This problem is an example of critically damped harmonic motion. A mass m = 3 kg is attached to both a spring with spring constant k = 243 N/m and a dash-pot with damping constant c = 54 N⋅s/m. The ball is started in motion with initial position x0 = 2 m and initial velocity v0 = −21 m/s. Determine the position function x(t) in meters. x(t) =
An m = 56.0−kg person running at an initial speed of v = 4.50 m/s jumps onto an M = 112−kg cart initially at rest (figure below). The person slides on the cart's top surface and finally comes to rest relative to the cart. The coefficient of kinetic friction between the person and the cart is 0.360 . Friction between the cart and ground can be ignored. (Let the positive direction be to the right. ) (a) Find the final velocity of the person and cart relative to the ground. (Indicate the direction with the sign of your answer.) m/s (b) Find the friction force acting on the person while he is sliding across the top surface of the cart. (Indicate the direction with the sign of your answer.) (c) How long does the friction force act on the person? (d) Find the change in momentum of the person. (Indicate the direction with the sign of your answer.) N⋅s Find the change in momentum of the cart. (Indicate the direction with the sign of your answer.) N⋅s (e) Determine the displacement of the person relative to the ground while he is sliding on the cart. (Indicate the direction with the sign of your answer.) m (f) Determine the displacement of the cart relative to the ground while the person is sliding. (Indicate the direction with the sign of your answer.) m
What is the phase constant for SMH with a(t) given in the figure if the position function x(t) has the form x = xmcos(ωt + φ) and as = 8 m/s2? (note that the answer should be from 0 to 2π) a (m/s2) Number Units
In the figured provided, a 40.46 kg crate is suspended 3.15 m above the ground and is attached to another crate of mass 57.8 kg on a table through a rope and pulley system. If the table is frictionless and the mass of the rope and pulley are negligible, what will the speed of the 40.46 kg crate be right before it hits the ground?
An object with mass 2.3 kg is executing simple harmonic motion, attached to a spring with spring constant k = 230 N/m. When the object is 0.014 m from its equilibrium position, it is moving with a speed of 0.50 m/s. Part A Calculate the amplitude of the motion. Express your answer to two significant figures and include the appropriate units. Submit Request Answer Part B Calculate the maximum speed attained by the object. Express your answer to two significant figures and include the appropriate units. Submit Request Answer
A 0.239 kg body undergoes simple harmonic motion of amplitude 8.46 cm and period 0.100 s. (a) What is the magnitude of the maximum force acting on it? (b) If the oscillations are produced by a spring, what is the spring constant? (a) Number Units (b) Number Units
A simple pendulum has a length of 52.1 cm and makes 83.9 complete oscillations in 2.00 min. (a) Find the period of the pendulum. s (b) Find the value of g at the location of the pendulum. m/s2
Review. A large block P attached to a light spring executes horizontal, simple harmonic motion as it slides across a frictionless surface with a frequency f = 1.50 Hz. Block B rests on it as shown in Figure P12.47, and the coefficient of static friction between the two is μs = 0.600. What maximum amplitude of oscillation can the system have if block B is not to slip? Figure P12.47 Problems 47 and 48.
A block is in SHM on the end of a spring, with position given by x = xmcos(ωt + φ). If φ = 0.393 rad, then at t = 0 what percentage of the total mechanical energy is potential energy? Number Units
A block is in SHM on the end of a spring, with position given by x = xmcos(ωt + φ). If φ = 0.585 rad, then at t = 0 what percentage of the total mechanical energy is potential energy? Number Units
An object oscillates in simple harmonic motion along the x-axis and the origin x = 0 as the equilibrium position with amplitude A = 4.0 cm and period T = 2.0 s. At t = 0, the particle first passes through x = 2.0 cm and moves in the negative direction of the x-axis, then the time when the particle pass through x = 2.0 cm for the second time is .
