In the figure, two concentric circular loops of wire carrying current in the same direction lie in the same plane. Loop 1 has radius 1.70 cm and carries 4.00 mA. Loop 2 has radius 2.50 cm and carries 5.70 mA. Loop 2 is to be rotated about a diameter while the net magnetic field B→ set up by the two loops at their common center is measured. Through what angle must loop 2 be rotated so that the magnitude of the net field is 110 nT?
A solid sphere of mass m and radius r rolls without slipping along the track shown in Figure P10.79. It starts from rest with the lowest point of the sphere at height h above the bottom of the loop of radius R, much larger than r. Figure P10.79 (a) What is the minimum value of h (in terms of R ) such that the sphere completes the loop? h = (b) What are the force components on the sphere at the point P if h = 3R? (Use R, m, r, and g for gravity, as necessary.) Fx = N Fy = N
Matt is driving a truck composed of a body (mB = 1000 kg) and four wheels (disks of mass mw = 50 kg, radius r = 0.4 m each) on a road (μs = 0.7, μD = 0.5) at 30 m/s. The truck body is w = 2 m wide and h = 2 m tall, with a center of gravity d = 2 m above the ground. He tries to round a corner of radius R = 20 m. W
An aircraft is making a circular turn. During the turn, the plane has a constant velocity of 250 ft/sec and a constant acceleration of 10 ft/sec2. The angle between the velocity and acceleration is 30∘ as shown in the diagram. Determine the radius of the turn.
A car is about to enter a circular loop of a roller coaster ride. The total mass of the car is 250 kg and the loop has a radius of 30 m. For safety reason, the normal acceleration in the loop is limited to 60 m/sec2. Determine the speed of the car and the centripetal force acting on the car.
Cars A and B are traveling around the circular racetrack. At the instant shown, A has a speed of 90 ft/s and increasing its speed at the rate of 15 ft/s2, whereas B has a speed of 105 ft/s and is decreasing its speed at 25 ft/s2. Use the Normal-Tangential (n−t) coordinate system for each car separately to answer the following: For Car A: (a) Redraw Car A and properly show the n-t coordinate system on the car, along with the unit vector. (b) Show the velocity vector and calculate the speed (magnitude) (c) Show the acceleration vector and find the magnitude. For Car B: (a) Redraw Car B and properly show the n-t coordinate system on the car, along with the unit vector. (b) Show the velocity vector and calculate the speed (magnitude) (c) Show the acceleration vector and find the magnitude.
(a) Calculate the moment of inertia (click for graphical table) of the contraption around the fulcrum. kgm2 (b) Calculate the torque about the fulcrum, using CCW as positive. Nm (c) Calculate the angular acceleration of the contraption, using CCW as positive. rad/s2 (d) Calculate the linear acceleration of the right end of the rod, using up as positive. m/s2
A 0.94 kg mass is attached to a light spring with a force constant of 34.9 N/m and set into oscillation on a horizontal frictionless surface. If the spring is stretched 5.0 cm and released from rest, determine the following. (a) maximum speed of the oscillating mass m/s (b) speed of the oscillating mass when the spring is compressed 1.5 cm m/s (c) speed of the oscillating mass as it passes the point 1.5 cm from the equilibrium position m/s (d) value of x at which the speed of the oscillating mass is equal to one-half the maximum value m
A puck of mass m = 1.50 kg slides in a circle of radius r = 16.0 cm on a frictionless table while attached to a hanging cylinder of mass M = 4.10 kg by a cord through a hole in the table. What speed keeps the cylinder at rest? Number Units
Suppose the ski patrol lowers a rescue sled and victim, having a total mass of 80.0 kg, down a θ = 56.0∘ slope at constant speed, as shown in the figure. The coefficient of friction between the sled and the snow is 0.100 . (a) How much work is done (in J) by friction as the sled moves 30.0 m along the hill? J (b) How much work is done (in J) by the rope on the sled in this distance? J (c) What is the work done (in J) by gravity on the sled? J (d) What is the total work done (in J)? J
A 3.23 kg block is pushed along a horizontal floor by a force F→ of magnitude 21.0 N at a downward angle θ = 40.0∘. The coefficient of kinetic friction between the block and the floor is 0.220. Calculate the magnitudes of (a) the frictional force on the block from the floor and (b) the block's acceleration. (a) Number Units (b) Number Units
Let be given a mathematical pendulum (Fig. 1) with mass m = 786 g, length l = 250 mm and angle φ as degree of freedom. The weight force FG acts on the mass, friction effects can be neglected. Figure 1: Mathematical pendulum [3]. (i) Set up the equation of motion with the angle φ as the system variable.
