15-15 The chute shown in Fig. P15-15 is 20 ft long and is used to transfer boxes from the street into the basement of a store. The kinetic coefficients of friction are μk = 0.25 between the box and the chute and μk = 0.40 between the box and the basement floor. If a 30−lb box is given an initial velocity of 10 ft/s when it is placed on the chute, determine a. The velocity of the box as it leaves the end of the chute. b. The distance d that the box will slide on the basement floor after it leaves the end of the chute. Fig. P15-15
A 2 kg hoop, with a radius of 0.6 m, is released with backspin onto a 25∘ incline. It is released smoothly, so it does not bounce. The kinetic coefficient of friction between the hoop and the surface is 0.4 and the initial speed of the center of the hoop is 2 m/s up slope, and the initial angular speed of the hoop is 3 rad/s clockwise. a. What are the initial linear acceleration, aC, of the center of the hoop (magnitude and direction)? b. What is the initial angular acceleration, α, the hoop (magnitude and direction)?
A pulley rotates without friction about a fixed axis at its center, Point O. To blocks hang from the pulley at different radii. a. What is the rate of change on angular momentum of the whole system about the center of the pulley? (i. e. what is the net moment of the whole system about Point O?) b. What is the total mass moment of inertia of the whole system about the center of the pulley? c. What is the angular acceleration of the pulley?
A uniform sphere has a mass of 8 kg and a radius of 0.1 m. It is rolling down a 20∘ incline without slipping. a. What is the angular acceleration, α, of the sphere? b. What is the acceleration of the center of the sphere, aC? c. What is the friction force that the incline is putting on the sphere?
The cabinet weighs 150 lbf. A mover pushes on it with a horizontal force P at a height of 4 ft as shown. The center of mass is 3.5 ft above the floor. The coefficient of friction between the cabinet and the floor is μ = 0.2. a. Draw the free body force diagram of the cabinet. b. Write the equations for the sum of vertical and horizontal forces, and solve for the horizontal force P supplied by the mover to just begin sliding the cabinet. c. Write the equation for the sum of the moments about a point at the base of the cabinet centered under the center of mass at "G." Solve for "x," the distance from the center of the bottom to where the normal force must act in order for the crate not to tip. d. Will the crate tip or slide? e. If the crate hits a rougher or smoother spot on the ground, at what coefficient of friction will the crate begin to tip?
The uniform concrete block in (Figure 1) has a weight of 300 lb. The coefficients of static friction are μA = 0.2, μB = 0.3, and between the concrete block and the floor, μ = 0.4. Figure 1 of 1 Part A Determine the smallest couple moment that can be applied to the 100−lb wheel that will cause impending motion. Express your answer to three significant figures and include the appropriate units. M =
A block of mass m = 100 kg is on an inclined plane as shown where ∅ = 20 degrees and θ = 40 degrees. The coefficient of static friction is μs = 0.35 and coefficient of kinetic friction is μk = 0.3 . Determine the friction force, F, acting on the block when force P with a magnitude of 200 N is applied to the block, which remains in equilibrium. Determine the magnitude of the force, P, required to initiate motion of the block up the slope from rest. Determine the magnitude of the friction force F acting on the block if P = 900 N.
Figure Q1.2 illustrates a crate with the mass of mc, which is initially at rest at a slope with angle of θ. A bullet of mass mb and velocity ub is fired into the crate and causes it to slide along the slope embedding itself in the crate. The coefficient of friction between the surface of the slope and the crate is given by μ. Ignore the aerodynamic drag during the process. Note that mc, θ, mb, ub, and μ are generated randomly. Determine:The velocity, (denoted v1), of the crate after moving L1, which is defined randomlyThe total travelled distance LThe total mechanical energy lost during the process Figure Q1.2
The coefficient of static friction between the 200−kg crate and the ground is μs = 0.2, while the coefficient of static friction between the 90−kg man's shoes and the ground is μs = 0.35. Determine if the man can move the crate.