A lab experiment is set up to investigate simple harmonic motion. A block is attached to an ideal spring, and it oscillates back and forth on a frictionless, horizontal surface. One end of the spring is fixed in place, and the other end of the spring is attached to the block, whose mass is 0.800 kg. The motion of the spring is expressed by x(t) = (0.100 m)cos[(17.0 rad/s)t]. When the block is at x = +0.070 m, its speed is closest to: A) 1.50 m/s B) 1.21 m/s C) 0.934 m/s D) 0.074 m/s E) None of these
A mass on a spring bounces up and down in simple harmonic motion, modeled by the function s(t) = −14cos(t) where s is measured in inches and t is measured in seconds. Find the rate at which the spring is oscillating at t = 7 seconds. v(7) = in/s. help (numbers)
The position function for a particle undergoing Simple Harmonic Motion is given below. The particle's velocity function is v = −40 sin4t v = 10 cos4t v = −10 sin4t v = 40 sin4t
A simple harmonic oscillator consists of a block of mass 1.30 kg attached to a spring of spring constant 420 N/m. When t = 0.560 s, the position and velocity of the block are x = 0.198 m and v = 4.040 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s?
A simple harmonic oscillator consists of a block of mass 2.80 kg attached to a spring of spring constant 400 N/m. When t = 1.80 s. the position and velocity of the block are x = 0.167 m and v = 4.490 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s? (a) Number Units (b) Number Units (c) Number Units
A simple harmonic oscillator consists of a 0.93 kg block attached to a spring (k = 230 N/m). The block slides on a horizontal frictionless surface about the equilibrium point x = 0 with a total mechanical energy of 3.0 J. (a) What is the amplitude of the oscillation? (b) How many oscillations does the block complete in 9.6 s ? Enter the integer number of complete cycles. (c) What is the maximum kinetic energy attained by the block? (d) What is the speed of the block at x = 0.12 m? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
A simple harmonic oscillator consists of a block of mass 3.50 kg attached to a spring of spring constant 190 N/m. When t = 2.00 s, the position and velocity of the block are x = 0.140 m and v = 4.130 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s?
Cart has a mass of 30 kg. Block A has a mass of 20 kg. No friction between the cart and the ground. Friction coefficients between the cart and block are: μs = 0.35 and μk = 0.30. a-) Determine whether the block will slide or not. b-) If the block slides, then calculate the time required for the block to displace on the cart for 1.5 m.
In the figure, a 4.5 kg block slides along a track from one level to a higher level after passing through an intermediate valley. The track is frictionless until the block reaches the higher level. There a frictional force stops the block in a distance d. The block's initial speed is v0 = 5.4 m/s, the height difference is h = 1.1 m, and μk = 0.602. Find d. Number Units
The drawing shows a collision between two pucks on an air-hockey table. Puck A has a mass of 0.0120 kg and is moving along the x axis with a velocity of +6.65 m/s. It makes a collision with puck B, which has a mass of 0.0240 kg and is initially at rest. The collision is not head-on. After the collision, the two pucks fly apart with the angles shown in the drawing. Find the speed of (a) puck A and (b) puck B.
As shown in the figure, you pull a loaded sled whose mass is 20 kg at constant speed in the x direction with a rope at an angle of θ = 25∘. The coefficient of kinetic friction between the snow and the sled is 0.25 . Consider the sled to the be the system. a) What are the surroundings? b) Draw a free-body diagram. c) What is the magnitude of the tension force in the rope? d) What is the magnitude of the normal force?
In the figure a fastidious worker pushes directly along the handle of a mop with a force F→. The handle is at an angle θ = 47∘ with the vertical, and μs = 0.65 and μk = 0.49 are the coefficients of static and kinetic friction between the head of the mop and the floor. Ignore the mass of the handle and assume that all the mop's mass m = 0.63 kg is in its head. (a) If the mop head moves along the floor with a constant velocity, then what is F (b) If θ is less than a certain value θ0, then F→ (still directed along the handle) is unable to move the mop head. Find θ0.
You promised your younger brother that you would give him a ride on hils sled. You first pull him with a force F directed upward at an angle of 25∘ to the horizontal. After a while you decide to push him from behind with the same force F directed downward at an angle of 25∘. There is significant friction between the sled and the ice surface. Which of the following statements is true regarding the acceleration of the sled? apull = apush apull > apush apull < apush not enough information
A box is on a rough surface that is inclined at an angle of 30.0∘ to the horizontal. A mass, m1 = 0.270 kg, is attached to a hanging mass of m2 = 105 g over an ideal pulley. a. Draw two free-body diagrams, one for each mass, showing all forces acting on them and chosen direction of motion. b. What is the value of μ that allows the block to slide down the incline at constant speed? Blank 1 c. The incline is then greased to remove the friction and the masses released again from rest. Find the tension in the string, in Newtons, Blank 2 and the acceleration of the box, in m/s2. Blank 3 d. How long, in seconds, does it take the box to slide a distance of 1.40 m along the incline? Blank 4 For this problem, SHOW ALL WORK including a free-body diagram of forces on each mass shown in the drawing below. The direction of accelerations should be clearly indicated on the sketch. Show all equations used before entering numbers. This problem should be well-structured. DO NOT ENTER UNITS WITH ANSWERS.
