A horizontal force P is applied to a block weighing 100 lb. The coefficient of friction between the block and the inclined surface is μs = 0.45. Determine the maximum force P which may be applied without causing motion. Consider and show all possibilities of motion.
A block of mass 3.00 kg is pushed up against a wall by a force P that makes an angle of 50∘ with the horizontal as shown in the figure. The coefficient of static friction between the block and the wall is 0.250. a) What is the minimum value of P that will keep the block from sliding down? b) What is the maximum value of P that will keep the block from sliding up?
An inclined plane of angle 20∘ has a spring of force constant k = 500 N/m fastened securely at the bottom so that the spring is parallel to the surface as shown. A block of mass 2.60 kg is placed on the plane at a distance d = 0.300 m from the spring. From this position, the block is projected downward toward the spring with speed v = 0.750 m/s. By what distance is the spring compressed when the block momentarily comes to rest?
A block is on an inclined surface. m = 25 kg and the coefficient of static friction is μ0 = 0.25. The acceleration of gravity is g = 9.8 m/s2. Find the value of P required to start the block moving up the incline.
The coefficient of static friction between the m = 3.95−kg crate and the 35.0∘ incline of the figure below is 0.290 . What minimum force F→ must be applied to the crate perpendicular to the incline to prevent the crate from sliding down the incline? N
A 550 lb block is supported by a horizontal floor. The coefficient of static friction mu between the block and the floor is assumed to be 0.5. Calculate the force P required to cause motion to impend. The force is applied to the block (a) horizontally and (b) downward at an angle of 35∗ with horizontal. (Do not forget to change the values on the pictures to what is provided in the text of the problem).
a) Figure 3(a) shows a 200 N block on an inclined surface was held by a horizontal force of 350 N. Determine whether the block will be held in equilibrium without moving up. The coefficient of static friction is 0.3. [11 Marks] Figure 3(a)
A body weighing 100 lbs rests on an inclined plane as shown. The coefficient of static friction between the body and the plane is 0.40. Compute the force P that will cause impending motion (a) Up the inclined plane (b) Down the inclined plane Compute the horizontal force P required to cause motion to impend up the plane for the 100−lb block shown. The coefficient of static friction between the block and plane is 0.25.
The box is stationary on the inclined surface. The coefficient of static friction between the box and the surface is μs. (a) If the mass of the box is 10 kg, α = 20∘, β = 30∘ and μs = 0.24, what force T is necessary to start the box sliding up the surface? (b) Show that the force T necessary to start the box sliding up the surface is minimum when tanβ = μs.
The 55−kg block rests on the horizontal surface, and a force P = 414 N, whose direction can be varied, is applied to the block. (a) If the block begins to slip when θ is reduced to 21∘, calculate the coefficient of static friction μs between the block and the surface. (b) If P is applied with θ = 34∘, calculate the friction force F. The force F is positive if to the right, negative if to the left. Answers: (a) μs = (b) F = N
A force P is applied to a block A of mass m = 4 kg as shown. The block sits on an inclined surface with q = 30∘ and a coefficient of static friction ms = 0.3. What is the minimum force P to start A moving up the incline? N
Problem #3 In the figure below a 3.00 kg block is being pushed up against a wall by a force P→ at an angle of θ = 50.0∘ with respect to the horizontal as shown. The coefficient of static friction between the block and the wall is given as 0.250 . (a) What are the possible values of ∥P→∥ that allow the block to remain stationary? (b) Explain what happens to the block if ∥P→∥ takes smaller or larger values. (c) Repeat the two previous parts, assuming that θ = 13.0∘.
A race track curve has a radius of 100 m and is banked at an angle of 68∘. For what speed was the curve designed, neglecting friction? Solve using first principles, not just a single memorized equation for full marks.
A 15kg uniform disk A with a radius of 0.4 m is rotating without friction about its center at 10 rad/s. Then another disk B is dropped onto the first disk. The second disk has a mass of 15 kg and radius of 0.3 m. The second disk is initially not rotating. There is friction between the disks. What is the angular speed of both disks when they stop slipping relative to each other? STATE 1 STATE 2
Determine the magnitude and direction of the friction force acting on the 77−kg block shown if, first, P = 92 N. The coefficient of static friction is 0.23 , and the coefficient of kinetic friction is 0.17 . The forces are applied with the block initially at rest. 34.9 N 139.8 N 710.5 N 46.3 N
Problem 3: Compute the horizontal force P required to cause motion to impend up the plane for the 180 lb block shown. The coefficient of static friction between the block and plane is 0.30 (4 Points)
The weight of the block in the drawing is 62.0 N. The coefficient of static friction between the block and the vertical wall is 0.550. (a) What minimum magnitude of the force F→ is required to prevent the block from sliding down the wall? (Hint: The static frictional force exerted by the block is directed upward, parallel to the wall.) (b) What minimum force is required to start the block moving up the wall? (Hint: The static frictional force is now directed down the wall.) (a) Number Units N (b) Number Units
Two bodies of masses m1 = 8 kg and m2 = 3 kg are connected by a light string passing over a smooth pulley at the edge of the table as shown in the figure. The coefficient of static friction between the surfaces (body and table) is 0.6. Will the mass m1 = 8 kg on the surface move? If not what value of m2 should be used so that mass 8 kg begins to slide on the table?