A 19-kg sled is being pulled along the horizontal snow-covered ground by a horizontal force of 32 N. Starting from rest, the sled attains a speed of 2.9 m/s in 8.3 m. Find the coefficient of kinetic friction between the runners of the sled and the snow. Number Units
A 4.0 kg box is released from rest on a frictionless ramp. The box slides from the ramp onto a rough horizontal surface with a friction coefficient μk = 0.50. The box slides 2.0 m horizontally until it stops. d What height was the box on the ramp?
A mass m = 1.05 kg slides without friction from rest on a surface making a quarter circle with radius R = 1.55 m as shown in Figure 1. Then it lands on the top surface of a cart with mass M = 11.3 kg, that slides without friction on a horizontal surface. (In practise this cart could be a slider on an air track). Between the top of the cart and the mass m, the coefficient of static friction is μs = 1.07 and the coefficient of kinetic friction is μk = 0.959. The mass m slides a distance along the top of the cart but does not fall off. Figure 1: Diagrammatic representation of a block of mass m at the top of a quarter-circle surface of radius R that slopes down and to the right with decreasing absolute gradient towards a cart of mass M. The cart itself is resting on a horizontal surface. Part 1) What is the speed of the mass m immediately before it lands on the cart, M? v = ms−1 Part 2) What is the speed of the cart, M, when there is no longer any relative movement between m and M? V = m/s Part 3) How much mechanical energy is lost during the collision? (while m comes to rest relative to M). ΔE = −J Enter a positive number in the box if the final mechanical energy is less than the initial mechanical energy.
Two test charges are located in the xy plane. Charge q1 = −4.250 nC and is located at x1 = 0.00 m, y1 = 0.6800 m. Charge q2 = 3.200 nC and is located at x2 = 1.500 m, y2 = 0.400 m. Calculate the x and y components, Ex and Ey, respectively, of the electric field E→ at the origin, (0, 0). The Coulomb force constant is 1/(4πϵ0) = 8.99×109 N⋅m2/C2. Ex = N/C Ey = N/C
A spring hangs vertically from a bracket at its unweighted equilibrium length, as shown in the left-most image. An object with mass m is attached to the lower end of the spring, and it is gently lowered until the spring reaches its new equilibrium length, as shown in the center figure. Referring to the right-most figure, the mass is raised until the spring returns to its original length, and then it is released from rest resulting in vertical oscillations. 50% Part (a) If the spring constant is 8.5 N/m, and the mass of the object is 0.45 kg, find the oscillation amplitude, in meters. A = m 50% Part (b) Find the maximum velocity, in meters per second, of the oscillating mass.
A square plane mirror of side length s hangs on a wall such that its bottom edge is a height h above the floor. The wall opposite the mirror is a distance d away. Marco, whose eyes are at the exact height of the center of the mirror, stands directly in front of the mirror at the center of its width. Derive an expression for the maximum distance x that Marco can stand from the mirror and still see the reflection of the bottom of the wall behind him. Assume that s < 2h. x = Enter your expression in terms of given values and rational coefficients.
Under constant pressure, the temperature of 2.17 mol of an ideal monatomic gas is raised 18.4 K. What are (a) the work W done by the gas, (b) the energy transferred as heat Q, (c) the change ΔEint in the internal energy of the gas, and (d) the change ΔK in the average kinetic energy per atom? (a) Number Units (b) Number Units (c) Number Units (d) Number Units