3 /143 SS A 2-oz bullet is fired horizontally with a velocity v1 = 1800 ft/sec into the 6−lb block of soft wood initially at rest on the horizontal surface. The bullet emerges from the block with the velocity v2 = 1200 ft/sec, and the block is observed to slide a distance of 8 ft before coming to rest. Determine the coefficient of kinetic friction μk between the block and the supporting surface.
22-75. A bullet of mass m has a velocity v0 just before it strikes the target of mass M. If the bullet embeds in the target, and the dashpot's damping coefficient is 0 < c < cc, determine the springs' maximum compression. The target is free to move along the two horizontal guides that are "nested" in the springs.
A 0.00880−kg bullet is fired straight up at a falling wooden block that has a mass of 4.18 kg. The bullet has a speed of 574 m/s when it strikes the block. The block originally was dropped from rest from the top of a building and had been falling for a time t when the collision with the bullet occurs. As a result of the collision, the block (with the bullet in it) reverses direction, rises, and comes to a momentary halt at the top of the building. Find the time t. Number Units
Suppose we equipped a shopping cart with a rocket. Since our cart is now extremely fast, instead of placing boxes inside the cart, we can place them against the front of the cart as pictured. We would like to know what force propulsion F, the rocket would need to keep the box from slipping, assuming there is friction between the cart and box with a co-efficient of static friction, μs. (a) Draw and label a free-body diagram of the entire system (which has a total mass M+m). Write down the corresponding Newton's laws in each direction. (b) Draw and label free-body diagrams for both the shopping cart and the box (mass of shopping cart is M, mass of box is m). Write down the corresponding equations again. (c) Find the force the rocket needs to provide to keep the box from slipping.
As the figure shows, a 0.50 kg block is pushed against a spring of constant 3.5 N/m and held at 0.60 m away from equilibrium position. The block then released from rest and starts sliding on a rough horizontal ground with coefficient of kinetic friction 0.3 and the spring returned to its relaxed length. How far will the block slide before it stops?
The figure below shows a crate with a mass of m = 3.80 kg on a ramp inclined at an angle of 35.0∘. The coefficient of static friction between the crate and the ramp is 0.265. Find the minimum magnitude of the force F→ (in N), applied to the crate in a direction perpendicular to the ramp, that will prevent the crate from sliding down the ramp. N
Problem 1 Suppose you have a section of wire that is 3.0 m in length. A bead, starting from rest, is to slide down the wire under the influence of gravity, then slide off of the end of the wire, and "fly" through the air until landing on the floor. The bead is to start at the left end of the wire, which is to be located 2.0 m above the floor and at x = 0. Your goal is to determine the optimal configuration of the wire to maximize the value of horizontal landing position (L) of the bead (see figure below), given: Sliding friction is negligible. The wire is shaped to be a section of a circle. The bead starts out heading straight down. Aerodynamic drag is negligible. Report the optimal radius of the circle (which produces the largest distance L) along with the corresponding value of L. (Since the length of the wire is set to be 3.0 m, choosing the radius of the circle determines everything else.)
What is the magnitude of the electric field at the point (5.10i^ − 4.30j^ + 4.60k^) m if the electric potential is given by V = 4.60xyz2, where V is in volts and x, y, and z are in meters? Number Units
A student throws a water balloon at an initial angle θ = 25∘ above the horizontal with initial speed v0 from a height h = 1.9 m. The target is located on the ground a horizontal distance d = 5.5 m from the student's feet. Assume that the balloon moves without air resistance. Use a Cartesian coordinate system with the origin at the balloon's initial position. Determine the magnitude of the balloon's initial velocity, v0, in meters per second. v0 = m/s
From the top of a tall building, a gun is fired. The bullet leaves the gun at a speed of 340 m/s, parallel to the ground. As the drawing shows, the bullet puts a hole in a window of another building and hits the wall that faces the window. Using the data in the drawing, determine the distances (a) D and (b) H, which locate the point where the gun was fired. Assume that the bullet does not slow down as it passes through the window.
Two boxes are stacked atop one another as shown. The bottom one has mass 3 m and the top has mass 4 m. We want to pull the top one with some force such that they move together. Assume there is zero friction between the ground and bottom box. However, there is friction between the two boxes, with static coefficient μs = 3/5 and kinetic coefficient μK = 1/5. (a) Assume we are pulling the top box with the largest force possible while still allowing the two boxes to move together. Draw a free-body diagram for each. (b) Use Newton's laws to determine the largest possible acceleration the top box can have so that the two boxes move together. (c) What is the maximum force we can pull the top box with?
