The figure shows a ball with mass m = 0.354 kg attached to the end of a thin rod with length L = 0.597 m and negligible mass. The other end of the rod is pivoted so that the ball can move in a vertical circle. The rod is held horizontally as shown and then given enough of a downward push to cause the ball to swing down and around and just reach the vertically upward position, with zero speed there. How much work is done on the ball by the gravitational force from the initial point to (a) the lowest point, (b) the highest point, and (c) the point on the right level with the initial point? If the gravitational potential energy of the ball-Earth system is taken to be zero at the initial point, what is it when the ball reaches (d) the lowest point, (e) the highest point, and (f) the point on the right level with the initial point? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units (f) Number Units
The figure shows a ball with mass m = 1.8 kg attached to the end of a thin rod with length L = 1.8 m and negligible mass. The other end of the rod is pivoted so that the ball can move in a vertical circle. (a) What initial speed must be given the ball so that it reaches the vertically upward position with zero speed? What then is its speed at (b) the lowest point and (c) the point on the right at which the ball is level with the initial point? (d) If the ball's mass were doubled, what would the answer to (a) be? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
In the figure, part of a long insulated wire carrying current i = 3.97 mA is bent into a circular section of radius R = 8.86 cm. What are (a) the x-component, (b) the y-component, and (c) the z-component of the magnetic field at the center of curvature C if the circular section lies in the plane of the page as shown? What are (d) the x-component, (e) the y-component, and (f) the z-component of the magnetic field at the center of curvature C if the circular section is perpendicular to the plane of the page after being rotated 90∘ counterclockwise as indicated? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units (f) Number Units
In the figure, block 1 has mass m1 = 440 g, block 2 has mass m2 = 550 g, and the pulley is on a frictionless horizontal axle and has radius R = 4.6 cm. When released from rest, block 2 falls 70 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.
What are the strength and direction of the electric field at the position indicated by the dot in the figure (Figure 1)? Figure 1 of 1 What is the strength of the electric field? Let r = 6.8 cm. Express your answer in newtons per coulomb. Specify the direction of the electric field as an angle below the horizontal. Express your answer in degrees to two significant figures.
How many coulombs of positive charge are in 0.827 mol of neutral molecular-hydrogen gas (H2)? Number Units
What is the direction of the magnetic field generated by this current loop? up down right left into the page out of the page
(a) A 0.5 kg teddy bear is nudged off a window sill and falls 2 m to the ground. Use conservation of energy what is its kinetic energy at the instant it hits the ground? What is its speed? (b) What assumptions or approximations did you make in this calculation? (c) A 1.0 kg flowerpot is nudged off a window sill and falls 2 m to the ground. What is its kinetic energy at the instant it hits the ground? What is its speed? (d) Compare the final speeds and kinetic energies of the two objects. How would you explain why they are the same or different? (e) Solve for the final speed of each object using kinematics (motion) equations instead of conservation of energy.
Three point charges are fixed in place in a right triangle, as shown in the figure. where y = 8.10 cm and z = 9.30 cm. What is the magnitude of the electric force on the +1.00−μC charge due to the other two charges?
Diamonds are measured in carats, and 1 carat = 0.200 g. The density of diamond is 3.51 g/cm3. (a) What is the volume of a 7.10-carat diamond? cm3 (b) What is the mass in carats of a diamond measuring 4.2 mL? carats
Part A A cylinder of mass M and radius R has a cylindrical hole of radius r centered on the axis. Find an expression for the moment of inertia of the cylinder. You should confirm that your answer agrees with expressions 12 MR2 when r = 0 (a solid disk) and MR2 when r = R (a cylindrical hoop). Express your answer in terms of some or all of the variables M, R, and r.
