In the figure, a metal wire of mass m = 26.5 mg can slide with negligible friction on two horizontal parallel rails separated by distance d = 3.15 cm. The track lies in a vertical uniform magnetic field of magnitude 42.3 mT. At time t = 0 s, device G is connected to the rails, producing a constant current i = 8.74 mA in the wire and rails (even as the wire moves). At t = 51.6 ms, what are the wire's (a) speed and (b) direction of motion?
You push a 3.0 kg block against a horizontal spring, compressing the spring by 11 cm. Then you release the block, and the spring sends it sliding across a tabletop. It stops 74 cm from where you released it. The spring constant is 370 N/m. What is the coefficient of kinetic friction between the block and the table? Number Units
A car of mass 1137 kg is being pulled up a smooth incline with a constant velocity. The plane makes an angle 25∘ with the horizontal. The car is being pulled by a rope inclined 31∘ with the plane. a) Draw the free body diagram showing all forces acting on the car b) Find the tension in the cable. c) What is the normal force on the car?
In the figure the battery has potential difference V = 11.0 V, C2 = 3.10 μF, C4 = 4.80 μF, and all the capacitors are initially uncharged. When switch S is closed, a total charge of 10.0 μC passes through point a and a total charge of 9.00 μC passes through point b. What are (a) C1 and (b)C3?
A block of mass m1 = 2.0 kg and block of mass m2 = 1.0 kg are connected by a string of negligible mass and rest on a horizontal plane that has coefficient of kinetic friction μk = 0.18. Block 2 is pushed by an inclined force of magnitude 20 N and angle, θ = 34∘. a) Draw the forces acting on both blocks. b) What is the normal force acting on each block? c) Find the acceleration of the blocks. d) What is the tension in the string?
A capacitor consists of two charged disks of radius 4.6 m separated by a distance s = 2 mm (see the figure). The magnitude of the charge on each disk is 70 μC. Consider points A, B, C, and D inside the capacitor, as shown in the diagram. The distance s1 = 1.3 mm, and the distance s2 = 0.8 mm. (Assume the +x axis is to the right, the +y axis is up, and the +z axis is out.) (a) What is the electric field inside the capacitor? E→ = N/C (b) First, calculate the potential difference VB−VA. What is Δl→ along this path? Δi→ = m What is VB−VA? VB = VA = volts (c) Next, calculate the potential difference VC−VB. What is Δi→ along this path? Δi = m What is VC = VB? VC−VB = volts (d) Finally, calculate the potential difference VA−VC. What is Δi→ along this path? Δi→ = m What is VA = VC? VA−VC = volts
A mechanical system (see diagram) is comprised of 2 blocks of massed M and m (m > M) that are attached to each other via a massless, inelastic string, passing around 2 massless, frictionless pulleys. The blocks are also attached to 2 springs of spring constants k1 and k2 respectively. The coefficient of kinetic friction between the incline and M is μk. Initially, when the system is at rest, both springs are un-stretched. When the system is released, m accelerates downwards initially. During the motion, all strings remain tight. Given parameters: M, m, k1, k2, θ, μk, d (a) (4 pts) Draw free-body diagrams for masses M and m after the system is released from rest and m accelerates downward. (b) (3 pts) Find the relationship between the instantaneous speeds vM for mass M and vm for mass m. Show detailed derivation of that relationship. (c) (8 pts) Find the speed vM of block M, when it has moved a distance d up the incline.
A capacitor consists of two charged disks of radius 3.0 m separated by a distance s = 2 mm (see the figure). The magnitude of the charge on each disk is 48 μC. Consider points A, B, C, and D inside the capacitor, as shown in the diagram. The distance s1 = 1.6 mm, and the distance s2 = 0.8 mm. (Assume the +x axis is to the right, the +y axis is up, and the +z axis is out.) Part 1 (a) What is the electric field inside the capacitor? E→ = < > N/C (b) First, calculate the potential difference VB−VA. What is Δl→ along this path? Δl→ = < > m What is VB−VA? VB−VA = V (c) Next, calculate the potential difference VC−VB. What is Δl→ along this path? Δl→ = < > m What is VC−VB? VC−VB = v (d) Finally, calculate the potential difference VA−VC. What is Δl→ along this path? Δl→ = < > m What is VA−VC? VA−VC = v
By means of a rope whose mass is negligible, two blocks are suspended over a pulley, as the drawing shows. The pulley can be treated as a uniform solid cylindrical disk. The downward acceleration of the 44.0-kg block is observed to be exactly 1/4 the acceleration due to gravity. Noting that the tension in the rope is not the same on each side of the pulley, find the mass of the pulley.
A particle of mass 9.35 g and charge 73.3 μC moves through a uniform magnetic field, in a region where the free-fall acceleration is −9.8j^ m/s2 without falling. The velocity of the particle is a constant 16.3i^ km/s, which is perpendicular to the magnetic field. What, then, is the magnetic field?
3. (18 pts) In the diagram below, a block (m2 = 1.5 kg) is at rest on the right edge of a large slab (m1 = 9.0 kg). There is a coefficient of kinetic friction between m1 and m2 equal to 0.2. The slab, in turn, is sitting on a slippery floor with effectively zero friction (μk = 0). The slab is 4.0 meters wide, and the block is 0.5 meters wide. A constant horizontal force F→ is applied to the block, pulling it to the left. It takes two seconds for the block to reach the other side of the slab. (a) How far (in meters) is the bottom slab pulled along in that time? (b) What is the magnitude of F→? *Hint: The block starts with its right side lined up with the right side of the slab, and ends up with its left side lined up with the left side of the slab. Determine an expression for the distance the slab moves in terms of how far the block moves. Use an inertial reference frame, i. e. static origin on the right side of the table.