Identical 45 μC charges are fixed on an x axis at x = ±3.1 m. A particle of charge q = −13 μC is then released from rest at a point on the positive part of the y axis. Due to the symmetry of the situation, the particle moves along the y axis and has kinetic energy 1.1 J as it passes through the point x = 0, y = 4.2 m. (a) What is the kinetic energy of the particle as it passes through the origin? (b) At what negative value of y will the particle momentarily stop? (a) Number Units (b) Number Units
Two charges are located in the xy plane: charge q1 = −2.60 nC is located at (x = 0.00 m, y = 0.640 m); charge q2 = 3.00 nC is located at (x = 1.30 m, y = 0.450 m. Calculate the x and y components, Ex and Ey, respectively, of the net electric field E→ at the origin. The value of the Coulomb force constant is 1/(4πϵ0) = 8.99×109 N⋅m2/C2. Ex = N/C Ey = N/C
A soldier is tasked with measuring the muzzle velocity of a new rifle. Knowing the principles of projectile motion, the soldier decides to perform a simple experiment at the indoor firing range. The soldier hangs a target a distance of d = 1.10×102 m from the end of the barrel. The rifle is mounted so that the bullet exits moving horizontally at the same height as the 2 bull's-eye. After six trials, the soldier tabulates the values they measured for the distance h from the bull's-eye to the bullet strike. Vertical Displacement Data What is the most accurate muzzle velocity vm that the soldier can report to their sergeant? vm = m/s What is the uncertainty σvm in this measurement? σνm = ± m/s
In a particular Cartesian coordinate system, the y and z-components of the acceleration are zero and the x-component varies as given by the following function: ax = (2 m/s3)t − (4 m/s4)t2 + (35 m/s2)e−t/F, where the elapsed time t is in seconds and the constant F = 1.0 second. At time t0 = 0 seconds, the particle was at position x0 = 7 meters with a velocity directed in the positive x-direction and having magnitude 15 meters per second. Part (a) Find the instantaneous acceleration, in meters per second squared, at elapsed time t = 1.6 seconds. Part (b) Find the instantaneous velocity, in meters per second, at elapsed time t = 1.6 seconds. Part (c) Find the position, in meters, of the particle at elapsed time t = 1.0 second.
A diverging lens (f = −11.0 cm) is located 17.0 cm to the left of a converging lens (f = 28.0 cm). A 2.80-cm-tall object stands to the left of the diverging lens, exactly at its focal point. (a) Determine the distance of the final image relative to the converging lens. (b) What is the height of the final image (including the proper algebraic sign)? (a) Number Units (b) Number Units
An Australian emu is running due north in a straight line at a speed of 13.0 m/s and slows down to a speed of 9.20 m/s in 3.30 s. (a) What is the magnitude and direction of the bird's acceleration? (b) Assuming that the acceleration remains the same, what is the bird's velocity after an additional 2.30 s has elapsed? (a) Number Units (b) Number Units
During a tennis match, a player serves the ball at 29.5 m/s, with the center of the ball leaving the racquet horizontally 2.44 m above the court surface. The net is 12.0 m away and 0.900 m high. When the ball reaches the net, (a) what is the distance between the center of the ball and the top of the net? (b) Suppose that, instead, the ball is served as before but now it leaves the racquet at 5.00∘ below the horizontal. When the ball reaches the net, what now is the distance between the center of the ball and the top of the net? Enter a positive number if the ball clears the net. If the ball does not clear the net, your answer should be a negative number. Use g = 9.81 m/s2. (a) Number Units (b) Number Units
A 2.03 kg book is placed on a flat desk. Suppose the coefficient of static friction between the book and the desk is 0.442 and the coefficient of kinetic friction is 0.240. How much force is needed to begin moving the book? N How much force is needed to keep the book moving at constant speed once it begins moving?
