A small ball of radius a and mass m rolls without slipping on a semi-circle of radius R. The semi-circle is the top surface of a block of mass M that is free to move along a horizontal surface without friction. Determine the equations of motion.
Required information Problem 12.052 - A curve in a speed track A curve in a speed track has a radius of 1, 200 ft and a rated speed of 120 mi/h. A racing car starts skidding on the curve when traveling at a speed of 180 mi/h. Problem 12.052.b - Coefficient of static friction Determine the coefficient of static friction between the tires and the track under the prevailing conditions. (Round the final answer to three decimal places.) The coefficient of static friction between the tires and the track is
As shown in the figure below, a box of mass m = 55.0 kg (initially at rest) is pushed a distance d = 63.0 m across a rough warehouse floor by an applied force of FA = 228 N directed at an angle of 30.0∘ below the horizontal. The coefficient of kinetic friction between the floor and the box is 0.100. Determine the following. (For parts (a) through (d), give your answer to the nearest multiple of 10.) (a) work done by the applied force WA = J (b) work done by the force of gravity Wg = J (c) work done by the normal force WN = J (d) work done by the force of friction Wf = J (e) Calculate the net work on the box by finding the sum of all the works done by each individual force. WNet = J (f) Now find the net work by first finding the net force on the box, then finding the work done by this net force. WNet = J
Assume the three blocks (m1 = 1.0 kg, m2 = 2.0 kg, and m3 = 3.5 kg) portrayed in the figure below move on a frictionless surface and a force F = 48 N acts as shown on the 3.5 kg block. (a) Determine the acceleration given this system (in m/s2 to the right). m/s2 (to the right) (b) Determine the tension in the cord connecting the 3.5 kg and the 1.0 kg blocks (in N). N (c) Determine the force exerted by the 1.0 kg block on the 2.0 kg block (in N). N (d) What If? How would your answers to parts (a) and (b) of this problem change if the 2.0 kg block was now stacked on top of the 1.0 kg block? Assume that the 2.0 kg block sticks to and does not slide on the 1.0 kg block when the system is accelerated. (Enter the acceleration in m/s2 to the right and the tension in N.) acceleration m/s2 (to the right) tension N
An assistant for a football team carries a 32.0 kg cooler of water from the top row of the stadium, which is a distance h = 22.5 m above the field level, down to the bench area on the field. The speed of the cooler is constant throughout the trip. Calculate the work WA done by the assistant on the cooler of water. WA = Calculate the work Wgrav done by the force of gravity on the cooler of water. Wgrav =
See Conceptual Example 6 to review the concepts involved in this problem. A 13.6-kg monkey is hanging by one arm from a branch and swinging on a vertical circle. As an approximation, assume a radial distance of 79.6 cm is between the branch and the point where the monkey's mass is located. As the monkey swings through the lowest point on the circle, it has a speed of 1.20 m/s. Find (a) the magnitude of the centripetal force acting on the monkey and (b) the magnitude of the tension in the monkey's arm. (a) Number Units (b) Number Units
A "swing" ride at a carnival consists of chairs that are swung in a circle by 15.8 m cables attached to a vertical rotating pole, as the drawing shows. Suppose the total mass of a chair and its occupant is 160 kg. (a) Determine the tension in the cable attached to the chair. (b) Find the speed of the chair. (a) Number Units (b) Number Units
Masses A and C are connected by a cord as shown below. The middle mass, B, is held motionless by some method which is not drawn. A force is applied to mass A so that A and C move at constant speed. (Remember that B is motionless.) If the coefficient of kinetic friction between all surfaces is μk = 0.35, what is the applied force F?