Two particles with charges +4e and −4e are initially very far apart (effectively an infinite distance apart). They are then fixed at positions that are 4.57×10−12 m apart. What is EPEfinal − EPEinitial , which is the change in the electric potential energy? Number Units
As shown in the figure, a block of mass 5.80 kg, initially at rest on a horizontal surface without friction, is attached to a spring with k = 6.84×103 N/m. The spring is fixed at its other end. A bullet of mass 8.30 grams and velocity v = 810 m/s hits the block and embeds itself. Assume the compression of the spring is negligible until the bullet is embedded within the block (the spring is in its relaxed state). What is the speed of the block immediately after the collision? v = m/s What is the amplitude of simple harmonic motion resulting from the collision? xm = m
Determine the stopping distance for a skier moving down a slope with friction with an initial speed of 20 m/s as shown in Figure Q1-d. Assume μk = 0.18 and θ = 5∘, and x = 110 m. [12 marks]
The car has a mass of 1200 kg and a center of mass at point G. If the car is rear wheel drive, and the front wheels are free to turn. a) Draw a Free Body Diagram of the situation (10 points) b) If the coefficient of friction between the tires and road is μs = μk = 0.70 determine the maximum acceleration it can have. (20 points) c) If it accelerates with this acceleration to a top speed of 40 m/s, determine the time it takes to travel 500 m. (10 points)
A buoy floating in the ocean is bobbing in simple harmonic motion with period 6 seconds and amplitude 5 ft. Its displacement d from sea level at time t = 0 seconds is 0 ft, and initially it moves upward. (Note that upward is the positive direction.) Give the equation modeling the displacement d as a function of time t. d =
A block of mass M = 6.20 kg, at rest on a horizontal frictionless table, is attached to a rigid support by a spring of constant k = 6080 N/m. A bullet of mass m = 9.60 g and velocity V→ of magnitude 510 m/s strikes and is embedded in the block (the figure). Assuming the compression of the spring is negligible until the bullet is embedded, determine (a) the speed of the block immediately after the collision and (b) the amplitude of the resulting simple harmonic motion. (a) Number Units (b) Number Units
An observer sits in front of a speaker attached to a spring. The speaker oscillates with an amplitude of 0.500 m and reaches a minimum distance of d = 1.00 m from the observer. The mass of the speaker is m = 9.0 kg and the spring constant is k = 22.0 N/m. The speaker emits a pure 350.0 Hz tone as it oscillates in simple harmonic motion. The speed of sound in air is v = 343 m/s.
The velocity of a certain simple harmonic oscillator is given by v = −(7.15 m/s)sin(3.24t). What is the amplitude of the simple harmonic motion? None of these. 3.24 m 1.45 m 2.21 m 0.681 m 2.10 m
A 0.500−kg particle has a speed of 1.90 m/s at point (A) and kinetic energy of 7.70 J at point B. (a) What is its kinetic energy at (A)? J (b) What is its speed at B? m/s (c) What is the net work done on the particle by external forces as it moves from (A) to (B)? J
In the figure, a physical pendulum consists of a uniform solid disk (of radius R = 29.2 cm) supported in a vertical plane by a pivot located a distance d = 8.46 cm from the center of the disk. The disk is displaced by a small angle and released. What is the period of the resulting simple harmonic motion? Number Units
The electrons in the beam of a television tube have a kinetic energy of 3.53×10−15 J. Initially, the electrons move horizontally from west to east. The vertical component of the earth's magnetic field points down, toward the surface of the earth, and has a magnitude of 2.55×10−5 T. What is the acceleration of an electron due to this field component? Number Units
Problem 1. The grooved pulley of mass m is acted on by a constant force F through a cable, which is wrapped securely around the exterior of the pulley. The pulley supports a cylinder of mass M, which is attached to the end of a cable, which, in turn, is wrapped securely around an inner hub. If the system is stationary when the force F is first applied, determine the upward velocity of the supported mass after 3 s. Use the values m = 40 kg, M = 10 kg, ro = 225 mm, ri = 150 mm, IO = 25600 mkgmm2, and F = 75 N. Assume no mechanical interference for the indicated time frame, and neglect friction in the bearing at O. What is the time-averaged value of the force in the cable that supports the 10−kg mass?
