Consider the mechanical system shown above. If the block is displaced by 0.4 meters upward, what is the change in potential energy (in Joules) of the block, assuming m = 3 kg?
Three point charges, Q1 = 21.4 μC, Q2 = −34.6 μC, and Q3 = 67.3 μC are positioned at three corners of a square as shown in the figure. A fourth point charge is located at the open corner at point A with a charge of QA = 17.5 μC. The square has height y of 60.1 cm and width x of 60.1 cm. Calculate the magnitude F of the net force on the charge at point A. F =
Gold, which has a density of 19.32 g/cm3, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (a) If a sample of gold with a mass of 8.264 g, is pressed into a leaf of 8.717 μm thickness, what is the area of the leaf? (b) If, instead, the gold is drawn out into a cylindrical fiber of radius 2.800 μm, what is the length of the fiber? (a) Number Units (b) Number Units
The drawing shows an equilateral triangle, each side of which has a length of 3.08 cm. Point charges are fixed to each corner, as show The 4.00 μC charge experiences a net force due to the charges qA and qB. This net force points vertically downward and has a magnitude of 249 N. Determine (a) charge qA, (b) charge qB.
(Electric force and field). Two charges, Q1 and Q2 of equal magnitude are placed at positions (0, −d/2, 0) and (0, +d/2, 0) respectively. Calculate the electric field at position (0, 0, z) when: a) Both charges are positive, and b) Q1 is positive, and Q2 is negative. What does the electric field become for the case z≫d for both cases a) and b) above?
An electron travels at speed |v|→ = 0.994 c, where c = 3×108 m/s is the speed of light. It travels in the direction given by the unit vector v^ = < 0.740, −0.185, −0.647⟩. The mass of an electron is 9×10−31 kg. Part 1 (a) What is the value of γ = 1 1−(|v|→/c)2? You can simplify the calculation if you notice that (|v|→/c) = 0.994 γ =
A raft is made of 11 logs lashed together. Each is 42 cm in diameter and has a length of 6.4 m. Part A How many people can the raft hold before they start getting thefir feet wet, assuming the average person has a mass of 65 kg? Do not neglect the weight of the logs. Assume the specific gravity of wood is 0.60. Express your answer using two significant figures. N =
The acceleration of a block on an incline in the absence of friction is related to the angle of the incline by the equation, a = gsinθ where θ is the incline angle and g is the acceleration due to gravity. Assuming this equation is correct, use your measured acceleration to determine the value of g? Recall that you used a 4 cm block under one end of a 1.2 meter long track. How does your value compare to the actual value of g = 9.8 m/s2?
A hollow ball with radius R = 2 cm has a charge of -1 nC spread uniformly over its surface (see the figure). The center of the ball is at P1 = < −3, 0, 0 > cm. A point charge of 6 nC is located at P3 = < 5, 0, 0 > cm. (The diagram below is not drawn exactly to scale.) P2 P3 Part 1 What is the net electric field at location P2 = ⟨0, 4, 0⟩ cm? E→ = < > N/C Part 2 At a particular instant an electron is at location P2. What is the net electric force on the electron at that instant? F→ = < > N
A particle with a charge of q = 1.8 C and a speed of v = 2.6 m/s travels in a magnetic field of strength B = 4.4 T that goes θ = 24∘ below the positive horizontal. What is the magnitude of the force in units of Newtons? Type your answer...
The figure shows two point charges of equal and opposite charge. Determine the magnitude of their net electric field (in N/C) at point P if q = 5.90 μC, d = 2.58 m, and x = 5.52 m. N/C
A magnetic current loop (magnetic dipole) points along the positive x^ axis. The loop consists of N = 66 turns, has a radius of 88.2 cm, and carries a current of 0.777 A. This dipole is immersed in a magnetic field B→ = 0.666x^ + 0.333y^ T. What is the magnitude of the torque acting on the magnetic dipole by the magnetic field? Give your answer in N⋅m. This is a positive number.