A freight train consists of two 7.00×105 kg engines and 50 cars with average masses of 4.50×105 kg. (a) What force (in N) must each engine exert backward on the track to accelerate the train at a rate of 2.00×10−2 m/s2 if the force of friction is 7.50×105 N, assuming the engines exert identical forces? This is not a large frictional force for such a massive system. Rolling friction for trains is small, and consequently trains are very energy-efficient transportation systems. (Enter the magnitude.) N (b) What is the magnitude of the force (in N) in the coupling between the 37 th and 38 th cars (this is the force each exerts on the other), assuming all cars have the same mass and that friction is evenly distributed among all of the cars and engines? (Assume both engines are at the front of the train.) N
Consider a charge Q1 = +2.0 μC fixed at a site with another charge Q2 (charge +9.0 μC, mass 7.0 μg) moving in the neighboring space. a) Calculate the potential energy of Q2 when it is 1.0 cm from Q1 U = J b) If Q2 starts from rest from a point 1.0 cm from Q1, what will its speed be when it is 2.0 cm from Q1? (Note: Q1 is held fixed in its place) v = ms
The speed of light in air is 2.997∗108 m/s, while the speed in water is 2.248∗108 m/s. If light travels through the air and hits the surface of the water with an incident and angle of π/6 radians, by how many radians does the angle change when it enters the water? 0.3844 0.1392 −0.3844 −0.1392
This problem deals with several aspects of an oscilloscope. You have an 14700 volt supply (Vsupply) for accelerating electrons to a speed adequate to make the front phosphor-coated screen glow when the electrons hit it. Once the electron has emerged from the accelerating region, it coasts through a vacuum at nearly constant speed. You can apply a potential difference of plus or minus 35 volts (Vplates) across the deflection plates to steer the electron beam up or down on the screen to paint a display (other deflection plates not shown in the diagram are used to steer the beam horizontally). Each of the two deflection plates is a thin metal plate of length L = 8 cm and width (into the diagram) 4 cm. The distance between the deflection plates is s = 5 mm. The distance from the deflection plates to the screen is d = 34 cm. When there is a 35 volt potential difference between the deflection plates, what is the deflection y of the electron beam where it hits the screen? An approximate treatment is fine, but state your assumptions. As is usually the case, it pays to carry out all of your calculations algebraically and only evaluate the final algebraic result numerically. Note the exaggerated vertical scale: the deflection is actually small compared to the distance to the screen. When leaving the accelerating plates, the electron's speed is close to the speed of light. Therefore, you must use K = (γ − 1)mc2 where γ = 1 /1 − (v/c)2 and c is the speed of light, 3×108 m/s. m
A non-linear spring is attached to a 2-kg mass sitting on a smooth surface as shown. The force exerted by the spring is given by the equation below, where x is in meters, and F is in Newtons. The mass initially compresses the spring 0.1 m and is released from rest. Find the maximum velocity of the mass.
A force of 880 newtons stretches a spring 4 meters. A mass of 55 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 10 m/s. Give the initial conditions. x(0) = m x′(0) = m/s Find the equation of motion. x(t) = m
The figure below shows a box-shaped closed surface with one it's edges lying on the x-axis, and its left edge located at x = a. The sides have lengths a = b = 0.400 m and c = 0.800 m. Throughout the region, there is a nonuniform electric field is given by E→ = (1.10 N/C + (3.40 N/(m2⋅C))x2) i^, where x is in meters. +x-direction. (a) What is the net electric flux through the closed surface (in N⋅m2/C)? N⋅m2 /C (b) What is the net charge enclosed by the surface (in C)? C
There is an electric flux of 34.5 N⋅m2/C through the square region shown in the figure. Each side of the square has a length of 0.100 m, n^ is the unit vector normal to the plane of the surface, and the electric field is at an angle of θ = 59.0∘ relative to the plane of the surface. Assuming that the field is uniform over the region shown, what is the magnitude E of the electric field? E = N/C
A closed surface with dimensions a = b = 0.400 m and c = 0.800 m is located as shown in the figure below. The left edge of the closed surface is located at position x = a. The electric field throughout the region is non-uniform and given by E→ = (1.60 + 5.00x2) i N/C, where x is in meters. (a) Calculate the net electric flux leaving the closed surface. (b) What net charge is enclosed by the surface?
