A 7.3 kg slender rod has a length of 3.2 m. A collar of negligible mass connects one of its ends, C, to a smooth circular bar which has a radius r = 22 m. End B rests on the wall, which has a coefficient of kinetic friction of μB = 0.3. If the bar is released from rest when θ = 25∘, determine the initial angular acceleration of the bar as well as the normal reaction forces NB and NC. [15]
A block slides down a straight ramp inclined at an angle of θ = 30∘, then slides horizontally off the end of a table as shown. There is no friction, and the block's speed leaving the table is the same as its speed at the end of the ramp. At what distance x from the bottom of the ramp should you release the block so that it lands in the bucket? 15 cm 49 cm 60 cm 30 cm 21 cm
A planet has a mass of 5.60×1023 kg and a radius of 3.75×106 m. (a) What is the acceleration due to gravity on this planet? (b) How much would a 53.8−kg person weigh on this planet? (a) Number Units (b) Number Units
A cube of mass m1 = 9.9 kg sits on top of a second cube of the same size, but of mass m2 = 0.6 kg, while both are in free-fall. Assume air resistance is negligible. What is the magnitude N of the normal force that the bottom cube exerts on the top cube? N =
A lamp hangs vertically from a cord in a descending elevator that decelerates at 1.3 m/s2. (a) If the tension in the cord is 84 N, what is the lamp's mass? (b) What is the cord's tension when the elevator ascends with an upward acceleration of 1.3 m/s2? (a) Number Units (b) Number Units
Concept Simulation 20.4 provides background for this problem and gives you the opportunity to verify your answer graphically. How many time constants (a decimal number) must elapse before a capacitor in a series RC circuit is charged to 77.0% of its equilibrium charge? Number Units
A bolt is dropped from a bridge under construction, falling 83 m to the valley below the bridge. (a) How much time does it take to pass through the last 17% of its fall? What is its speed (b) when it begins that last 17% of its fall and (c) just before it reaches the ground? (a) Number Unit (b) Number Unit (c) Number Unit
(a) What is the rate of energy loss in watts per square meter through a glass window 3.4 mm thick if the outside temperature is −21∘F and the inside temperature is +77∘F? (b) A storm window having the same thickness of glass is installed parallel to the first window, with an air gap of 6.3 cm between the two windows. What now is the rate of energy loss if conduction is the only important energy-loss mechanism? (The thermal conductivity of window glass is 1.0 W/m⋅K, and of air is 0.026 W/m⋅K.) (a) Number Units (b) Number Units
A 1,440-N crate is being pushed across a level floor at a constant speed by a force F→ of 200 N at an angle of 20.0∘ below the horizontal, as shown in the figure a below. a b (i) (a) What is the coefficient of kinetic friction between the crate and the floor? (Enter your answer to at least three decimal places.) (b) If the 200−N force is instead pulling the block at an angle of 20.0∘ above the horizontal, as shown in the figure b, what will be the acceleration of the crate? Assume that the coefficient of friction is the same as that found in part (a). m/s2
Point charges Q1 = 3.5 μC and Q2 = 9.0 μC are located at r→1 = (5.0i^ − 2.0j^ + 6.0 k^) m and r→2 = (8.0i^ + 4.0j^ − 9.0k^) m. What is the force (in N) of Q2 on Q1? (Express your answer in vector form.) F→21 = ( ) N
In the figure below, m1 = 10.8 kg and m2 = 3.6 kg. The coefficient of static friction between m1 and the horizontal surface is 0.60, and the coefficient of kinetic friction is 0.30. (a) If the system is released from rest, what will its acceleration be? (Enter the magnitude of the acceleration.) m/s2 (b) If the system is set in motion with m2 moving downward, what will be the acceleration of the system? (Enter the magnitude of the acceleration.) m/s2
A bolt is dropped from a bridge under construction, falling 84 m to the valley below the bridge. (a) How much time does it take to pass through the last 30% of its fall? What is its speed (b) when it begins that last 30% of its fall and (c) just before it reaches the ground? (a) Number Unit (b) Number Unit (c) Number Unit
In our discussions of orbits, we assumed that a very massive planet was stationary at the origin, and that a satellite moved around it. In reality both objects move around each other, although the massive planet makes a very small motion. Now consider two equal mass asteroids, each with mass 1.3×109 kg, orbiting each other in perfect circles. If the diameter of the circle is 4 km, what is the speed of the asteroids relative to the stationary center of mass?
In a popular amusement park ride, a rotating cylinder of radius R = 2.20 m is set in rotation at an angular speed of 6.20 rad/s, as in the figure shown below. The floor then drops away, leaving the riders suspended against the wall in a vertical position. What minimum coefficient of friction between a rider's clothing and the wall is needed to keep the rider from slipping? Hint: Recall that the magnitude of the maximum force of static friction is equal to μsn, where n is the normal force-in this case, the force causing the centripetal acceleration. (a)
A spherical water drop 1.3 μm in diameter is suspended in calm air due to a downward-directed atmospheric electric field of magnitude E = 452 N/C. (a) What is the magnitude of the gravitational force on the drop? (b) How many excess electrons does it have? (a) Number Units (b) Number Units
Two spherical objects are separated by a distance of 2.92×10−3 m. The objects are initially electrically neutral and are very small compared to the distance between them. Each object acquires the same negative charge due to the addition of electrons. As a result, each object experiences an electrostatic force that has a magnitude of 4.56×10−21 N. How many electrons did it take to produce the charge on one of the objects?