Point charges of 6.50 μC and −2.25 μC are placed 0.350 m apart. (Assume the negative charge is located to the right of the positive charge. Include the sign of the value in your answers.) (a) Where can a third charge be placed so that the net force on it is zero? m to the right of the −2.25 μC charge (b) What if both charges are positive? m to the right of the 2.25 μC charge
An oscillating dipole antenna 1.91 m long with a maximum 36.5 mV potential creates a 500 Hz electromagnetic wave. (a) What is the maximum electric field strength created? V/m (b) What is the corresponding maximum magnetic field strength in the electromagnetic wave? T (c) What is the wavelength of the electromagnetic wave? m
21.79 CALC Positive charge Q is distributed uniformly along the x-axis from x = 0 to x = a. A positive point charge q is located on the positive x-axis at x = a+r, a distance r to the right of the end of Q (Fig. P21.79). (a) Calculate the x- and y-components of the electric field produced by the charge distribution Q at points on the positive x-axis where x > a. (b) Calculate the force (magnitude and direction) that the charge distribution Q exerts on q. (c) Show that if r≫a, the magnitude of the force in part (b) is approximately Qq/4πϵ0 r2. Explain why this result is obtained. Figure P21.79
A dipole is centered at the origin, and is composed of charged particles with charge +e and −e, separated by a distance 7×10−10 m along the y axis. The +e charge is on the −y axis, and the −e charge is on the +y axis. A proton is located at < 0, 1×10−8, 0 > m. What is the force on the proton, due to the dipole? F⇀ = N An electron is located at <−1×10−8, 0, 0 > m. What is the force on the electron, due to the dipole? F⇀ = N (Hint: Make a diagram! Note that one approach is to calculate magnitudes, then figure out directions from your diagram.)
Points A and B are nearby an electron in otherwise empty space as shown. The potential is chosen to be zero very far away from the electron. The potential at point A is the potential at point B, and the electric field energy density at point A is the electric field energy density at point B. 0 θ less than, greater than the same as, greater than less than, less than greater than, greater than the same as, less than the same as, the same as greater than, less than greater than, the same as less than, the same as
A mass Y attached to a rope is moving in uniform circular motion on a frictionless table as shown on the diagram. The circular path of constant radius r is shown with the dotted line. The mass X is hanging from the lower end of the rope. The masses of X and Y can be adjusted. What independent adjustments to mass X and mass Y could produce uniform circular motion at a lower speed v, but with the same radius r? A. B. C.
FIGURE 6.6 shows a metre rule of mass 80 g if freely hinged at the end O. The other end of the ruler is raised until the rule is horizontal. It is then released. The moment of inertia of the rod is 13 ML2. Determine the angular acceleration of the rule immediately after it is released [ANS:14.7 rads-2]
A particle moving along a straight line has an initial velocity v0 = 10 m/s. If its acceleration a is given as a function of displacement s as shown, determine its velocity v(m/s) at s = 10 m.
A block 61.7 kg block is suspended on an inclined surface at angle θ = 50.7∘ by a cable attached to a winch, as shown in the figure. The coefficients of friction between the block and inclined surface are: μs = 0.66, μk = 0.48 What is the maximum tension in the cord, T, such that the block does not slip? If the maximum tension, evaluated in the previous part, is marginally exceeded, what is the acceleration of the crate up the slope? Number Units
An eagle is flying horizontally at 7.4 m/s with a fish in its claws. It accidentally drops the fish. (a) How much time passes before the fish's speed doubles? (b) How much additional time would be required for the speed to double again? (a) Number Units (b) Number Units
Two flat mirrors are perpendicular to each other. An incoming beam of light makes an angle of θ = 20∘ with the first mirror, as shown in the figure. First mirror What angle ϕ will the outgoing beam make with respect to the normal of the second mirror? ϕ =
An eagle is flying horizontally at a speed of 4.50 m/s when the fish in her talons wiggles loose and falls into the lake 4.40 m below. (a) Determine the speed of the fish just before it hits the water. m/s (b) Determine the angle of the velocity of the fish below the horizontal just before it hits the water. degrees (c) Determine the total time of flight of the fish after its release from the eagle's talons. s
A periscope (see figure below) is useful for viewing objects that cannot be seen directly. It can be used in submarines and when watching golf matches or parades from behind a crowd of people. Suppose the object is a distance p1 from the upper mirror and the centers of the two flat mirrors are separated by a distance h. (a) What is the distance of the final image from the lower mirror? (Use any variable or symbol stated above as necessary.) d = behind the lower mirror (b) Is the final image real or virtual? real virtual (c) Is it upright or inverted? upright inverted (d) What is its magnification?