Assume the system accelerates with block "A" moving downward. The coefficient of kinetic friction between the blocks and the ramp is 0.15 The tension force between B and C is 120 N. Find the acceleration of the whole system. [4]
Mass m1 lies on a horizontal platform having a coefficient of kinetic friction, μ. It is connected by a string to mass m2 which hangs over the edge of the platform. Suppose m1 = 10 kg, m2 = 1 kg, and μ = 0.2. Ignoring the friction associated with the string. Write down the equations of motion. Solve the equations of motion for the acceleration, a, and the tension, T. Find their numerical values.
A block of mass m1 = 4 kg is positioned on a ramp. with μs = 0.7 and μk = 0.5 a second mass m2 = 3 kg is suspended from the ramp. The blocks initially are at rest. a. Draw free body diagrams for both blocks (2 points) b. What is the tension in the string? (2 points) c. What angle is the ramp if there is no friction present? (2 points) d. If the ramp angle is 30 degrees, what is the magnitude of the static friction? Does it point up or down the ramp? (2 points)A rain storm comes and slickens the ramp, lowering μs. What's the minimum value of μs for which the block does not start sliding if the ramp is still at 30 degrees? (3 points)The ramp slickens to exactly the value you found in part 2, but a bird lands on the 4 kg mass increasing its mass by 1 kg. Does the box move? If so what is its acceleration? (4 points)
Q3. The coefficient of static friction between the 100−kg crate and the ground is μs = 0.3, while the coefficient of static friction between the 70−kg man's shoes and the ground is μs = 0.4. Determine if the man can move the crate. Assume that the crate is to be on the verge of sliding. g = 10 N/kg
A 500 g block in the Figure below is pushed up the incline with an initial speed of 2.0 m/s. How far up the incline will it go before it stops if the coefficient of friction between it and the incline is 0.150 (Use the work-energy method only)?
A 4.00−kg block rests between the floor and a 3.00−kg block as shown in the figure. The 3.00−kg block is tied to a wall by a horizontal rope. If the coefficient of static friction is 0.800 between each pair of surfaces in contact, what horizontal force F must be applied to the 4.00−kg block to make it move? (g = 9.8 m/s2) A) 21.1 N B) 16.2 N C) 78.4 N D) 54.9 N E)23.5 N
A contestant in a winter games event pulls a 39.0 kg block of ice across a frozen lake with a rope over his shoulder as shown in the figure. The coefficient of static friction is 0.1 and the coefficient of kinetic friction is 0.03 . (a) Calculate the minimum force F (in N) he must exert to get the block moving. N (b) What is its acceleration (in m/s2 ) once it starts to move, if that force is maintained? m/s2
Determine whether the block shown in the figure is in equilibrium and find the magnitude and direction of the friction force when θ = 40∘ and P = 399 N. Given: μs = 0.20 and μk = 0.15. The block is in equilibrium. The magnitude and direction of the friction force is N
I. Block A has a mass of 12 kg and block B has a mass of 8 kg. You push on block A with a 100.0 N force. For parts (a) & (b), assume no friction. (a) What are the accelerations of the blocks? (b) Now the force is turned to the left, and the push becomes a pull. What are the accelerations of the blocks? (c) Now assume a coefficient of kinetic friction of μ = 0.100. What are the block accelerations in parts (a) and (b) in this case?
II. You are pulling up two boxes as shown. The force holding the top box on the bottom block is friction and the coefficient of static friction is μs = 0.500 for both interfaces. You want to move the blocks at a slow constant speed. What force do you need to accomplish this?
A conducting rod with length 0.153 m, mass 0.150 kg, and resistance 78.9 Ω moves without friction on metal rails as shown in the following figure. A uniform magnetic field with magnitude 1.50 T is directed into the plane of the figure. The rod is initially at rest, and then a constant force with magnitude 1.90 N and directed to the right is applied to the bar. Part A How many seconds after the force is applied does the bar reach a speed of 25.9 m/s? Express your answer with the appropriate units. t =
You are analyzing an Atwood machine with masses m1 and m2 connected over a pulley by a massless, unstretchable string. The left-hand mass, m1, rests on an inclined plane forming an angle, θ = 30∘, with the horizontal direction and has a coefficient of kinetic friction, μ. Suppose m1 = 1 kg, m2 = 2 kg, and μ = 0.2 Determine the equations of motion for the masses m1 and m2. Solve the equations of motion for the acceleration, and the tension. Find their numerical values.
