The system shown in the figure below is used to lift an object of mass m = 26.5 kg. A constant downward force of magnitude F is applied to the loose end of the rope such that the hanging object moves upward at constant speed. Neglecting the masses of the rope and pulleys, find the following. (a) Find the required value of F. N (b) Find the tensions T1′T2′ and T3. (T3 indicates the tension in the rope which attaches the pulley to the ceiling.) T1 = N T2 = N T3 = N (c) Find the work done by the applied force in raising the object a distance of 1.50 m. kJ
The figure shows a system used to stabilize and realign a broken leg by applying a horizontal force. (Let m = 7.05 kg and θ = 60.0∘, and assume the pulleys are frictionless.) (a) What is the tension (in N) in the rope supporting the leg? N (b) What is the force (in N) exerted to the right on the leg? (Enter the magnitude.) N
A charge of −24 μC is distributed uniformly throughout a spherical volume of radius 14.0 cm. Determine the electric field (in N/C) due to this charge at the following distances from the center of the sphere. (Enter the radial component of the electric field.) (a) 3.0 cm E→ = (N/C)r^ (b) 8.0 cm E→ = (N/C)r^ (c) 30.0 cm E→ = (N/C)r^
A 66.3-kg circus performer is fired from a canhon that is elevated at an angle of 41.2∘ above the horizontal. The cannon uses strong elastic bands to propel the performer, much in the same way that a slingshot fires a stone. Setting up for this stunt involves stretching the bands by 2.68 m from their unstrained length. At the point where the performer flies free of the bands, his height above the floor is the same as that of the net into which he is shot. He takes 1.96 s to travel the horizontal distance of 21.5 m between this point and the net. Ignore friction and air resistance and determine the effective spring constant of the firing mechanism.
A man is driving his SUV with speed 55.0 mi/h on a horizontal stretch of road. (a) When the road is wet, the coefficient of static friction between the road and the tires is 0.102. Find the minimum stopping distance (in m). m (b) When the road is dry, μs = 0.605. Find the minimum stopping distance (in m). m
A 8.1-kg rock and a 3.8×10−4−kg pebble are held near the surface of the earth. (a) Determine the magnitude of the gravitational force exerted on each by the earth. (b) Calculate the magnitude of the acceleration of each object when released.
(8.) A 6.0 kg box is sitting at rest on the floor as shown. The coefficient of static friction between the box and the floor is μs = 0.25. What is the minimum horizontal pushing force, P→, needed to get the box to start moving? (a) Any amount of pushing force will make the box move. (b) P = 14.7 N (c) P = 58.8 N (d) P = 73.5 N (e) P = 235.2 N
Switch S in in the figure is closed at time t = 0, to begin charging an initially uncharged capacitor of capacitance C = 18.4 μF through a resistor of resistance R = 20.6 Ω. At what time is the potential across the capacitor equal to that across the resistor? Number Units
In the figure how much charge is stored on the parallel-plate capacitors by the 17.0 V battery? One is filled with air, and the other is filled with a dielectric for which k = 2.20; both capacitors have a plate area of 8.80×10−3 m2 and a plate separation of 3.70 mm. Number Units
Three objects are connected by light strings as shown in the figure below. The string connecting the m1 = 5.65−kg object and the m2 = 3.75−kg object passes over a light frictionless pulley. (a) Determine the acceleration of each object. object m1 magnitude m/s2 object m1 direction --- Select--- object m2 magnitude m/s2 object m2 direction --- Select--- object m3 magnitude m/s2 object m3 direction --- Select--- (b) Determine the tension in the two strings. string between m1 and m2 N string between m2 and the 3.00−kg object N
Determine the distance s to which the 63-kg painter can climb without causing the 4.7-m ladder to slip at its lower end A. The top of the 19−kg ladder has a small roller, and at the ground the coefficient of static friction is 0.31. The mass center of the painter is directly above her feet. Assume L = 4.7 m, a = 1.68 m. Answer: s = m
An astronaut is being tested in a centrifuge. The centrifuge has a radius of 11.0 m and, in starting, rotates according to θ = 0.300t2, where t is in seconds and θ is in radians. When t = 2.30 s, what are the magnitudes of the astronaut's (a) angular velocity, (b) linear velocity, (c) tangential acceleration, and (d) radial acceleration? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
