Figure (a) below shows a metal block hanging from a spring scale, with the scale measuring 5.25 N. In figure (b), the suspended block is submerged in water, and the now scale reads 3.90 N. What is the density (in kg/m3) of the block? (Hint: the free-body diagram to the right of figure (b) shows the forces acting on the block, with B→ and T→ pointing up and Mg→ pointing down.) a b kg/m3
The figure shows a cross section across a long cylindrical conductor of radius a = 2.42 cm carrying uniform current 71.3 A. What is the magnitude of the current's magnetic field at radial distance (a) 0, (b) 1.02 cm, (c) 2.42 cm (wire's surface), (d) 4.23 cm? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
The figure shows a bicycle wheel resting against a small step whose height is h = 0.100 m. The weight and radius of the wheel are W = 28.0 N and r = 0.320 m. A horizontal force F→ is applied to the axle of the wheel. As the magnitude of F→ increases, there comes a time when the wheel just begins to rise up and loses contact with the ground. What is the magnitude of the force when this happens?
A uniform rod of length 0.81 m and mass 0.91 kg is supported horizontally by a collar that is attached to a vertical wall, as shown. A second uniform rod of length 0.27 m and mass 0.23 kg is attached to the first, with the far ends of the rods aligned as shown. What is the magnitude of the total torque, in newton meters, exerted on the longer rod due to the force of gravity? Assume that the axis extends perpendicularly out of the page and is located at the collar, which has negligible length. |Στg| = N⋅m
A uniformly dense rigid rod is pivoted around a frictionless hinge to form a physical pendulum, as shown in the figure. The length of the rod, denoted by L in the figure is 1.9 m and the mass of the rod is 3 kg. The distance between the hinge and the center of mass of the rod is L/4. What is the angular frequency of small amplitude oscillations of this pendulum?
Bicyclists in the Tour de France do enormous amounts of work during a race. For example, the average power per kilogram generated by Lance Armstrong (m = 75.0 kg) is 6.50 W per kilogram of his body mass. (a) How much work does he do during a 145−km race in which his average speed is 12.0 m/s? (b) Often, the work done is expressed in nutritional Calories rather than in joules. Express the work done in part (a) in terms of nutritional Calories, noting that 1 joule = 2.389×10−4 nutritional Calories. (a) Number Units (b) Number Units
Bicyclists in the Tour de France do enormous amounts of work during a race. For example, the average power per kilogram generated by Lance Armstrong (m = 75.0 kg) is 6.50 W per kilogram of his body mass. (a) How much work does he do during a 145−km race in which his average speed is 12.0 m/s? (b) Often, the work done is expressed in nutritional Calories rather than in joules. Express the work done in part (a) in terms of nutritional Calories, noting that 1 joule = 2.389×10−4 nutritional Calories. (a) Number Units (b) Number Units
A block of mass m = 3.37 kg is attached to a spring with spring constant k = 785 N/m. It is initially at rest on an inclined plane that is at an angle of θ = 28.3∘ with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is μk = 0.19. In the initial position, where the spring is compressed by a distance of d = 0.151 m, the mass is at its lowest position and the spring is compressed the maximum amount. Take the initial gravitational potential energy of the block as zero.