An object oscillates with simple harmonic motion along with x axis. Its displacement from the origin varies with time according to the equation x = (4.00 m)cos(πt + π/4) Where t is in seconds and the angles in the parentheses are in radians. (a) Determine the amplitude, frequency and period of the motion. (b) Calculate the velocity and acceleration of the object at time t. (c) Using the results in part(b), determine the position, velocity and acceleration of the object at t = 1.0 s (d) Determine the maximum speed and acceleration of the object.
In the figure, two blocks (m = 2.50 kg and M = 10.5 kg) and a spring (k = 210 N/m) are arranged on a horizontal frictionless surface. The coefficient of static friction between the two blocks is 0.340. What amplitude of simple harmonic motion of the spring-blocks system puts the smaller block on the verge of slipping over the larger block? Number Units
A block of mass M = 5.60 kg, at rest on a horizontal frictionless table, is attached to a rigid support by a spring of constant k = 5490 N/m. A bullet of mass m = 9.00 g and velocity v→ of magnitude 510 m/s strikes and is embedded in the block (the figure). Assuming the compression of the spring is negligible until the bullet is embedded, determine (a) the speed of the block immediately after the collision and (b) the amplitude of the resulting simple harmonic motion. (a) Number Units (b) Number Units
A physical pendulum in the form of a planar object moves in simple harmonic motion with a frequency of 0.280 Hz. The pendulum has a mass of 2.00 kg, and the pivot is located 0.400 m from the center of mass. Determine the moment of inertia of the pendulum about the pivot point. kg⋅m2
The angle (with respect to the vertical) of a simple pendulum is given by θ = θmcos[(5.88 rad/s)t + ϕ]. If at t = 0, θ = 0.0450 rad and dθ/dt = −0.160 rad/s, what are (a) the phase constant ϕ and (b) the maximum angle θm ? (Hint: Don't confuse the rate dθ/dt at which θ changes with the ω of the SHM.) (a) Number Unit (b) Number Unit
The figure gives the position of a 10.0 g block oscillating in SHM on the end of a spring. The horizontal axis scale is set by ts = 36.0 ms. What are (a) the maximum kinetic energy of the block and (b) the number of times per second that maximum is reached? (Hint: Measuring a slope will probably not be very accurate. Find another approach.) (a) Number Units (b) Number Units
A simple pendulum has a mass of 0.350 kg and a length of 4.00 m. It is displaced through an angle of 7.0∘ and then released. Using the analysis model of a particle in simple harmonic motion, calculate the following. (Give your answer to the thousandths place.) (a) What is the maximum speed of the bob? 4.0 m/s (b) What is the maximum angular acceleration of the bob? 4.97 rad/s2 (c) What is the maximum restoring force of the bob? 4. N (d) Solve parts (a)through (c) by using other analysis models. (Hint: you may need to use separate analysis models for each part.) maximum speed 4. D. m/s maximum angular acceleration rad/s2 maximum restoring force 4.97 N (e) Compare the answers.
A mass sits on a frictionless horizontal surface and is attached to a wall by a horizontal spiral spring, as shown in the figure. When the spring is compressed (block moved to x = −6.0 cm) and released, it executes simple harmonic motion with a frequency of 1.25 Hz. a) Determine the position of the block at t = 0.5 s. b) Find the distance the block has moved during the first 0.5 seconds. c) Draw, in the space provided, a graph showing the velocity of the block vs time for the first complete oscillation. Include relevant data on the axes.
On Earth, a block of mass m is attached to a spring and immersed in a liquid. As the block moves, the liquid always exerts a force with a constant magnitude Fd but pointing opposite to the direction of motion. The spring has a relaxed length L0 and stiffness ks. As shown in the diagram, the block is initially released from rest when the length of the spring is 2∗L0. The bottom surface supporting the block is frictionless. Assume that the positive x-axis points to the right. Determine the new velocity of the block T seconds after leaving your hand. Assume T is small enough that the direction of the force doesn't change through this time period. Express your answer as a vector in terms of m, L, L0, ks, Fd and T. Determine the new net force on the block T seconds after leaving your hand. Assume T is small enough that the direction of the force doesn't change through this time period. Express your answer as a vector in terms of m, L, L0, ks, Fd and T.