In the figure R1 = 140 Ω, R2 = R3 = 62.0 Ω, R4 = 79.4 Ω, and the ideal battery has emf ε = 6.00 V. (a) What is the equivalent resistance? What is i in (b) resistance 1, (c) resistance 2, (d) resistance 3, and (e) resistance 4? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units
In the figure find the equivalent capacitance of the combination. Assume that C1 = 13.6 μF, C2 = 6.00 μF, and C3 = 5.91 μF. Number Units
A particle of charge +1.8 μC is released from rest at the point x = 94 cm on an x axis. The particle begins to move due to the presence of a charge Q that remains fixed at the origin. What is the kinetic energy of the particle at the instant it has moved 29 cm if (a)Q = +46 μC and (b) Q = −46 μC? (a) Number Units (b) Number Units
(a) Figure (a) shows a nonconducting rod of length L = 8.80 cm and uniform linear charge density λ = +8.11 pC/m. Take V = 0 at infinity, What is V at point P at distance d = 9.60 cm along the rod's perpendicular bisector? (b) Figure (b) shows an identical rod except that one half is now negatively charged. Both halves have a linear charge density of magnitude 8.11 pC/m. With V = 0 at infinity, what is V at P? (a) (b) (a) Number Units (b) Number Units
In the figure, a stone is projected at a cliff of height h with an initial speed of 48.0 m/s directed at an angle θ0 = 67.0∘ above the horizontal. The stone strikes at A, 5.45 s after launching. Find (a) the height h of the cliff, (b) the speed of the stone just before impact at A, and (c) the maximum height H reached above the ground. Use 8 = 9.80 m/s2. (a) Number Units (b) Number Units (c) Number Units
Two isolated, concentric, conducting spherical shells have radii R1 = 0.520 m and R2 = 1.50 m, uniform charges q1 = +3.10 μC and q2 = +3.60 μC, and negligible thicknesses. What is the magnitude of the electric field E at radial distance (a) r = 4.10 m, (b) r = 0.660 m, and (c) r = 0.340 m? With V = 0 at infinity, what is V at (d)r = 4.10 m, (e) r = 1.50 m, (f) r = 0.660 m, (g) r = 0.520 m, (h) r = 0.340 m, and (i) r = 0? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units (f) Number Units (g) Number Units (h) Number Units (i) Number Units
Problem 1: (Charges on a rectangle) Consider the following collection of charges below located around a a×b rectangle. Given that Q > 0, (a) Find the components of the net electric field, E→, at the point P, located at the center of the rectangle. (b) Find the magnitude of the electric field and sketch the components and net direction. (c) If an electron were to start at rest from this point would it accelerate? If so, in which direction would its acceleration be?
In the figure three thin plastic rods form quarter-circles with a common center of curvature at the origin. The uniform charges on the rods are Q1 = +72 nC, Q2 = +3.2Q1, and Q3 = −8.3Q1. What is the net electric potential at the origin due to the rods? Number Units
In the figure the capacitances are C1 = 1.5 μF and C2 = 2.5 μF, and both capacitors are charged to a potential difference of V = 86 V but with opposite polarity as shown. Switches S1 and S2 are now closed. (a) What is now the potential difference between points a and b? What now is the charge on capacitor (b) 1 and (c) 2?
A heavy sled is being pulled by two people, as shown in the figure. The coefficient of static friction between the sled and the ground is μs = 0.579, and the kinetic friction coefficient is μk = 0.435. The combined mass of the sled and its load is m = 381 kg. The ropes are separated by an angle ϕ = 28.0∘, and they make an angle θ = 30.1∘ with the horizontal. Assuming both ropes pull equally hard, what is the minimum rope tension Tmin required to get the sled moving? Tmin = f this rope tension is maintained after the sled starts moving, what is the sled's acceleration a? a =
A simple ohmmeter is made by connecting a 2.50 V battery in series with a resistance R and an ammeter that reads from 0 to 1.00 mA, as shown in the figure. Resistance R is adjusted so that when the clip leads are shorted together, the meter deflects to its full-scale value of 1.00 mA. What external resistance across the leads results in a deflection of (a) 11.3%, (b) 54.3%, and (c) 92.6% of full scale? (d) If the ammeter has a resistance of 18.8 Ω and the internal resistance of the battery is negligible, what is the value of R? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
A circular-motion addict of mass 82.0 kg rides a Ferris wheel around in a vertical circle of radius 10.0 m at a constant speed of 7.10 m/s. (a) What is the period of the motion? What is the magnitude of the normal force on the addict from the seat when both go through (b) the highest point of the circular path and (c) the lowest point? (a) Number Units (b) Number Units (c) Number Units
GIVEN: M1 = 55.5 kgm2 = unknown θ = 27.3∘ friction = 13.7 N NOT SHOWN -- draw it yourself The hanging mass is causing the crate to accelerate upward along the incline at a rate of 1 m/s2. There is friction but it is not shown on the diagram, because you need to decide for yourself how it should appear. Deduce the magnitude of each force vector shown in the diagram: If the acceleration is upward along the incline a = b = N. c = N. d = N. e = N. f = N. g = N. (This is the force arrow, not gravitational acceleration).