A 3.02 kg block is pushed along a horizontal floor by a force F→ of magnitude 34.0 N at a downward angle θ = 40.0∘. The coefficient of kinetic friction between the block and the floor is 0.240. Calculate the magnitudes of (a) the frictional force on the block from the floor and (b) the block's acceleration. (a) Number Units (b) Number Units
Determine whether the block shown is in equilibrium and find the magnitude and direction of the friction force when θ = 35∘ and P = 106 lb. Given: μs = 0.3 and μk = 0.2. The block is in equilibrium. The magnitude and direction of the friction force is lb
A 20.0 kg crate is subjected to a constant force of 100 N as shown in the figure. When the distance it is pulled is s = 15.0 m the crate is moving at 8.0 m/s. Determine its speed when s = 25 m. The coefficient of kinetic friction between the crate and the ground is 0.25 . Use the principle of work and energy.
To measure the static friction coefficient between a 1.6−kg block and a vertical wall, the setup shown in the drawing is used. A spring (spring constant = 510 N/m ) is attached to the block. Someone pushes on the end of the spring in a direction perpendicular to the wall until the block does not slip down. The spring is compressed by 0.039 m. (a) Draw the free-body diagram showing the forces that act on the block. (b) What is the coefficient of static friction?
The bob of a simple pendulum of length l = 0.85 m dropped from a horizontal position strikes a block at rest of the same mass, placed at middle on a horizontal table that total width and height is 0.65 m, 1 m respectively and the friction μ = 0.45 at what position does the block stop? (Note: the energy is conservation during strikes)
A man on a motorcycle plans to make a jump as shown In the figure. If he leaves the ramp with a speed of 35.0 m/s and has a speed of 32.5 m/s at the top of his trajectory, determine his maximum height (h) above the end of the ramp. Ignore friction and air resistance. m
Block A has a mass of 2.75 kg, and Block B has a mass of 1.25 kg. The coefficient of kinetic friction between A and the plane is 0.30 . Block A has an initial velocity of 3.00 m/s down the plane. Find a) the acceleration of Block A. b) the tension in the cable.
As shown in the figure, a block of mass m is at rest on a ramp inclined 30∘ to the horizontal, and another block of mass 2 3 m at rest on a ramp inclined 60∘. Two blocks are connected by a light, inextensible cord, and the cord passes on a light, frictionless pulley. The other end of the block of mass m is connected to an spring with a force constant k. The spring is neither compressed nor extended. (a) What is the maximum distance the blocks will move when the inclines are frictionless? Express the answer in terms of m, k, and the gravitational acceleration g. (b) Repeat (a) when the coefficients of kinetic friction are 1/3 for both blocks. (c) What is the change in the internal energy of the system composed of the blocks, the inclines, and the spring?
The log has a mass of 500 kg and rests on the ground for which the coefficients of static and kinetic friction are μs = 0.5 and μk = 0.4 respectively. The winch delivers a horizontal towing force T to its cable at A which varies as shown in the graph. Determine the speed of the log when t = 5 s. Originally the tension in the cable is zero.
Two masses are connected by a cable, as shown in the figure for this question. M1 = 12 kg and M2 = 20 kg. M1 has a coefficient of friction of μ1 = 1.0 and M2 has a coefficient of friction of μ2 = 0.4. Determine the minimum value of P required to make masses M1 and M2 move. Ans. P = 115.7 N
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. The flywheel shown has a radius of 20 in. , a weight of 340 lbs, and a radius of gyration of 15 in. A 120 - lb block A is attached to a wire that is wrapped around the flywheel, and the system is released from rest. The effect of friction is neglected. Problem 16.033. b - Speed of hanging mass Determine the speed of block A after it has moved 5 ft. The speed of block A after it has moved 5 ft is ft/s.