A certain man has a mass of 86.0 kg and a density of 996 kg/m3 (excluding the air in his lungs). (a) Calculate his volume (in m3). m3 (b) Find the buoyant force (in N) air exerts on him. N (c) What is the ratio of the buoyant force to his weight? buoyant force weight
In the figure, three connected blocks are pulled to the right on a horizontal frictionless table by a force of magnitude T3 = 23.4 N. If m1 = 16.5 kg, m2 = 21.2 kg, and m3 = 31.6 kg, calculate (a) the magnitude of the system's acceleration, (b) the tension T1, and (c) the tension T2. (a) Number Units (b) Number Units (c) Number Units
Mass m = 1.45 kg is suspended vertically at rest by an insulating string connected to a circuit partially immersed in a magnetic field as in the figure below. The magnetic field has magnitude B = 2.40 T and the length l = 0.790 m. (i) HINT (a) Find the current I (in A). A (b) If E = 115 V, find the required resistance R (in Ω). Ω
A spool of paper forms a solid right circular cylinder with mass m = 1.5 kg and moves on a horizontal surface. Static friction between the paper and the table enforces rolling without slipping. Starting from rest, a physicist begins to draw on the loose end of paper that extends over the top of the spool as shown below. The tension is maintained at T = 3.0 N. You can neglect the mass of the paper that leaves the spool. (a) After the spool rolls to the right by a distance Δx = 2 m what length of paper has been pulled off the spool? (b) Sketch all forces acting on the spool of paper in this process. (Hint: remember static friction!) (c) Determine the acceleration of the spool. (Hint: It is not T/m)
In figure below, object slides with a constant velocity. Find work done by friction on the block from the top to bottom of the plane. 5 points Mass of the block = 0.65 Kg
A teacher used the equipment shown in the figure below to demonstrate the motor effect. The copper rod in the figure above has a length of 7 cm and a mass of 4×10−4 kg. When there is a current of 1.12 A the resultant force on the copper rod is 0 N. Calculate the magnetic flux density. Gravitational field strength = 9.8 N/kg [5 marks]
In Figure (a), an irregularly shaped plastic plate with uniform thickness and density (mass per unit volume) is to be rotated around an axle that is perpendicular to the plate face and through point O. The rotational inertia of the plate about that axle is measured with the following method. A circular disk of mass 0.55 kg and radius 2.3 cm is glued to the plate, with its center aligned with point O (see Figure (b)). A string is wrapped around the edge of the disk the way a string is wrapped around a top. Then the string is pulled for 4.6 s. As a result, the disk and plate are rotated by a constant force of 0.45 N that is applied by the string tangentially to the edge of the disk. The resulting angular speed is 110 rad/s. What is the rotational inertia of the plate about the axle? (a) (b) Number Units
Q1. A d-c current I = 4(mA) flows in a rectangular loop in xy - plane as in the figure below. Assuming a uniform magnetic flux density B = −y^0.6 + z^0.8 (T) in the region. The dimensions in m. a) Calculate the forces acting on each side of the wire loop. b) Find the torque on the loop.
An elevator car has a mass of 1000 kg and is carrying passengers having a combined mass of 800 kg. A constant frictional force of 4000 N retards its motion upward. What must be the minimum power delivered by the motor to lift the elevator car at a constant speed of 3.00 m/s.
Three uniformly charged large sheets with surface charge densities σ1 = +9.7 nC/m2, σ2 = −13.7 nC/m2 and σ3 = +15.7 nC/m2 are perpendicular to the y-axis, as shown below. Find the net electric field E→ at the point O.
5.3.21 The two capacitors in Fig. P5.3.21 were charged and then connected as shown. Determine the equivalent capacitance, the initial voltage at the terminals, and the total energy stored in the network. FIGURE P5.3.21
The quantity of charge Q in coulombs (C) that has passed through a point in a wire up to time t (measured in seconds) is given by Q(t) = t3 − 2t2 + 3t + 5. [The unit of current is an ampere 1 A = 1 C/s. ] (a) Find the current (in A) when t = 0.3 s. A (b) Find the current (in A) when t = 1 s. A At what time (in s) is the current the lowest? t = s
It is generally a good idea to gain an understanding of the "size" of units. Consider the objects and calculate the kinetic energy K of each one. A ladybug weighing 31.8 mg flies by your head at 4.15 km/h. Kladybug = J A 6.95 kg bowling ball slides (not rolls) down an alley at 23.3 km/h. Kbowling ball = J A car weighing 1060 kg moves at a speed of 43.5 km/h. Kcar =