The closed surface shown in the figure below has dimensions a = b = 0.5 m and c = 0.8 m. The left edge of the closed surface is located at x = a. The electric field throughout the region is nonuniform and is given by E→ = (3.0+2.0 x)i^ N/C, where x is in m. Calculate the net electric flux through the closed surface. A. 1.0 Nm2/C B. 0.4 Nm2/C C. 1.6 Nm2/C D. 0.2 Nm2/C E. 2.4 Nm2/C
A person in a kayak starts paddling, and it accelerates from 0 to 0.731 m/s in a distance of 0.506 m. If the combined mass of the person and the kayak is 82.7 kg, what is the magnitude of the net force acting on the kayak? Number Units
Give a numerical estimate of the minimum safe radius of curvature rmin for an unbanked, circular freeway on-ramp designed for a speed limit of 40 miles per hour. Assume wet road conditions. rmin = m
Two resistances, R1 and R2, are connected in series across a 12.0-V battery. The current increases by 0.200 A when R2 is removed, leaving R1 connected across the battery. However, the current increases by just 0.130 A when R1 is removed, leaving R2 connected across the battery. Find (a) R1 and (b) R2. (a) Number Units (b) Number Units
At time t = 0, a projectile is launched from ground level. At t = 2.00 s, it is displaced d = 50 m horizontally and h = 71 m vertically above the launch point. What are the (a) horizontal and (b) vertical components of the initial velocity of the projectile? (c) At the instant it reaches its maximum height above ground level, what is its horizontal displacement D from the launch point? (a) Number Unit (b) Number Unit (c) Number Unit
Three boxes, A, B, and C, are placed on a frictionless surface as shown in the diagram below. If you push on box A with a force of 8.25 N, find the contact force (in N) between each pair of boxes. Here mA = 5.85 kg, mB = 3.75 kg, and mC = 1.50 kg. contact force between A and B N contact force between B and C N
Consider the charge distribution given below. Determine the total Electric field at the origin and at the point (1, 2). Use the magnitude/unit vector notation (assume you know the charges magnitude and sign).
A toy submarine of mass m = 0.930 kg moves around a submerged circular track of radius R = 2.02 m. The submarine's engine provides a constant propulsion force of F = 4.98 N. When the sub is in motion, it is subject to a viscous drag force exerted by the water. This force is proportional to the sub's speed; the proportionality factor is C = 1.11 kg/s. Assuming it starts from rest at t = 0 s, the speed v(t) of the submarine at a later time t is given by v(t) = F/C(1−e−Ct/m) where e is the base of the natural logarithm. How much time has passed when the submarine's speed reaches 6.0×101% of its terminal value? What is the magnitude of the submarine's acceleration a at this time?
In the figure a butterfly net is in a uniform electric field of magnitude E = 4.4 mN/C. The rim, a circle of radius a = 9.7 cm, is aligned perpendicular to the field. The net contains no net charge. Find the magnitude of the electric flux through the netting. Number Units
Consider a line of charge of length L having total charge Q with uniform charge density as shown in the figure below. (A) Consider the electric field at a point P on the horizontal x-axis a distance r from the end of the line of charge as shown above. What direction does the electric field point? Briefly explain your answer. (B) Just from thinking about it (without too much calculation), what do you think the electric field should be (approximately) when r ≫ L? Briefly explain your thinking. (C) Now do a calculation to find an expression for the electric field at the point P. (D) Compare your answer to (C) in the limit where r ≫ L with your answer from (B). Do they agree? (They should!)
In the Bohr model of hydrogen, the electron moves in a circular orbit around the nucleus. Determine the angular speed of the electron, in revolutions per second when it is in (a) the ground state and (b) the n = 7 state. (a) Number Units (b)Number Units
A proton enters the uniform electric field produced by the two charged plates shown below. The horizontal extent is indicated in the drawing, and the vertical exten exaggerated for purposes of illustration. The magnitude of the electric field is 3.4×105 N/C, and the speed of the proton when it enters is 1.3×107 m/s. Part (a) At the point where the proton is exiting from the gap between the plates, its path has been deflected by a distance, d, as indicated on the drawing in the problem statement. Enter the correct value for d, expressed in millimeters. Part (b) At the point where the proton is exiting from the gap between the plates, its path has been deflected by an angle, θ, as indicated on the drawing in the problem statement. Enter the correct value for θ, expressed in degrees. θ = ∘