A loaded penguin sled weighing 61.0 N rests on a plane inclined at angle θ = 25.0∘ to the horizontal (see the figure). Between the sled and the plane, the coefficient of static friction is 0.300, and the coefficient of kinetic friction is 0.110. (a) What is the minimum magnitude of the force F→, parallel to the plane, that will prevent the sled from slipping down the plane? (b) What is the minimum magnitude F that will start the sled moving up the plane? (c) What value of F is required to move the sled up the plane at constant velocity? (a) Number Units (b) Number Units (c) Number Units
There are two blocks on a two-sided inclined plane. They are connected by a rope. The mass of the rope and the friction are negligibly small. Block 1 has the mass. The inclination angle of plane 1 is ∘. m1 = 3 kgα = 30 Block 2 has the mass. The angle of inclination of plane 2 is ∘. m2 = 9 kgβ = 45 Determine the amount of acceleration of the two blocks |a| = m/s2 For the gravitational acceleration, use the rounded value g = 10 m/s2. Round to one decimal place. Determine the amount of force exerted by the rope. |F| = For the gravitational acceleration, use the rounded value g = 10 m/s2. Round to one decimal place. Also specify the unit.
A 15.4 kg block is dragged over a rough, horizontal surface by a constant force of 93.3 N acting at an angle of 34.6∘ above the horizontal. The block is displaced 41.5 m, and the coefficient of kinetic friction is 0.215. The acceleration of gravity is 9.8 m/s2. μ = 0.215 Find the work done by the force of friction. Answer in units of J.
The maximum tension in the cord is 600 N. The pulley at A is free to rotate so that there is no friction between the belt and the pulley. The coefficient static friction at the fixed drums B and C is μ = 0.23 and the contact angle β is 135∘. Be sure to convert β to radians. Determine the largest mass of the cylinder that can be supported by the cord. Use the following equation for the belt tension based on the coefficient of friction and the contact angle, T2 = T1 eμβ
Consider the block shown to have a mass of 2700 kg. The coefficient of static friction are 0.15 between the two wedges and the block, and 0.12 between the block and the ground. What is the required magnitude of the forces P to lift the block?
Problem 1. You are trying to slide a heavy block-like object, of mass m, along a flat floor, with a coefficient of kinetic friction μk between the object and the floor. You wrap a rope around the object, and pull with a force of magnitude F. Your goal is to slide the block along the floor at some constant speed. You do not necessarily have to pull horizontally; you can pull at any angle α to the horizontal. (20 points total) (a) Find an expression for F as a function of α, μk, g, and m. ( 8 points) (b) What would be the optimum choice of α, so that the block can be pulled with the smallest value of F ? (8 points) (c) If μ = 0.6, what is the optimum value of F computed in part b ? (4 points)
In the figure, a block weighing 16.1 N, which can slide without friction on an incline at angle θ = 35.0∘, is connected to the top of the incline by a massless spring of unstretched length 0.430 m and spring constant 115 N/m. The block is initially at its equilibrium position. (a) How far from the top of the incline is the block's equilibrium point? (b) If the block is pulled slightly down the incline and released, what is the period of the resulting oscillations? (a) Number Units (b) Number Units
A 2.0−kg block was released from rest at point A. It then moves through point B until it finally stops at point C. The plane is inclined at an angle θ of 22.0∘ from the horizontal and the incline stands at a height h of 3.0 m. The coefficient of kinetic friction from point A to B is 0.40 . (a) What is the velocity of the block at point B ? (b) What is the coefficient of friction for the horizontal surface (from point B to C)?
Q3/ The 10-lb block has a speed of 4 ft/s when the force of F = (8t2) lb is applied. Determine the velocity of the block when it moves s = 28 ft. The coefficient of kinetic friction at the surface is μk = 0.25.