In Figure (a) below, a 10.26 V battery is connected to a resistive strip that consists of three sections with the same cross-sectional areas but different conductivities. Figure (b) gives the electric potential V(x) versus position x along the strip. The horizontal scale is set by x5 = 9.36 mm. Section 3 has conductivity 3.027×107(Ω⋅m)−1. What is the conductivity of section (a) 1 and (b) 2? (a) (b) x(mm) (a) Number Units (b) Number Units
The figure shows an arrangement in which four disks are suspended by cords. The longer, top cord loops over a frictionless pulley and pulls with a force of magnitude 95.8 N on the wall to which it is attached. The tensions in the shorter cords are T1 = 61.5 N, T2 = 44.0 N, and T3 = 7.36 N. What are the masses of (a) disk A, (b) disk B, (c) disk C, and (d) disk D? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
The space between two concentric conducting spherical shells of radii b = 1.90 cm and a = 1.20 cm is filled with a substance of dielectric constant K = 15.1. A potential difference V = 18.0 V is applied across the inner and outer shells. Determine (a) the capacitance of the device, (b) the free charge a on the inner shell, and (c) the charge q induced along the surface of the inner shell. (a) Number Units (b) Number Units (c) Number Units
In the figure, a 1.9-m-long vertical pole extends from the bottom of a swimming pool to a point 50.0 cm above the water. Sunlight is incident at angle θ = 48.0∘. What is the length in meters of the shadow of the pole on the level bottom of the pool? The water has an index of refraction of 1.33. Number Units
A fighter jet is launched from an aircraft carrier with the aid of its own engines and a steam-powered catapult. The thrust of its engines is 1.12×105 N. In being launched from rest it moves through a distance of 54.0 m and has a kinetic energy of 6.01×107 J at lift-off. What is the work done on the jet by the catapult? Number Units
A 1.40−kg object slides to the right on a surface having a coefficient of kinetic friction 0.250 (Figure a). The object has a speed of v1 = 3.30 m/s when it makes contact with a light spring (Figure b) that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distance d (Figure c). The object is then forced toward the left by the spring (Figure d) and continues to move in that direction beyond the spring's unstretched position. Finally, the object comes to rest a distance D to the left of the unstretched spring (Figure e). (a) Find the distance of compression d (in m). m (b) Find the speed v (in m/s) at the unstretched position when the object is moving to the left (Figure d). m/s (c) Find the distance D (in m) where the object comes to rest. m (d) What If? If the object becomes attached securely to the end of the spring when it makes contact, what is the new value of the distance D (in m) at which the object will come to rest after moving to the left? m
Chapter 09, Problem 36 A 8.47−m ladder with a mass of 21.1 kg lies flat on the ground. A painter grabs the top end of the ladder and pults straight upward with a force of 254 N. At the instant the top of the ladder leaves the ground, the ladder experiences an angular acceleration of 1.54 rad/s2 about an axis passing through the bottom end of the ladder. The ladser's center of gravity lies halfway between the top and bottom ends. (a) What is the net torque acting on the ladder? (b) What is the ladder's moment of inertia? (a) Number Units (b) Number Units
In the figure, a small 0.161 kg block slides down a frictionless surface through height h = 0.507 m and then sticks to a uniform vertical rod of mass M = 0.322 kg and length d = 2.46 m. The rod pivots about point O through angle θ before momentarily stopping. Find θ.
The above system has friction. m = 180 g and M = 230 g. You measured the base- side of the ramp to be 130 cm and the height of the ramp to be 18 cm at the pully. You start the sliding mass at the bottom of the ramp, and it takes. 634 seconds to reach the top of the ramp. The average Velocity is half the acceleration of the system given a constant non-zero acceleration and your system starting from rest, both of which are confirmed to have happened in this set-up. Determine the Acceleration of the system, the Force of Friction for the system, and the coefficient of friction for the system following the following process to help you. A) Make a list of known values and unknown values. B) Draw a free body diagram complete with directions for your system/systems. C) Write out the custom Newtons Second Law equations for your system/systems with just variables. D) Complete the algebra to solve for each of the three unknowns of your system in variable form. E) Plug in all the known and solved for values and give me the answer for each of the three asked for values.
