Consider the tank shown in (Figure 1). Take ρo = 900 kg/m3, ρw = 1000 kg/m3, and ρHg = 13550 kg/m3. Part A Determine the level h′ of water in the tube if the depths of oil and water in the tank are 0.6 m and 0.8 m, respectively, and the height of mercury in the tube is h = 0.050 m. Express your answer to three significant figures and include the appropriate units. h′ = Value Units
A block rests at the top of a frictionless inclined plane as shown in the image. The inclined plane makes an angle of 26.2∘ with the horizontal direction. If the mass of the block is 1.00 kg and it begins from rest, how fast will the block be moving after it has traveled 0.772 m down the plane? Report your answer in m/s.
A 5.56-Ω resistor is connected across a 9.00−V battery. The voltage between the terminals of the battery is observed to be only 7.13 V. Find the internal resistance of the battery. Number Units
A 40 kg block is at rest on the slope when a force F~ is applied to it. Determine the magnitude of F~ if the velocity of the block reaches 5 m/s when time t = 2 s. The coefficients of static and dynamic friction between the block and slope are 0.25 and 0.2, respectively.
The circular arc shown in the figure below has a uniform charge per unit length of 3.70×10−8 C/m. Find the potential at P, the center of the circle. (Take R = 1.99 m.)
A 2.0 m×4.0 m flat carpet acquires a uniformly distributed charge of −10 μC after you and your friends walk across it several times. A 5.0 μg dust particle is suspended in midair just above the center of the carpet. Part A What is the charge on the dust particle? Express your answer with the appropriate units.
The box-like Gaussian surface of the figure encloses a net charge of 20.0ε0 C and lies in an electric field given by E→ = [(11.0 + 3.40x)i^ − 4.50j^ + bzk^] N/C with x and z in meters and b constant. The bottom face is in the xz plane; the top face is in the horizontal plane passing through y2 = 1.00 m. For x1 = 1.80 m, x2 = 4.80 m, z1 = 1.90 m, and z2 = 3.90 m, what is b? Number Units
Three blocks of equal mass are suspended, but now some of them are moving. One block hangs from a rope attached to the ceiling and is stationary. Two hang on a rope that runs over a pulley. (The ropes and the pulley are massless.) The block on the left side of the pulley is going up. The block on the right side of the pulley is going down. The moving blocks are travelling at equal and constant speeds. Rank the tension in the three segments of rope from smallest to largest. 1 st choice Rope 1 - attached to the single block. 2 nd choice Rope 2 - attached to the left block on the pulley. 3rd choice Rope 3 - attached to the right block on the pulley.
The equipotential lines in a region of electric field are shown in the diagram below. For each path indicated below, what is the work done by the electric field in moving a charge q = +3.7×10−7 C along that path? Here V0 = +130 V. (a) from A to B WAB = ∫J (b) from A to C WAC = J (c) from A to D WAD = J (d) from D to C WDC = J
Use the model for projectile motion, assuming there is no air resistance and g = 32 feet per second per second. The quarterback of a football team releases a pass at a height of 6 feet above the playing field, and the football is caught by a receiver 40 yards directly downfield at a height of 4 feet. The pass is released at an angle of 35∘ with the horizontal. (a) Find the speed (in ft/sec) of the football when it is released. (Round your answer to three decimal places.) ft/sec (b) Find the maximum height (in ft) of the football. (Round your answer to one decimal place.) ft (c) Find the time (in sec) the receiver has to reach the proper position after the quarterback releases the football. (Round your answer to one decimal place.) sec
A 2.0 kg block sits on a 4.0 kg block that is on a frictionless table. The coefficients of friction between the blocks are μs = 0.70 and μk = 0.20. (a) What is the maximum force F that can be applied to the 4.0 kg block if the 2.0 kg block is not to slide? N (b) If F is half this value, find the acceleration of each block. m/s2 (2.0 kg block) m/s2 (4.0 kg block) Find the magnitude of the force of friction acting on each block. N(2.0 kg block) N(4.0 kg block) (c) If F is twice the value found in (a), find the acceleration of each block. m/s2 (2 kg block) m/s2 (4 kg block)
A 4.890 kg block of wood rests on a steel desk. The coefficient of static friction between the block and the desk is μs = 0.555 and the coefficient of kinetic friction is μk = 0.205. At time t = 0, a force F = 16.4 N is applied horizontally to the block. State the force of friction applied to the block by the table at times t = 0 and t > 0. t = 0 N t > 0 N Consider the same situation, but this time the external force F is 33.0 N. Again, state the force of friction acting on the block at times t = 0 and t > 0. t = 0 N t > 0 N
Robin would like to shoot an orange in a tree with his bow and arrow. The orange is hanging yf = 5.00 m above the ground. On his first try, Robin releases the arrow at v0 = 36.0 m/s at an angle of θ = 30.0∘ above the horizontal. The arrow has an initial height of y0 = 1.50 m, and its tip is x = 55.0 m away from the target orange. Treating the arrow as a point projectile and neglecting air resistance, what is the height of the arrow once it has reached the horizontal position x of the orange? Use g = 9.81 m/s2 for the acceleration due to gravity. height of the arrow: m For his second try, Robin decides to change his position but release the arrow using the same speed and angle as his first try. Assume that the orange remains in the same position. How far from the orange should Robin stand in order to hit the orange? There may be more than one correct distance. 6.4 m 108 m 11.6 m 60.2 m 103 m
A force F of 10 N acts on two blocks on a frictionless surface. a) What is the acceleration of the system? Express your answer using two significant figures. a = m/s2 b) What is the magnitude of the force that block A exerts on block B? Express your answer using two significant figures. FAB = N c) What is the direction of the force that block A exerts on block B? A - to the left B - to the right d) What is the magnitude of the force that block B exerts on block A? Express your answer using two significant figures. FBA = N e) What is the direction of the force that block B exerts on block A? A - to the left B - to the right
(3.0.25) In the diagram below, a 2.5 kg book is pushed along a ceiling at constant velocity by a force P→. The coefficient of kinetic friction between the ceiling and the book is 0.80. (a) Set up a free body diagram which shows all forces acting on the book. Following all steps learned in class, write down expressions for each component of each force. (b) Find the magnitude of P→.
The uniform bar AB of mass m and length L is leaning against the corner with θ ≈ 0 when end B is given a slight nudge so that end A starts sliding down the wall as B slides along the floor. Assuming that friction is negligible between the bar and the two surfaces against which it is sliding, determine the angle θ at which end A will lose contact with the vertical wall.