A car accelerates down a hill (see figure below), going from rest to 26.0 m/s in 5.20 s. A toy inside the car hangs by a string from the car's ceiling. The ball in the figure represents the toy, of mass 0.560 kg. The acceleration is such that the string remains perpendicular to the ceiling. (a) Determine the angle θ. (b) Determine the tension in the string. N
Children are playing with a remote-controlled toy jeep in an open horizontal field. At some time, the jeep is located (relative to a rock which they are using as the origin) at r→0 = (14.0i^ − 7.50j^) m and has a velocity of v→0 = (8.00i^ + 3.00 j^) m/s. If, for a time interval Δt = 10.0 s, the jeep experiences a constant acceleration a→ and acquires a new velocity v→ = (2.00i^ − 19.50j^) m/s, determine the following for the jeep. (Express your answer in vector form.) (a) position vector at time t = 10.0 s r→(t = 10.0 s) = m (b) velocity vector time t = 5.00 s v→(t = 5.00 s) = m/s
The accompanying figure shows the position versus time curve for an automobile over a period of time of 5 s. Use the line segments shown in the figure to estimate the instantaneous velocity of the automobile at time t = 2 s and again at time t = 4 s. Round your answers to two decimal places, if required. Instantaneous velocity at t = 2 s = m/s Instantaneous velocity at t = 4 s = m/s
The following graph shows the velocity of an object in one dimension over time. At 5 s, the acceleration of the object is [Select] and the object is [ Select ] At 12.5 s, the acceleration of the object is [Select ] and the object is [Select ] At 25 s, the acceleration of the object is [ Select] and the object is [Select]
The drawing shows three particles that are moving with different velocities. Two of the particles have mass m, and the third has a mass 2 m. The third particle has a velocity of v3 = +5.2 m/s. At the instant shown, the center of mass (cm) of the three particles is at the coordinate origin. What is the velocity vcm (magnitude and direction) of the center of mass? Velocity of center of mass = Number Units direction
A baseball player hits the ball and then runs down the first base line at 17 ft/s. The first baseman fields the ball and then runs toward first base along the second base line at 16 ft/s. Determine how fast the distance between the two players is decreasing at a moment when the hitter is 16 ft from first base and the first baseman is 12 ft from first base. (Use decimal notation. Give your answer to one decimal place.) distance change: ft/sec
A racetrack has the shape of an inverted cone, as the drawing shows. On this surface the cars race in circles that are parallel to the ground. (a) Draw the free-body diagram showing the forces that act on the car, assuming the friction force equals zero in this case. (b) For a speed of 34.0 m/s, at what value of the distance d should a driver locate his car if he wishes to stay on a circular path without depending on friction?
The ball's initial velocity is as shown below moving at an unspecified angle ϕ. Pay special attention to labelling slopes and axis intercepts and treat the ball's initial position as the origin (both time and space) for the plots. (a) Fill in and justify the plots below as a function of time, regarding the ball's motion. (b) Analyze: how much work has been done on the ball when x = 0 and t > 0? Label this point on the appropriate plot.
Two isolated, concentric, conducting spherical shells have radii R1 = 0.520 m and R2 = 1.50 m, uniform charges q1 = +3.10 μC and q2 = +3.60 μC, and negligible thicknesses. What is the magnitude of the electric field E at radial distance (a) r = 4.10 m, (b) r = 0.660 m, and (c) r = 0.340 m? With V = 0 at infinity, what is V at (d)r = 4.10 m, (e) r = 1.50 m, (f)r = 0.660 m, (g)r = 0.520 m, (h) r = 0.340 m, and (i) r = 0? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units (f) Number Units (g) Number Units (h) Number Units (i) Number Units
What must be the distance in meters between point charge q1 = 23.3 μC and point charge q2 = −69.0 μC for the electrostatic force between them to have a magnitude of 6.02 N? Number Units
Three charges lie on the x-axis. Charge q1 = 2.20 μC is at x = −30.0 cm, charge q2 = −3.00 μC is at the origin, and charge q3 = 3.30 μC is at x = 10.0 cm. Calculate the potential energy Uelectric of the system of charges. Uelectric =
An initially neutral piece of plastic is has 7.6×1015 electrons removed from it. Determine the net charge of the plastic (in μC).
An electric dipole has a dipole moment of 1.6×10−15 Cm. The dipole moment vector is initially oriented at θ = 26.96∘ to the +x-axis. How much work will be done by an electric field 4.66 MN/C(−i^) to bring the dipole to its stable equilibrium position (in nJ)?