In the figure provided, there is a crate of mass 4.16 kg on top of another crate of mass 2.77 kg. The coefficient of friction between the lower crate and the floor is μk = 0.450 and the coefficient of static friction between the two crates is μs = 0.820. If the crates start at rest and a force is applied to the right so that both move a distance of 7.65 m, what is the minimal amount of time required in which this can be accomplished without the top crate sliding on the lower crate?
The wheel in the figure has eight equally spaced spokes and a radius of 38 cm. It is mounted on a fixed axle and is spinning at 2.8 rev/s. You want to shoot a 24-cm-long arrow parallel to this axle and through the wheel without hitting any of the spokes. Assume that the arrow and the spokes are very thin. What minimum speed must the arrow have?
A 1.40 kg object slides to the right on a surface having a coefficient of kinetic friction 0.250 (Fig. P7.54). The object has a speed of vi = 2.80 m/s when it makes contact with a light spring that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distance d. The object is then forced toward the left by the spring and continues to move in that direction beyond the spring's unstretched position. The object finally comes to rest a distance D to the left of the unstretched spring. Figure P7.54 (a) Find the distance of compression d. m (b) Find the speed v at the unstretched position when the object is moving to the left. m/s (c) Find the distance D where the object comes to rest. m
A Texas cockroach of mass 0.208 kg runs counterclockwise around the rim of a lazy Susan (a circular disk mounted on a vertical axle) that has a radius 14.2 cm, rotational inertia 5.20×10−3 kg⋅m2, and frictionless bearings. The cockroach's speed (relative to the ground) is 1.56 m/s, and the lazy Susan turns clockwise with angular velocity ω0 = 3.63 rad/s. The cockroach finds a bread crumb on the rim and, of course, stops. (a) What is the angular speed of the lazy Susan after the cockroach stops? (b) Is mechanical energy conserved as it stops? (a) Number Units (b)
In an RLC circuit such as that of the figure assume that R = 6.62 Ω, L = 50.8 mH, fd = 73.3 Hz, and εm = 31.4 V. For what values of the capacitance would the average rate at which energy is dissipated in the resistance be (a) a maximum and (b) a minimum? What are (c) the maximum dissipation rate and the corresponding (d) phase angle and (e) power factor? What are (f) the minimum dissipation rate and the corresponding (g) phase angle and (h) power factor? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units
A small block of mass m slides without friction around the loop-the-loop apparatus shown below. (The apparatus is not drawn to scale. Use the following as necessary: m, g, and R for the radius of the loop.) (a) If the block starts from rest at A, what is its speed at B? vB = (b) What is the force of the track on the block at B? (Enter the magnitude.) F =
(hrw8 c10 p66) A uniform spherical shell of mass M = 1.5 kg and radius R = 12.0 cm rotates about a vertical axis on frictionless bearings (see the figure). A massless cord passes around the equator of the shell, over a pulley of rotational inertia I = 3.42×10−3 kgm2 and radius r = 6.0 cm, and its attached to a small object of mass m = 4.0 kg. There is no friction on the pulley's axle; the cord does not slip on the pulley. What is the speed of the object after it has fallen a distance h = 0.8 m from rest: Use work - energy considerations.
A block of mass m2 is placed on a frictionless table with another block m3 placed on top of it. The surface between m2 and m3 has a coefficient of static friction μs. The block m2 is connected with another block m1 by a massless rope which wraps around a massless pulley as shown in the right figure. The rope does NOT slip over the pulley when moving. The block m1 is connected with a spring of force constant k whose other end is fixed to the ground. The spring is stretched with an amount h away from its equilibrium point and the whole system is released from rest. (a) Find the minimum value of μs such that the block m3 can remain on block m2 without falling off. (b) After we release the system, what is the speed of m1 when the spring returns to its equilibrium position?
In the figure below, what is the potential difference Vd-Vc between points d and c if E1 = 4.9 V, E2 = 1.8 V, R1 = R2 = 15 Ω, and R3 = 6.7 Ω, and the batteries are ideal?