In the figure a nonconducting rod of length L = 8.15 cm has charge −q = −4.34 fC uniformly distributed along its length. (a) What is the linear charge density of the rod? What are the (b) magnitude and (c) direction (positive angle relative to the positive direction of the x axis) of the electric field produced at point P, at distance a = 14.2 cm from the rod? What is the electric field magnitude produced at distance a = 58 m by (d) the rod and (e) a particle of charge −q = −4.34 fC that replaces the rod? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units
A proton initially has v→ = (−2.00)i^ + (5.40)j^ + (7.80)k^ and then 4.30 s later has v→ = (−17.0)i^ + (5.40)j^ + (11.0)k^ (in meters per second). (a) For that 4.30 s, what is the proton's average acceleration a→ avg in unit vector notation, (b) in magnitude, and (c) the angle between a→ avg and the positive direction of the x axis? (a) Number i^ k^ Units (b) Number Units (c) Number Units
In the figure the capacitances are C1 = 1.1 μF and C2 = 3.5 μF, and both capacitors are charged to a potential difference of V = 100 V but with opposite polarity as shown. Switches S1 and S2 are now closed. (a) What is now the potential difference between points a and b? What now is the charge on capacitor (b) 1 and (c) 2? (a) Number Units (b) Number Units (c) Number Units
The electric field in a region is given by E→ = a b+cx i^, where a = 150 N⋅m/C, b = 2.2 m, and c = 5.2. What is the net charge (in C) enclosed by the shaded volume shown below? C
Suppose a NASCAR race car rounds one end of the Martinsville Speedway. This end of the track is a turn with a radius of approximately 57.0 m. The track is completely flat and the race car is traveling at a constant 24.5 m/s (about 55 mph) around the turn. What is the race car's centripetal acceleration ac? ac = m/s2 Which force is responsible for the centripetal acceleration in this case? normal friction gravity weight What is the minimum coefficient of static friction μs between the race car's tires and the track necessary to keep the car from skidding into the wall on the outside of the turn? μs =
Problem 1: Plate Stack Consider a stack of 5 metal plates as shown below. They are 10 cm squares; in other words, they have an area A = (0.1 m)x(0.1 m). The distance between each plate is d = 0.1 mm. Each plate is charged up with ±10 nC (the sign of the charge is indicated in the drawing: alternating plus and minus charges). a) Draw the E-field between the plates (direction and relative magnitude). b) Calculate the E-field between the plates. c) Calculate the electric potential V between the plates. d) Make plots of the E-field magnitude and electric potential vs x. Include numbers and units. (You can declare one plate to be at V = 0).
A car of mass m drives around a "banked curve" of radius r where the road surface is inclined at an angle of θ. The coefficient of static friction between the tires and the road is μs. Express your answers in terms of r, θ, μs and g. (a) a) Calculate the "ideal" speed for the car to drive so that it doesn't tend to slide up or down the incline. b) Calculate the minimum speed the car can drive without sliding down the incline. c) Calculate the maximum speed the car can drive without sliding up the incline.
A 0.600-kg wood block is firmly attached to a very light horizontal spring k = 200 N/m as shown in the figure. It is noted that the block-spring system, when compressed 5.00 cm and released, stretches out 4.00 cm beyond the equilibrium position before stopping and turning back. What is the coefficient of kinetic friction between the block and the table?
The 2.60 kg physics book shown is connected by a string to a 467.0 g coffee cup. The book is given a push up the slope (call this direction positive) and released with a speed of 2.04 m/s. The coefficients of friction are μs = 0.478 and μk = 0.227. What is the acceleration of the book if the slope is inclined at 22.1∘?
In the figure particles 2 and 4, of charge −e, are fixed in place on a y axis, at y2 = −11.1 cm and y4 = 5.55 cm. Particles 1 and 3, of charge e, can be moved along the x axis. Particle 5, of charge +e, is fixed at the origin. Initially particle 1 is at x1 = −11.1 cm and particle 3 is at x3 = 11.1 cm. (a) To what x value must particle 1 be moved to rotate the direction of the net electric force F→ net on particle 5 by 30∘ counterclockwise? (b) With particle 1 fixed at its new position, to what x value must you move particle 3 to rotate back to its original direction?
A block of mass M rests on a block of mass M1 = 5.00 kg which is on a tabletop (see figure below). A light string passes over a frictionless peg and connects the blocks. The coefficient of kinetic friction μk at both surfaces equals 0.330. A force of F = 41.0 N pulls the upper block to the left and the lower block to the right. The blocks are moving at a constant speed. Determine the mass of the upper block. (Express your answer to three significant figures.) kg