.
A particle has a charge of +2.30 μC and moves from point A to point B, a distance of 0.230 m. The particle experiences a constant electric force, and its motion is along the line of action of the force. The difference between the particle's electric potential energy at A and B is EPEA − EPEB = +8.20×10−4 J. (a) Find the magnitude of the electric force that acts on the particle. (b) Find the magnitude of the electric field that the particle experiences.
Suppose the gravitational torque on the apple is τ→grav = (3.92 N⋅m)i^ + (0 N⋅m)j^ + (−5.89 N⋅m)k^. What is the mass of the apple? m = kg
A sample is bombarded by incident X-rays, and free electrons in the sample scatter some of the X-rays at an angle of θ = 119.0∘ with respect to the incident X-rays, as shown in the drawing. The scattered X rays have a momentum whose magnitude is 1.973×10−24 kg⋅m/s. Determine the wavelength (in nm) of the incident X-rays. (For accuracy, use h = 6.626×10−34 J⋅s, c = 2.998×108 m/s, and m = 9.109×10−31 kg for the mass of an electron.)
Use Lenz's law to answer the following questions concerning the direction of induced currents. Figure P31.28 (a) What is the direction of the induced current in resistor R in Figure P31.28 a when the bar magnet is moved to the left? (b) What is the direction of the current induced in the resistor R after the switch S in Figure P 31.28 b is closed? (c) What is the direction of the induced current in R when the current I in Figure P31.28 c decreases rapidly to zero? (d) A copper bar is moved to the right while its axis is maintained in a direction perpendicular to a magnetic field as shown in Figure P31.28 d. If the top of the bar becomes positive relative to the bottom, what is the direction of the magnetic field?