In the figure R1 = 15.7 Ω, R2 = 8.19 Ω, and the ideal battery has emf E = 120 V. What is the current at point a if we close (a) only switch S1, (b) only switches S1 and S2, and (c) all three switches? (a) Number Units (b) Number Units (c) Number Units
1 Discrete Charge System The figure below shows the neutral unit cell of a two-dimensional hexagonal ionic lattice, with alternating positive and negative ions at the vertices of a hexagon. Adjacent ions are separated by a distance a, and each is a distance a from the origin. 1.1 Assuming each ion can be modeled as a point charge, find an expression for the electrostatic energy required to assemble this unit cell. 1.2 How much energy is required to remove one of the positive ions?
The uniform solid block in the figure has mass 25.5 kg and edge lengths a = 0.613 m, b = 1.30 m, and c = 0.0824 m. Calculate its rotational inertia about an axis through one corner and perpendicular to the large faces. Number Units
(a) In the figure what value must R have if the current in the circuit is to be 0.85 mA? Take ε1 = 2.4 V, ε2 = 3.7 V, and r1 = r2 = 3.4 Ω. (b) What is the rate at which thermal energy appears in R? (a) Number Units (b) Number Units
A block of mass m = 4.0 kg is released from rest at the top of an incline plane that makes an angle of 25∘ with the horizontal. It slides down a distance d = 7.0 m along the incline. What is the Angular Momentum of the block with respect to point X shown below. Approximate the block as a point mass. Assume negligible friction tetween the block and the incline. Magnitude of acceleration due to gravity is 10.0 m/s2. Select the closest answer.
A light cord is passed around a frictionless pulley and connected to the two masses as shown, with m2 pulled by a constant horizontal force, F. The coefficient of kinetic friction between m1 and m2 is the same as that between m2 and the horizontal surface. Find an expression for μk (in terms on F, m1, m2 and any constants needed) if the blocks are to move with constant speed.
Problem Statement: Dianne the Duck is moving along a straight line in a river. The net force on Dianne is shown on the graph below. (a) What is the total work done on Dianne as she moves from x = 0 m to x = 10 m? (b) If Dianne's mass is 1.25 kg, and she initially started her 10 m trip with a speed of 2.828 m/s (i. e. when she passed x = 0), what is her speed when she reaches x = 10 m?
At time t, r→ = 9.80t2 i^ − (7.60t + 3.70t2)j^ gives the position of a 3.0 kg particle relative to the origin of an xy coordinate system (r→ is in meters and t is in seconds). (a) Find the torque acting on the particle relative to the origin at the moment 4.75 s (b) Is the magnitude of the particle's angular momentum relative to the origin increasing, decreasing, or unchanging? (a) k Units (b)
Consider the diagram of the two charges shown below. The charge qA = -1.50 x 10−8 C. The charge qB = 2.00×10−8 C. The distance x = 1.50 m and the distance y = 2.60 m. What is the electric field due to the charges at point P. Fields to the right are considered positive and fields to the left are considered negative. If the field is to the left include a negative sign in your answer. If the field is to the right do NOT include the positive sign in your answer. You field should be given in N/C to 1 decimal place. Do NOT include units in your answer.
Point charges W, X, Y, and Z each have the same magnitude charge of 4.46×10−6 C. Two of the charges are positive as shown and two are negative. The corners of the square are 10.0 cm long. Draw the vector diagram and calculate the net force on point Y. [5 marks]
The figure shows a rigid structure consisting of a circular hoop of radius R and mass m, and a square made of four thin bars, each of length R and mass m. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of 4.3 s. If R = 1.1 m and m = 1.5 kg, calculate the angular momentum about that axis. Number Units
(5.) A 6.4-kg mass is hung from a spring whose spring constant k = 150 N/m. The mass is released from rest with the spring unstretched. Ignoring air resistance, how fast will the mass be going after it has fallen a distance d = 0.52 m? (a) v2 = 1.96 m/s (b) v2 = 2.52 m/s (c) v2 = 3.77 m/s (d) v2 = 3.19 m/s (e) v2 = 5.81 m/s