Consider the set of masses and springs shown above. Use ω2 = k/m. Write down the equations of motion (Newton's 2nd law/forces) for each of the masses. Assume that the motion of each mass i is described by xi[t] = Aieiαt Write down the linear equations (in terms of ω, Ai and α) that the equations of motion imply. You do not need to solve this.
Three point charges, Q1, Q2, and Q3 are arranged in a triangle as shown in the figure. Point charge Q1 has a charge of 5.16 nC. Point charge Q2 has a charge of 6.52 nC. Point charge Q3 has a charge of 2.25 nC. Point charges Q1 and Q2 are separated by a distance D12 of 0.146 m. Point charges Q2 and Q3 are separated by a distance D23 of 0.625 m. Point charges Q1 and Q3 are separated by a distance D13 of 0.578 m.
An electron is placed in an xy plane where the electric potential depends on x and y as shown in the figure (the potential does not depend on z). The scale of the vertical axes is set by Vs = 500. V. In unit-vector notation, what is the electric force on the electron? x(m) y(m) Number i^ + j^ Units
Two electrons are fixed 3.64 cm apart. Another electron is shot from infinity and stops midway between the two as the figure shows. What is its initial speed? Number Units
An ice block of mass 5.5 kg slides down a rough surface of a ramp with at an angle θ = 520 while an ice worker pulls on the block by a rope with a force F→r = 35 N and is directed up the ramp. The coefficient of kinetic friction between the ice block and the rough surface is μk = 0.09. The block slides through a distance, d = 0.50 m along the ramp downward. Find out a. the work done by the gravitational force. b. the work done by the frictional force. c. the work done by the applied force. d. the change of kinetic energy of the block. e. the velocity at the end of the displacement if starts with a velocity of 2.0 m/s.
Two neutral conducting spheres, A and B, are supported by insulating stands. The spheres are initially touching each other. A particle with a positive charge +Q is brought near the sphere A as shown. First, explain what is happening microscopically inside the conducting spheres (if anything at all) when the charge is brought near. Draw a diagram to illustrate this. Is there a net force on the particle with the +Q charge at this time? Explain your reasoning. Without touching the metal spheres, the person holding the base of sphere B now pulls it 4 cm to the right. Is there a net force on sphere A? Explain your reasoning. When sphere B is moved, does the net force on the particle +Q increase, decrease, or remain the same? Explain your reasoning. After sphere B is moved, is there a net force on it by sphere A? Explain your reasoning.
The 10-lb block has a speed of 4 ft/s when the force of F = (8t2) lb is applied. The coefficient of kinetic friction at the surface is μk = 0.2. (Figure 1) Figure 1 of 1 Part A Determine the velocity of the block when it moves s = 27 ft. Express your answer in feet per second to three significant figures. v = ft/s Submit Request Answer Return to Assignment Provide Feedback
Three point charges are located along the as shown below. q1 = −5.0 μC, q2 = 10.0 μC, q3 = 4.0 μC, a = 1.0 cm. Figure 6: Problem 1. (a) What are the x and y components of the electric filed at the origin O due to charge q1? (4 pt) (b) What are the x and y components of the electric filed at the origin due to q2? (4 pt) (c) What are the x and y components of the electric filed at the origin due to q3? (4 pt) (d) What are the x and y components of the net electric filed at the origin from all three charges? What are its magnitude and direction? (4 pt) (e) What are the x and y components of an electron's acceleration at the origin? (4 pt) Bonus: A fourth charge is placed at (x, y) = (−4a, 0). What should be its value to ensure that the x-component of the new net electric field at the origin is zero (3 pt)
An electron with a speed of 4.67×108 cm/s in the positive direction of an x axis enters an electric field of magnitude 1.93×103 N/C, traveling along a field line in the direction that retards its motion. (a) How far will the electron travel in the field before stopping momentarily, and (b) how much time will have elapsed? (c) If the region containing the electric field is 4.48 mm long (too short for the electron to stop within it), what fraction of the electron's initial kinetic energy will be lost in that region? (a) Number Units (b) Number Units (c) Number Units
An electron initially at rest, is placed at electric field of 4.0×104 N/C directed to the west. The distance between the plates is 2.0 cm a) What is the acceleration of the electron due to the electric field? b) What will be the speed of the electron after it leaves the hole. Show the sketch of the two plates?
An electron enters a region of uniform electric field with an initial velocity of 61 km/s in the same direction as the electric field, which has magnitude E = 53 N/C. (a) What is the speed of the electron 1.9 ns after entering this region? (b) How far does the electron travel during the 1.9 ns interval?