A hanging weight, with a mass of m1 = 0.360 kg, is attached by a string to a block with mass m2 = 0.850 kg as shown in the figure below. The string goes over a pulley with a mass of M = 0.350 kg. The pulley can be modeled as a hollow cylinder with an inner radius of R1 = 0.0200 m, and an outer radius of R2 = 0.0300 m; the mass of the spokes is negligible. As the weight falls, the block slides on the table, and the coefficient of kinetic friction between the block and the table is μk = 0.250. At the instant shown, the block is moving with a velocity of vi = 0.820 m/s toward the pulley. Assume that the pulley is free to spin without friction, that the string does not stretch and does not slip on the pulley, and that the mass of the string is negligible. (a) Using energy methods, find the speed of the block (in m/s ) after it has moved a distance of 0.700 m away from the initial position shown. m/s (b) What is the angular speed of the pulley (in rad/s) after the block has moved this distance? rad/s
Two objects are connected to a string, and the string is hung over a pulley connected to the ceiling, as shown in the figure below. (i) released from rest. The pulley's axis has negligible friction. The mass of the string is small enough to be ignored, and the string does not slip on the pulley, nor does it stretch. (a) How much time (in s) does it take object m1 to hit the floor after being released? Δt1 = s (b) How would your answer to part (a) change if the mass of the pulley were neglected? (Enter the time, in seconds, it takes object m1 to hit the floor if the mass of the pulley were neglected.) Δt2 = s
A container full of explosives is sliding down a hill toward a village at 50.0 m/s. The container and explosives have a total mass of 7.50×104 kg. Two superheroes arrive at the same time and begin pushing on the container to stop it. The flying superhero pushes horizontally with a force of 2.00×105 N. The standing superhero pushes up the slope with a force of 2.00×105 N. They manage to stop the container in 200 m. The hill has a constant slope of 40.0∘ relative to the horizontal. a. Use the work-energy theorem (chapter 7 style) to find the net work done on the container. b. Use the definition of work to find the work done by each of the forces listed. (The force from the flying superhero, the force from the standing superhero, the force of gravity, and the normal force) c. How much work must have been done by kinetic friction? d. How strong was the kinetic frictional force? e. What was the coefficient of kinetic friction?
Two blocks are set up as shown. Static friction holds the following system at rest. The pulley has no mass. The coefficient of static friction is μk = 0.700. The mass of the block on the horizontal surface is m1 = 33.0 kg. a. Sketch all the forces acting on each of the blocks. (Sketch them on the images or as free-body diagrams. ) b. What is the largest value for m2 such that the system stays at rest? c. What is the tension in the rope when m2 is at this maximum value?
Knowing that the coefficient of static friction between the tires and the road is 0.7 for the automobile shown, determine the maximum possible acceleration on a level road, assuming four-wheel drive.
! Required information Problem 18.029 - Bowling ball with back spin - DEPENDENT MULTI-PART PROBLEM - ASSIGN ALL THE PARTS A 14 lb bowling ball is thrown onto a lane with a backspin angular speed ω0 = 10 rad/s and forward velocity v0 = 17 mph. After a few seconds, the ball starts rolling without slip and moving forward with a speed vf = 17.2 ft/s. Let r = 4.25 in. be the radius of the ball, and let kG = 2.6 in. be its radius of gyration. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Problem 18.029. b - Work of friction on the ball Determine the work done by friction on the ball from the initial time until the time that the ball starts rolling without slip. (Round the final answer to five decimal places. Include a minus sign if necessary) The work done by friction on the ball is ft⋅lb.
A 40−kg vase has a 200−mm-diameter base and is being moved using a 100−kg utility cart as shown. The cart moves on the ground with μk = 0.10. Knowing the coefficient of static friction between the vase and the cart is μs = 0.4, determine the maximum force F that can be applied if the vase is not to slide or tip.
The cart shown below moves across the table top as the block falls. What is the acceleration of the cart? Neglect friction and assume the following data: m1 = 2.0 kg, m2 = 4.0 kg, I = 0.4 kg−m2, r = 20 cm
Two forces act on a 4.5−kg block at rest on a rough level surface as shown. The coefficient of kinetic friction is μc = 0.02. The block moves 20 m from its initial position. (a) Find the work done by FN (the normal force). (4 points) (b) Find the work done by the frictional force. (4 points) (c). Find the net work done on the block. (4 points) (d) Use the Work-Energy Theorem to find the final velocity of the block. (3 points)
In the figure below, a horizontal spring is used to launch an object towards an incline. Assume that there is no friction. The spring constant is 40.0 N/m. The object has mass 0.50 kg. The incline is 30.0∘ to the horizontal. The spring is compressed 0.20 m, then the block is released. After leaving the spring, the object travels horizontally a short distance before reaching the incline. (a) Determine the initial speed of the block just before reaching the incline. (b) After travelling 0.10 metres along (parallel to) the incline, what is the speed of the object? (c) Determine the maximum distance along the incline the block travels before it stops and reverses direction.