A plane flies 417 km east from city A to city B in 42.0 min and then 923 km south from city B to city C in 1.40 h. For the total trip, what are the (a) magnitude and (b) direction of the plane's displacement, the (c) magnitude and (d) direction of its average velocity, and (e) its average speed? Give your angles as positive or negative values of magnitude less than 180 degrees, measured from the +x direction (east). (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units
A ring of charge is centered at the origin in the vertical direction. The ring has a charge density of λ = 3.99×10−6 C/m and a radius of R = 3.55 cm. Find the total electric field, E, of the ring at the point P = (2.02 m, 0.00 m). The Coulomb force constant is k = 1/(4πϵ0) = 8.99×109 N⋅m2 /C2. E = N/C Find the expression for the electric field, E∞, of the ring as the point P becomes very far from the ring (x ≫ R) in terms of the radius R, the distance x, the total charge on the ring q, and the constant k = 1/(4πϵ0). E∞ =
A straight rod of length L = 23.80 cm carries a uniform charge density λ = 1.50×10−6 C/m. The rod is located along the y-axis from y1 = 0.00 to y2 = L. The Coulomb force constant is k = 8.99×109 N⋅m2/C2. Find the expression for the electric field along the y-axis Ey at a point P. What is the magnitude of the electric field at y0 = 45.00 cm? Ey = N/C
Two circular plates, each with a radius of 3.22 cm, have equal and opposite charges of magnitude 1.652 μC. Calculate the electric field between the two plates. Assume that the separation distance is small in comparison to the diameter of the plates. electric field: The plates are slowly pulled apart, doubling the separation distance. Again, assume the separation distance remains small in comparison to the diameter of the plates. What changes occur with the electric field between the plates? The electric field increases by a factor of 2. The electric field decreases by a factor of 4. The electric field decreases by a factor of 2. The electric field increases by a factor of 4. The electric field stays the same.
Two long, charged, thin-walled, concentric cylindrical shells have radii of 3.3 and 6.7 cm. The charge per unit length is 6.4× 10−6 C/m on the inner shell and −7.7×10−6 C/m on the outer shell. What are the (a) magnitude E and (b) direction (radially inward or outward) of the electric field at radial distance r = 5.7 cm? What are (c) E and (d) the direction at r = 9.2 cm? (a) Number Units (b) (c) Number Units (d)
68 A salamander of the genus Hydromantes captures prey by launching its tongue as a projectile: The skeletal part of the tongue is shot forward, unfolding the rest of the tongue, until the outer portion lands on the prey, sticking to it. Figure 2-24 shows the acceleration magnitude a versus time t for the acceleration phase of the launch in a typical situation. The indicated accelerations are a2 = 400 m/s2 and a1 = 100 m/s2. What is the outward speed of the tongue at the end of the acceleration phase? Figure 2-24 Problem 68.
Vectors A→ and B→ lie in an xy plane. A→ has magnitude 5.9 and angle 102∘;B→ has components Bx = −5.20 and By = −6.67. (a) What is 5A→⋅B→? What is 4A→×3B→ in unit-vector notation ((b), (c) and (d) for i^, j^ and k^ components respectively)? (e) What is the angle between the directions of A→ and 4 A→×3 B→? What is A→+3.00 k^ in unit-vector notation ((f), (g) and (h) for i^, j^ and k^ components respectively) and magnitude-angle notation with spherical coordinates (i) for magnitude, (j) for θ and (k) for ϕ)?
The plates of a spherical capacitor have radii 53.6 mm and 57.2 mm. (a) Calculate the capacitance. (b) What must be the plate area of a parallel-plate capacitor with the same plate separation and capacitance? (a) Number Units (b) Number Units
A projectile is fired with an initial speed of 210 m/s and angle of elevation 60∘. (Use g = 9.8 m/s2. Round your answers to the nearest whole number.) (a) Find the range (in m) of the projectile. m (b) Find the maximum height (in m) reached. m (c) Find the speed (in m/s) at impact. m/s
A child of mass 28 kg swings at the end of an elastic cord. At the bottom of the swing, the child's velocity is horizontal, and the speed is 8 m/s. At this instant the cord is 4.36 meters long. At this instant, what is the parallel component of the rate of change of the child's momentum? Newtons At this instant, what is the perpendicular component of the rate of change of the child's momentum? Newtons At this instant, what is the net force acting on the child? Newtons What is the magnitude of the force that the elastic cord exerts on the child? Newtons The relaxed length of the elastic cord is 4.29 meters. What is the stiffness of the cord? N/m