The three blocks below are connected by strings over frictionless, massless pulleys. The coefficient of friction is 0.350 with the table (a) Draw free body diagrams for each object (b) Find the acceleration of each object. (c) Find the tension between each object (T12, T23).
Find the mass M of an object in the shape of a right circular cylinder of height 7 and radius 5 if its mass density is proportional to the square of the distance from the axis of the cylinder. (Give an exact answer. Use symbolic notation and fractions where needed. Use k as a constant of proportionality.) M =
A curve that has a radius of 90 m is banked at an angle of θ = 10.8∘. A 1000 kg car navigates the curve at 65 km/h without skidding. What is the minimum coefficient of static friction μs between the pavement and the tires? μs =
A student of mass 65.4 kg, starting at rest, slides down a slide 21.2 m long, tilted at an angle of 28.1∘ with respect to the horizontal. If the coefficient of kinetic friction between the student and the slide is 0.103 , find the force of kinetic friction, the acceleration, and the speed she is traveling when she reaches the bottom of the slide. (Enter the magnitudes.) HINT (a) the force of kinetic friction (in N) N (b) the acceleration (in m/s2) m/s2 (c) the speed she is traveling (in m/s) m/s
Violeta is skiing along a circular ski trail that has a radius 3.1 km long. She starts at the 3 -o'clock position (the easternmost point on the trail) and travels in the counterclockwise direction. Violeta stops skiing when she is −1.824 km east and 2.506 km north of the ski trail's center. Imagine an angle with its vertex at the center of the ski trail that subtends the path Violeta skis. a. How many radians has the angle swept out since Violeta started skiing? radians b. How many km has Violeta traveled since she started skiing? km
Consider a truck that has a weight of 18000 N, performing a full stop from a speed of 100 km/h on a grade with an angle of 6∘ as shown in the figure. It has a brake application that develops a steady brake force of 8000 N. The truck has a frontal area of 8 m2 and a drag coefficient of 0.6 . Determine the following: 1 - The deceleration. 2- The stopping distance. 3- The time required to reach a full stop. 4- The energy dissipated. 5- The brake power at initial application. 6- The average brake power over the stop.
The 8 kg cylinder A and 3 kg block B shown below are released from rest. Determine the speed of block A after it has moved 2 m starting from rest. What would be the speed of block A after it moves 2 m if the masses were reversed, i.e. , if mA = 3 kg and mB = 8 kg instead? Neglect the mass of the cables and pulleys.
A tension force of 135 N inclined at 15.0∘ above the horizontal is used to pull a 27.0 kg storage crate a distance of 4.10 m on a rough surface. If the crate moves at a constant speed, find (a) the work done by the tension force and (b) the coefficient of kinetic friction between the crate and surface. HINT (a) the work done by the tension force (in J) J (b) the coefficient of kinetic friction between the crate and surface
A woman pulls on a 6.00 - kg crate, which in turn is connected to a 4.00−kg crate by a light rope. The light rope remains taut. If the two crates move at constant speed, a. the 6.00−kg crate exerts more force on the 4.00−kg crate than the 4.00−kg crate exerts on the 6.00−kg crate. b. the 6.00−kg crate exerts as much force on the 4.00−kg crate as the 4.00−kg crate exerts on the 6.00−kg crate. c. the 6.00−kg crate exerts less force on the 4.00−kg crate than the 4.00−kg crate exerts on the 6.00−kg crate. d. No enough information to tell. Superman throws a 2400−N rock. What horizontal force must Superman apply on the rock to give it a horizontal acceleration of 12.0 m/s2 ? a. 2400 N b. 200 N c. 2939 N d. None of the above The car in the figure has a mass of 1000 kg and is held constant on the frictionless ramp by means of the light cable. The magnitude of the component of the car's weight in the direction parallel to the ramp is approximately a. 8400 N b. 4142 N c. 8882 N d. 5047 N
Two connected crates with masses 4 kg and 6 kg, sit on a frictionless surface. A woman pulls horizontally on the 6 kg crate with a force that gives the crate an acceleration of 2 m/s2. Find the tension T in the rope. a. 6 N b. 7 N c. 4 N d. 8 N A man (m = 75 kg) is inside an elevator that is moving upward with acceleration 2 m/s2. What is the normal force on the man? Neglect friction. a. 585 N b. Cannot tell c. 735 N d. 885 N
Using the principles of equilibrium to be developed in Chapter 3 , you will soon be able to verify that the tension in cable AB is 86.13% of the weight of the cylinder of mass m, while the tension in cable AC is 35.91% of the suspended weight. Write each tension force acting on point A as a vector if the mass m is 68 kg. Answers: TAB = ( i + ј) N TAC = ( i + ј) N
Problem No. 2.4 (pg. 38) A cable pulls on a flange with a tension force as shown (see textbook for figure). Using the slope-triangle method or right angle trigonometric method solve for the horizontal (x component) and vertical (y component) components of the tension force. What is the direction of force (angle measured counterclockwise about left end point of a line resting horizontally)? A. 22.6 degree B. 24.6 degree C. 65.4 degree D. 67.4 degree
A uniform Electric Field exists in the region between two oppositely charged plane parallel plates. A proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate 1.60 cm distant from the first in a time interval 1.5×10−6 seconds. A. Find the magnitude of the Electric Field in N/C. B. The speed of the proton when it strikes the negatively charged plate in km/s.