A ladder leans against a house as shown below. A painter stands on the ladder such that his feet are 3.0 m above the ground. The ladder is 5.0−m long. The ladder reaches the house at a point 4.7 m above the ground. The ladder weighs 120 N, and the painter weighs 680 N. Assume that there is no friction at the point where the ladder touches the house. (a) Sketch a free-body diagram of the forces acting on the ladder. (b) Determine the magnitude and direction of the friction force between the ladder and the ground.
A box of mass m = 8 kg is pulled by a rope at an angle of Θ = 30∘ by a rope of tension T = 100 N. The block moves in the +x direction. Find both: the work done by the rope AND the change in kinetic energy of the block after the block moves 10 m for the following 2 scenarios: There is no friction. There is kinetic friction with coefficient μ = . 1
Two blocks are set up as shown. The blocks are released from rest and static friction is not enough to hold them. The pulley has no mass. The system moves to the right. The coefficient of kinetic friction is μk = 0.350 and θ = 35.0. The mass of the block on the ramp is m1 = 25.0 kg and the mass of the hanging block is m2 = 40 kg. a. Sketch and label all the forces acting on each of the blocks. (You may draw these forces on the image or in free-body diagrams.) b. What is the rate of acceleration of the blocks? c. What is the tension in the rope?
A spring is used to propel a 20 oz ball up a rod. The spring has a free length of 12 in. and ak = 0.75 lb/in. The coefficient of friction between the ball and the rod is μk = 0.35. Determine the maximum speed for the ball. Answer needs to be in inches per second (in/s)
In the figure, a 1 kg block slides along a frictionless track from one level to a higher level after passing through an intermediate valley. At the higher level, the surface has a coefficient of kinetic friction μk = 0.5. This friction force stops the block in a distance d = 2 m. The height difference h = 1 m. Find initial velocity vo. a) 1.20 m/s b) 2.24 m/s c) 20.15 m/s d) 0.33 m/s e) 6.26 m/s
The man of mass m1 = 90 kg and the woman of mass m2 = 77 kg are standing on the platform of mass m0 = 100 kg which moves with negligible friction and is initially at rest with s = 0. The woman holds still at x2 = 1 m. The man walks from the end of the platform at A for 1 meter in the direction shown (x1) : what displacement s results from this movement? The length of platform, l, is 5 meters.
A horizontal uniform circular disk has a mass 2 m. The disk is free to rotate about the z axis and initially at rest. A man having mass m begins to run along the edge in a circular path whose radius is approximated to be R. If he maintains a speed of v0 relative to the disk, what is the angular velocity of the disk? Neglect friction. v0/R v0/(2R) 3v0/(2R) 2v0/(3R) v0/(3R)
In the figure, a uniform plank, with a length L of 4.75 m and a weight of 630 N, rests on the ground and against a frictionless roller at the top of a wall of height h = 2.36 m. The plank remains in equilibrium for any value of θ = 70.0∘ or more, but slips if θ < 70.0∘. Find the coefficient of static friction between the plank and the ground. Number Units
Crate A is traveling down the incline with a speed of 2.9 m/s when in the position shown. It later strikes and becomes attached to crate B. Determine the distance d moved by the pair after the collision. The coefficient of kinetic friction is μk = 0.27 for both crates. Answer: d = m
Problem 3: The following crate has a mass of 50−kg. It is in contact with the ground. If (a) P = 200 N and (b) P = 400 N. The coefficients of static and kinetic friction between the crate and ground μs = 0.3 and μk = 0.2. Determine the friction developed between the ground and the crate. (25 %)