A swan on a lake becomes airborne by flapping its wings and running on top of the water. The swan must reach a velocity of 6.50 m/s to take off, and it accelerates from rest at an average rate of 0.350 m/s2. What distance Δx does the swan travel before becoming airborne? Δx = m How much time t does it take for the swan to become airborne? t = s
A light ray enters a rectangular block of plastic at an angle θ1 = 44.6∘ and emerges at an angle θ2 = 75.9∘, as shown in the figure below. (a) Determine the index of refraction of the plastic. (b) If the light ray enters the plastic at a point L = 50.0 cm from the bottom edge, how long does it take the light ray to travel through the plastic? ns
Use g = 9.8 m/s2. The classic Millikan oil drop experiment was the first to obtain an accurate measurement of the charge on an electron. In it, oil drops were suspended against gravity by a vertical electric field. Assume the oil drop to be 1.90 μm in radius and have a density of 900 kg/m3. (a) Find the weight of the drop. N (b) If the drop has a single excess electron, find the magnitude of the electric field strength needed to balance its weight. N/C
Plastic beads can often carry a small charge and therefore can generate electric fields. Three beads are oriented such that q2 is between q1 and q3. The sum of the charge on q1 and q2 is q1 + q2 = −2.6 μC, and the net charge of the system of all three beads is zero. What charge does each bead carry? q1 = μC q2 = μC q3 = μC
A positive charge q is fixed at point (−4, −3) and a negative charge −q is fixed at point (−4, 0). Determine the net electric force F→net actíng on a negative test charge −Q at the origin (0, 0) in terms of the given quantities and the permittivity of free space ϵ0. Enter your expression using ij unit vector notation and rational coefficients. F→net =
In the Millikan oil-drop experiment illustrated in the figure below, an atomizer (a sprayer with a fine nozzle) is used to introduce many tiny droplets of oil between two oppositely charged parallel metal plates. Some of the droplets pick up one or more excess electrons. The charge on the plates is adjusted so that the electric force on the excess electrons exactly balances the weight of the droplet. The idea is to look for a droplet that has the smallest electric force and assume it has only one excess electron. Suppose we are using an electric field of 3.65×104 N/C. The charge on one electron is 1.60×10−19 C. Calculate the radius of an oil drop of density 829 kg/m3 for which its weight could be balanced by the electric force of this field on one electron. μm
A projectile is launched at ground level with an initial speed of 48.0 m/s at an angle of 35.0∘ above the horizontal. It strikes a target above the ground 3.10 seconds later. What are the x and y distances from where the projectile was launched to where it lands? x distance m y distance m
A small block of mass m and charge Q is placed on an insulated, frictionless, inclined plane of angle θ as in the figure below. An electric field is applied parallel to the incline. (a) Find an expression for the magnitude of the electric field that enables the block to remain at rest. (Use any variable or symbol stated above along with the following as necessary: g for the acceleration due gravity.) E = (b) If m = 5.51 g, Q = −7.28 μC, and θ = 26.5∘, determine the magnitude and the direction of the electric field that enables the block to remain at rest on the incline. magnitude N/C direction ---Select--
A projectile is fired up the inclined plane with the initial velocity shown. Compute the maximum height h, measured perpendicular to the plane, that is reached by the projectile.
The electric field in a region of space has the components Ey = Ez = 0 and Ex = (5.90 N/(C⋅m))x. Point A is on the y axis at y = 3.40 m, and point B is on the x axis at x = 4.10 m. What is the potential difference (in V) VB−VA? Number Units
A test charge of +8 μC is placed halfway between a charge of +6 μC and another of +7 μC separated by 19 cm. (a) What is the magnitude of the force (in N) on the test charge? N (b) What is the direction of this force (away from or toward the +6 μC charge)? away from the +6 μC charge toward the +6 μC charge