A student (whose mass is M1 = 68 kg) is hanging on to a rope (of negligible mass). The rope is hung over a frictionless pulley and is connected at its other end to a crate of mass M2 = 84 kg, as in the figure. The crate is initially hoisted up then allowed to fall while the student continues to hang on to the rope and is lifted up by the rope. What is the magnitude of the acceleration of the student while the crate falls? Your answer should be in m/s2, but enter only the numerical part in the box.
In class we solved the following example problem: The 0.5 lb pellet is pushed against the spring and released from rest at A. Neglecting friction, determine the smallest deflection of the spring for which the pellet will travel around the loop and always remain in contact with the loop. Now, solve the same problem to determine the smallest deflection of the spring required if the section AB has a length of 2 feet and has a coefficient of friction of 0.25 (the section BD is frictionless). (7.5 points)
A crate with a mass of 60 kilogram crate is resting on a flat horizontal surface. The coefficient of static friction between the crate and the surface is μs = 0.5. There are two forces that are applied to the crate. P1 = 250 lbs and P2 = 125 lbs. Determine and state whether the crate will remain stationary or begin to move.
In the figure, a 0.27 kg block of cheese lies on the floor of a 950 kg elevator cab that is being pulled upward by a cable through distance d1 = 2.1 m and then through distance d2 = 10.9 m. (a) Through d1, if the normal force on the block from the floor has constant magnitude FN = 3.49 N, how much work is done on the cab by the force from the cable? (b) Through d2, if the work done on the cab by the (constant) force from the cable is 93.90 kJ, what is the magnitude of FN? (a) Number Units (b) Number Units
Coaxial cable. The inner and outer cylindrical conductors of a long coaxial cable have diameters a = 0.181 mm and b = 2.88 mm. What is the capacitance per unit length? Number Units
An object with total mass M = 15.6 kg is sitting at rest at the origin when it explodes into three pieces. One piece with mass m1 = 4.85 kg moves up and to the left at an angle of θ1 = 23.0∘ above the negative x-axis with a speed of v1 = 27.9 m/s. A second piece with mass m2 = 5.40 kg moves down and to the right at an angle of θ2 = 28.0∘ to the right of the negative y-axis at a speed of v2 = 20.1 m/s. A third piece with mass m3 moves with velocity v→3. What is the magnitude pf of the final momentum of the system comprising all three pieces? pf = kg⋅m/s
In the figure here, a cylinder having a mass of 1.1 kg can rotate about its central axis through point O. Forces are applied as shown: F1 = 1.2 N, F2 = 9.3 N, F3 = 5.3 N, and F4 = 7.4 N. Also, r = 7.3 cm and R = 15 cm. Taking the clockwise direction to be negative, find the angular acceleration of the cylinder. (During the rotation, the forces maintain their same angles relative to the cylinder.) Number Unit
A rack of seven spherical bolwing balls (each 7.20 kg, radius of 10.1 cm) is positioned along a line located a distance d = 0.980 m from a point P, as shown in the figure. Calculate the magnitude of the gravitational force F the bowling balls exert on a ping-pong ball of mass 2.70 g, centered at point P. F = N
The figure below shows a uniformly charged rod with total charge Q = 12.0 nC. The distance d = 10.0 cm, and the rod is L = 50.0 cm long. With V = 0.00 at infinity, find the electric potential at Point a in the figure. V
The drawing shows three objects. They are connected by strings that pass over massless and friction-free pulleys. The objects move starting from rest, and the coefficient of kinetic friction between the middle object and the surface of the table is 0.147. (a) What is the acceleration of the three objects? (b) Find the tension in the string attached to the 25.0 kg object. (c) Find the tension in the string attached to the 10.0 kg object. (a) Number Units (b) Number Units (c) Number Units
In the figure, the coefficient of kinetic friction between the surface and the blocks is μk. If M = 0.0 kg, find an expression for the magnitude of the acceleration of either block (in terms of F, μk, and g). μk is typed as "muk" (i.e., "mu" and the lower case letter "k") without the quotations.
(a) What is the minimum force of friction required to hold the system of Figure P4.74 in equilibrium? (b) What coefficient of static friction between the 100. −N block and the table ensures equilibrium? (c) If the coefficient of kinetic friction between the 100.−N block and Figure P4.74 the table is 0.250, what hanging weight should replace the 50.0−N weight to allow the system to move at a constant speed once it is set in motion?
The spring shown below is compressed 50 cm and used to launch a 100 kg physics student. The track is frictionless until it starts up the incline. The student's coefficient of kinetic friction on the 30∘ incline is 0.15. How far up the incline, in meters, does the student go?