The 2225−N block shown in the figure is in contact with 45∘ incline. The coefficient of static friction is 0.25. Compute the value of the incline force P (parallel to the incline) necessary to (a) just start the block up the incline or (b) just prevent motion down the incline.
The following diagram shows a crate on an incline. The coefficient of kinetic friction (μk) between the crate and the incline is 0.1. The velocity of the box is zero, at which point in time it is subjected to a constant horizontal force F = 20 N. Determine the crate's velocity two seconds later. Weight of crate = 137 N
A 30−kg package is placed on an incline when a force P is applied to it as shown on the figure. The coefficients of static and kinetic friction between the package and the incline are 0.2 and 0.1, respectively. The motion of the package depends on the magnitude of the force P. (a) Determine the range of values for P for which the package will remain stationary on the inclined plane. (b) Assuming the package is initially stationary, determine its velocity and position 10 seconds after the force P is reduced to zero, i.e. P = 0.
Block A in the figure has mass mA = 4.20 kg, and block B has mass mB = 2.10 kg. The coefficient of kinetic friction between block B and the horizontal plane is μk = 0.530. The inclined plane is frictionless and at angle θ = 32.0∘. The pulley serves only to change the direction of the cord connecting the blocks. The cord has negligible mass. Find (a) the tension in the cord and (b) the magnitude of the acceleration of the blocks. (a) Number Units (b) Number Units
Block A of weight 1200 N rests on a rough horizontal plane. The coefficient of static friction between the surfaces of the block and the plane is 0.40. If the block is at the verge of motion under the action of the force, P, draw a free-body diagram for the block and determine the value of P.
In order to avoid a 11.7 kg box to fall, you press the box to the wall. the coefficient of static friction between box and wall is 0.6. What is the minimum force you have to apply in order to keep the box in place.
(a) Determine the tension T which the shipworkers must develop in the cable to lower the 115−lb crate at a slow steady speed. The effective coefficient of friction at the railing is μ = 0.26. (b) What would be the value of T in order to raise the crate? Assume W = 115 lb. Answers: (a) T = Ib (b) T = Ib
Two identical boxes are placed on a floor. The coefficient of static friction between the boxes and the floor is 0.35. A force P1 is applied to the left box and causes it to move at a constant velocity. A force P2 is applied to the right box and causes it to move at a constant velocity. What can be inferred about the relative magnitudes of the forces P1 and P2? A. P1 > P2 B. P1 = P2 C. P1 < P2 D. There is not enough information to infer anything about the relative magnitudes.
The 599−N force is applied to the 116-kg block, which is stationary before the force is applied. Determine the magnitude and direction of the friction force F exerted by the horizontal surface on the block. The force is positive if to the right, negative if to the left. Answer: F = N
The weight of the block in the drawing is 85.0 N. The coefficient of static friction between the block and the vertical wall is 0.590. (a) What minimum magnitude of the force F→ is required to prevent the block from sliding down the wall? (Hint: The static frictional force exerted by the block is directed upward, parallel to the wall.) (b) What minimum force is required to start the block moving up the wall? (Hint: The static frictional force is now directed down the wall.) (a) Number Units (b) Number Units
A block of mass 0.24 kg, is placed on a flat surface inclined at angle θ relative to horizontal (as in the figure) and is initially at rest. The coefficient of static friction, μs, is 0.45 and the coefficient of kinetic friction, μk is 0.24. The angle θ is increased slowly. What is the largest value of θ (in degrees) such that you should expect the block to remain at rest and not begin to move down the incline? θmax = degrees If θ = 52 degrees and the block starts to accelerate down the incline, what is the magnitude of the acceleration? |a→| = m/s2
A 150-lb block is placed on a 29∘ incline and released from rest. The coefficient of static friction between the block and the incline μs is 0.31. (a) Determine the maximum and minimum values of the initial tension T in the spring for which the block will not slip when released. (b) Calculate the friction force F (positive if up the slope, negative if down) on the block if T = 77 lb. Assume W = 150 lb, θ = 29∘. Answers: (a) Tmax = lb, Tmin = Ib (b) F = Ib
A 120 lb block rests on a horizontal floor, as shown. The coefficient of static friction between the block and the floor is 0.20. sketch the free body diagram for the block impending motion with P pulling on the block as the diagram shown calculate the pulling force P that will cause block impending motion to the left. [lb].