A point charge Q of mass 3.23 g hangs from the horizontal ceiling by a light 55.5 cm thread. When a horizontal electric field of magnitude 1, 075.4 N/C is turned on, the charge hangs away from the vertical as shown in the figure. Determine the charge Q (in μC)
Four identical charges Q = 6.18 μC are placed the following coordinates (in meters), (0, 0), (0, 1.5), (1.5, 1.5), (1.5, 0). Determine the magnitude of the net force on the charge at (0, 0) (in mN).
Find the x and y components of the electric field produced by q1 and q2 in the figure shown below at point A and point B. (Take q1 = 2.05 μC and q2 = −1.04 μC.) Point A EX = Ey = Point B Ex = Ey =
Problem 6: Suppose a 67-kg mountain climber has a 0.78 cm diameter nylon rope. Randomized Variables m = 67 kg d = 0.78 cm l = 41 m By how much does the mountain climber stretch her rope, in centimeters, when she hangs 41 m below a rock outcropping? Assume the Young's modulus of the rope is 5×109 N/m2. ΔL =
The skateboarder in the figure is coasting down a ramp, and there are three forces acting on her: her weight W→ (magnitude = 684 N), a frictional force f→ (magnitude = 221 N) that opposes her motion, and a normal force F→N (magnitude = 598 N). Determine the net work done (a) by the weight W→, (b) by the frictional force f→, and (c) by the normal force F→N when she coasts for a distance of 10.6 m. (a) (b) (a) Number Units (b) Number Units (c) Number Units
The earth rotates once per day about an axis passing through the north and south poles, an axis that is perpendicular to the plane of the equator. Assuming the earth is a sphere with a radius of 6.38×106 m, determine the speed and centripetal acceleration of a person situated (a) at the equator and (b) at a latitude of 62.0∘ north of the equator. (a) v = Units ac = Units (b) v = Units ac = Units
Fight for the fish (2 pts). Three penguins are fighting over a freshly caught fish. A top view of the magnitude and direction of the three forces is shown in the diagram to the right. (a) Determine the resultant or net force acting upon the fish. (b) Determine the acceleration of the 5-kg fish.
A uniform electric field exists in a region between two oppositely charged plates. An electron is released from rest at the surface of the negatively charged plate and strikes the surface of the opposite plate, 2.6 cm away, in a time 1.4×10−8 s. (a) What is the speed of the electron as it strikes the second plate? (b) What is the magnitude of the electric field? (a) Number Units (b) Number Units
The figure below shows three edge views of a square loop with sides of length ℓ = 0.290 m in a magnetic field of magnitude 3.00 Calculate the magnetic flux (in Wb) through the loop oriented perpendicular to the magnetic field, 60.0∘ from the magnetic field, and parallel to the magnetic field. (i) HINT (a) perpendicular to the magnetic field Wb (b) 60.0∘ from the magnetic field Wb (c) parallel to the magnetic field Wb
Problem # 4 (20 points): The electric field in the region of space shown to the right is given by E^ = −5.0j^ + 6.0k N/C where y and x are in meters. What is the magnitude of the electric flux through the front-side face of the cube shown to the right? What is the net flux through the whole cube?
Children are playing with a remote-controlled toy jeep in an open horizontal field. At some time, the jeep is located (relative to a rock which they are using as the origin) at r→0 = (14.0i^ − 7.50j^) m and has a velocity of v→0 = (8.00i^ + 3.00j^) m/s. If, for a time interval Δt = 10.0 s, the jeep experiences a constant acceleration a→ and acquires a new velocity v→ = (2.00i^ − 19.50j^) m/s, determine the following for the jeep. (Express your answer in vector form.) (a) position vector at time t = 10.0 s r→(t = 10.0 s) = m (b) velocity vector time t = 5.00 s v→(t = 5.00 s) = m/s
During a storm, a tree limb breaks off and comes to rest across a barbed wire fence at a point that is not in the middle between two fence posts. The limb exerts a downward force of 271 N on the wire. The left section of the wire makes an angle of 11.6∘ relative to the horizontal and sustains a tension of 496 N. Find the (a) magnitude and (b) direction (as an angle relative to horizontal) of the tension that the right section of the wire sustains. (a) Number Units (b) Number Units
Deflecting a compass needle (a) Which of the following statements are correct? Select all that apply. The magnetic field under the wire, due to the current, points to the West. Conventional current in the wire flows upward (North). Conventional current in the wire is flowing downward (South). The magnetic field under the wire, due to the current, points North. The magnetic field under the wire, due to the current, points to the East. Electron current in the wire is flowing upward (North). (b) Calculate the amount of conventional current flowing in the wire. The measurement was made at a location where the horizontal component of the Earth's magnetic field is BEarth ≈ 2×10−5 tesla. A