The capacitor shown in (Figure 1) is connected to a 80.0−V battery. Calculate the electric field everywhere between the capacitor plates. Enter your answers in volts per meter separated by a comma. Submit Request Answer Part B Find both the free charge on the capacitor plate and the induced charge on the faces of the glass dielectric plate. Enter your answers in coulombs separated by a comma. Figure 1 of 1
An isolated charged soap bubble of radius R0 = 4.25 cm has a potential of V0 = 323.0 V at its surface. If the bubble shrinks to a radius that is 43.0% of the initial radius, by how much ΔU does its electrostatic potential energy change? ΔU = J Assume that the charge on the bubble is spread evenly over the surface, and that the total charge on the bubble remains constant. Use k = 8.99×109 N⋅m2/C2 for the Coulomb force constant.
A conducting sphere of radius a having a charge Q, is surrounded by a dielectric shell with permittivity ϵ(r) = ϵ0(b/r) for a ≤ r ≤ b. (a) Determine the electric flux density, D, the electric field, E and the polarization vector P everywhere. (b) Determine the polarization surface charge on a and b, and volumetric polarization charge within a < r < b. (c) Verify that the total polarization charge associated with the dielectric sphere is zero. In this case both the surface and volumetric polarization charge must be taken into account. (d) If a grounded conducting shell of radius b surrounds the sphere, what is the capacitance of this system?
Two positive point charges +4.00 μC and +2.00 μC are placed at the opposite corners of a rectangle as shown in the figure. (k = 1/4πε0 = 8.99×109 N⋅m2/C2) (a) What is the potential at point A (relative to infinity) due to these charges? (b) What is the potential at point B (relative to infinity) due to these charges?
A 2.1-kg model rocket is launched vertically and reaches an altitude of h = 82 m with a speed of 38 m/s at the end of the powered flight, time t = 0. As the rocket approaches its maximum altitude it explodes into two parts A and B, and the mass of part A, mA = 0.5 kg, and the remaining mass of the rocket is in part B. Part A is observed to strike the ground 93 m west of the launch point at t = 8 s. Determine the y -position of part B at that time.
In downhill speed skiing a skier is retarded by both the air drag force on the body and the kinetic frictional force on the skis. Suppose the slope angle is θ = 42.0∘, the snow is dry snow with a coefficient of kinetic friction μk = 0.0430, the mass of the skier and equipment is m = 87.0 kg, the cross-sectional area of the (tucked) skier is A = 1.30 m2, the drag coefficient is C = 0.160, and the air density is 1.20 kg/m3. (a) What is the terminal speed? (b) If a skier can vary C by a slight amount dC by adjusting, say, the hand positions, what is the corresponding variation in the terminal speed? Give your answer in terms of the given values and dC (need derivative for given values). (a) Number Units (b) Number dC Units
A student is skateboarding down a ramp that is 8.29 m long and inclined at 18.7∘ with respect to the horizontal. The initial speed of the skateboarder at the top of the ramp is 2.90 m/s. Neglect friction and find the speed at the bottom of the ramp. Number Units
A car (m = 1790 kg) is parked on a road that rises 16∘ above the horizontal. What are the magnitudes of (a) the normal force and (b) the static frictional force that the ground exerts on the tires?
A particle with charge Q = 4.60 μC is located at the center of a cube of edge L = 0.100 m. In addition, six other identical charged particles having q = −0.5 μC are positioned symmetrically around Q as shown in the figure below. Determine the electric flux through one face of the cube. kN⋅m2/C
The values of the components in a simple series RC circuit containing a switch (see figure below) are C = 1.00 μF, R = 2.00×106 Ω, and ε = 10.0 V. At the instant 3.1 s after the switch is closed. (a) (b) t < 0 (c) t > 0 (a) Calculate the charge on the capacitor. q = μC (b) Calculate the current in the resistor. I = nA (c) Calculate the rate at which energy is being stored in the capacitor. rate = nW (d) Calculate the rate at which energy is being delivered by the battery. Pbattery = nW
As shown in the figure below, a 2.25 kg block is released from rest on a ramp of height h. When the block is released, it slides without friction to the bottom of the ramp, and then continues across a surface that is frictionless except for a rough patch of width 15.0 cm that has a coefficient of kinetic friction μk = 0.590. Find h (in m) such that the block's speed after crossing the rough patch is 3.10 m/s. (Enter a number.) m
The drawing shows a baggage carousel at an airport. Your suitcase has not slid all the way down the slope and is going around at a constant speed on a circle ((r = 11.0 m) as the carousel turns. The coefficient of static friction between the suitcase and the carousel is 0.940, and the angle θ in the drawing is 11.3∘. How much time is required for your suitcase to go around once? Assumme that the static friction between the suitcase and the carousel is at its maximum. Number Units