In the figure particle 1 of charge +6e is above a floor by distance d1 = 3.10 mm and particle 2 of charge +7e is on the floor, at distance d2 = 7.40 mm horizontally from particle 1. What is the x component of the electrostatic force on particle 2 due to particle 1? Number Units
A force vector points at an angle of 61.4∘ above the +x axis. It has a y component of +153 newtons (N). Find (a) the magnitude and (b) the x component of the force vector. (a) Number Units (b) Number Units
The magnitude of a force vector F→ is 88.0 newtons ( N. The x component of this vector is directed along the +x axis and has a magnitude of 78.8 N. The y component points along the +y axis. (a) Find the angle between F→ and the +x axis. (b) Find the component of F→ along the +y axis. (a) Number Units (b) Number Units
The magnitude of a force vector F→ is 89.4 newtons (N). The x component of this vector is directed along the +x axis and has a magnitude of 72.4 N. The y component points along the +y axis. (a) Find the angle between F→ and the +x axis. (b) Find the component of F→ along the +y axis. (a) Number Units (b) Number Units
An object with mass 3 kg moves from a location <22, 36, −41> m near the Earth's surface to location <−27, 11, 48> m. What is the change in the potential energy of the system consisting of the object plus the Earth? (Assume that the +y axis points vertically up from the ground.) J
Sphere A has a mass of 24 kg and a radius of 75 mm, while sphere B has a mass of 3 kg and a radius of 50 mm. If the spheres are traveling initially along the parallel paths with the speeds shown, determine the velocities of the spheres immediately after impact. Specify the angles θA and θB with respect to the x-axis made by the rebound velocity vectors. The coefficient of restitution is 0.4 and friction is neglected. Problem 3/262. Sphere A magnitude m/s direction - counterclockwise from the +x axis Sphere B magnitude m/s direction - counterclockwise from the +x axis
In the figure, a uniform sphere of mass m = 1.27 kg and radius r = 0.104 m is held in place by a massless rope attached to a frictionless wall a distance L = 3.38 m above the center of the sphere. Find (a) the tension in the rope and (b) the force on the sphere from the wall. (a) Number Units (b) Number Units
Sphere A collides with sphere B as shown in the figure. If the coefficient of restitution is e = 0.63, determine the velocity of each sphere immediately after impact. Motion is confined to the x-y plane. Answers: vA = ( i + j) m/s vB = ( i + j) m/s
Sphere A has a weight of 33 lb and a radius of 7 in. , while sphere B has a weight of 6 lb and a radius of 4 in. If the spheres are traveling initially along the parallel paths with the speeds shown, determine the velocities of the spheres immediately after impact. Specify the angles θA and θB with respect to the x-axis made by the rebound velocity vectors. The coefficient of restitution is 0.40 and friction is neglected. Enter positive numbers for the angles θ. Answers: vA = ft/sec, θA = vB = ft/sec, θB =
The pulley and the hanging mass have the same value of mass, m. The system starts from rest and is released. The string exerts a torque of 1/3 mgR about the axis of the pulley, and the angular acceleration of the pulley is (2 g)/(3 R) The string exerts a torque of 2/3 mgR about the axis of the pulley, and the angular acceleration of the pulley is g/(3 R) The string exerts a torque of 1/3 mgR about the axis of the pulley, and the angular acceleration of the pulley is g/(3 R) The string exerts a torque of 2/3 mgR about the axis of the pulley, and the angular acceleration of the pulley is (2 g)/(3 R)