The loop of wire shown below is hooked up to a circuit, powered by a 5V EMF. The loop has a radius of R = 5.3 cm. What should the resistance of the resistor be (in Ohms) in order to produce a 5.0E-7 T magnetic field in the center of the loop, at point P? Answer a. 2.51 b. 119 c. 1.19
(8%) Problem 8: A conducting rod spans a gap of length L = 0.045 m and acts as the fourth side of a rectangular conducting loop, as shown in the figure. A constant magnetic field with magnitude B = 0.65 T pointing into the paper is in the region. The rod is pulled to the right by an external force, and moves with constant speed v = 0.11 m/s. The resistance in the wire is R = 170 Ω. Randomized L = 0.045 mB = 0.65 Tv = 0.11 m/sR = 170 Ω 14% Part (b) Express the change in the magnetic flux, ΔΦ, in terms of B, L, v and Δt. 14% Part (c) Express the magnitude of the average emf induced in the loop, ε, in terms of B, L, v. 14% Part (d) Calculate the emf, in volts. 14% Part (e) Express the current induced in the loop, I, in terms of ε and R. 14% Part (f) Calculate the value of I, in amperes. 14% Part (g) What is the direction of the current?
As shown in Figure Q1, two magnetic fields exist in the regions enclosed by three boundaries, l1, l2, and l3. Uniform magnetic field B1 = 2×10−6 T is directed out the page. Uniform magnetic field B2 is directed into the page. The value of B2 is unknown. Then, a proton has a mass equal to 1.67×10−27 kg, has a charge of 1.6×10−19 C, and moves into B1 from point A. The velocity of the proton is vertically upward. The blue dotted line is the trajectory of the proton, which is composed of two quarter circles. The distance between l1 and l2 is d = 5 m. The distance from point A to l3 is dA = 2 m. (1) Find the initial speed v0 of the proton. (2) Find the magnitude of the magnetic field B2. Figure Q1.
A magnetic field has a magnitude of 0.0011 T, and an electric field has a magnitude of 5.5×103 N/C. Both fields point in the same direction. A positive 1.7−μC charge moves at a speed of 4.3×106 m/s in a direction that is perpendicular to both fields. Determine the magnitude of the net force that acts on the charge. Number Units
Potential and Potential Energy: Three point charges are arranged as shown in the figure below. a. Find the electric field at point A. (Give as a vector, either as ı^ and ȷ^ or magnitude and direction.) b. Find the potential at point A. c. If an electron is placed at point A and released, what is the magnitude of its final velocity?
The circuit shown below is in a uniform magnetic field that is into the page. The current in the circuit is (1.2×10^−1)A. At what rate is the magnitude of the magnetic field changing? Use T/s for your answer. Note: Use a positive sign if the rate is increasing or a negative sign if the rate is decreasing. Note: Your answer is assumed to be reduced to the highest power possible. Your Answer: x10 Answer
In the figure, a slab of mass m1 = 40 kg rests on a frictionless floor, and a block of mass m2 = 12 kg rests on top of the slab. Between block and slab, the coefficient of static friction is 0.60, and the coefficient of kinetic friction is 0.40. A horizontal force F→ of magnitude 109 N begins to pull directly on the block, as shown. In unit-vector notation, what are the resulting accelerations of (a) the block and (b) the slab? (a) Number i^ + j^ Units (b) Number i^ + j^ Units
When an electron moves from A to B along an electric field line in the figure, the electric field does 3.99×10−19 J of work on it. What are the electric potential differences (a) VB−VA, (b) VC−VA, and (c) VC−VB? (a) Number Units (b) Number Units (c) Number Units
A 20 N horizontal force F→ pushes a block weighing 3.0 N against a vertical wall. The coefficient of static friction between the wall and the block is 0.57, and the coefficient of kinetic friction is 0.37. Assume that the block is not moving initially. (a) Will the block move? Yes No (b) In unit-vector notation, what is the force exerted on the block by the wall? N
The loop in the image is moving through the magnetic field, of strength 0.200 T, at a speed of 44.0 m/s. If the resistance in the loop is 1.00 Ω and the width of the wire is x = 4.00 cm, what is the magnitude and direction of the induced current? Magnitude: Direction: counterclockwise. clockwise.