In the given system, the coefficient of friction between the object and the inclined plane is 0.2. Calculate the values that the inclined plane angle can take if the system's balance is maintained. (30P)?
The wheel of radius 0.7 ft rolls without slipping on the horizontal surface with a constant angular velocity ω. At the instant when θ = 40∘, point A on the wheel has a speed of 2.3 ft/sec. Calculate the angular velocity of the wheel and the speeds of the center O and point B on the wheel. (ω = 3.89 rad/sec, vO = 2.72 ft/sec, vB = 4.93 ft/sec)
Problem 1: The angular velocity of the disk is defined by ω = (5t2 + 2) rad/s, where t is in seconds. Determine the magnitudes of the velocity and acceleration of point A on the disk when t = 0.5 s.
The angular position of a point on the rim of a rotating wheel is given by θ = 4.0t - 3.0t2 + t3, where θ is in radians and t is in seconds. What are the angular velocities at (a) t = 2.0 s and (b) t = 4.0 s? (c) What is the average angular acceleration for the time interval that begins at t = 2.0 s and ends at t = 4.0 s? What are the instantaneous angular accelerations at (d) the beginning and (e) the end of this time interval?
Point A of the circular disk is at the angular position θ = 0 at time t = 0. The disk has angular velocity ω0 = 0.30 rad/s at t = 0 and subsequently experiences a constant angular acceleration a = 2.1 rad/s2. Determine the velocity and acceleration of point A in terms of fixed i and j unit vectors at time t = 1.3 s. Answers: vA = aA =
A truck accelerates uniformly from rest and after 5 seconds the 50−cm radius wheels on the truck have an angular velocity ωf = 47 rad/s. (a) What is the magnitude of the angular acceleration, α, of the wheels? α = rad/s2 (± 0.1 rad/s2) (b) What is the magnitude of the final velocity, vf, of the truck? vf = m/s (± 0.1 m/s) (c) Through what total angle does each wheel turn in this time? θ = rad( ± 1 rad)
The two ends of a length of chain are attached so that the chain makes a circle. If the chain is then spun very quickly, it can roll along the ground like a bicycle tire without crumpling. Consider the rolling chain shown in the figure. Assume the chain has uniform linear mass density μ and its center of mass moves to the right at a speed v0. (a) Determine the tension in the chain in terms of μ and v0. Assume the weight of an individual link is negligible compared to the tension. T = (b) If the loop rolls over a small bump, the resulting deformation of the chain causes two transverse pulses to propagate along the chain, one moving clockwise and one moving counterclockwise. What is the speed of the pulses traveling along the chain? (Use any variable or symbol stated above as necessary.) v = (c) Through what angle (in rad) does each pulse travel during the time interval over which the loop makes one revolution? (Assume the angle is measured clockwise from the ground. ) clockwise-traveling pulse rad counterclockwise-traveling pulse rad
radius of A = 0.075 m, radius of B = 0.225 m, radius of D = 0.125 m αA = 4.5 rad/s2 (constant) Initially at rest. (a) Vc after 3 secs? (b) Δxc after 3 secs?
The disk has an angular acceleration d = 8 rad/s2 and angular velocity z = 3 rad/s at the instant shown in Figure 5. ω = 3 rad/s α = 8 rad/s2 Figure 5 If it does not slip at A, determine the acceleration of point B.
A cord is wrapped around the rim of a solid cylinder of radius 0.38 m, and a constant force of 40 N is exerted on the cord, as shown in the following figure. The cylinder is mounted on frictionless bearings, and its moment of inertia is 5.1 kg⋅m2. (Enter the magnitudes. ) (a) Use the work energy theorem to calculate the angular speed of the cylinder (in rad/s) after 6.2 m of cord have been removed. rad/s (b) If the 40 N force is replaced by a 40 N weight, what is the angular speed of the cylinder (in rad/s) after 6.2 m of cord have unwound? rad/s
The 10−kg disk is rotating with w = 4 rad/s. If the 100−N force is applied, as shown, what will be the direction of the acceleration of the center of the disk? To the right To the right and downward Downward Perpendicular to the line joining point O and the the force
The 10−kg disk of Fig of Q1, is rotating with w = 4 rad/s. If the 100−N force is applied, as shown, what will be the direction of the reaction force on the pin? Leftward Rightward Downward Up and leftward Down and rightward
Point A of the circular disk is at the angular position θ = 0 at time t = 0. The disk has angular velocity ω0 = 0.21 rad/s at t = 0 and subsequently experiences a constant angular acceleration α = 2.3 rad/s2. Determine the velocity and acceleration of point A in terms of fixed i and j unit vectors at time t = 1.1 s. Answers: vA = ( i + j) m/s aA = ( i + j) m/s2
Angular acceleration of a cylinder - four forces A uniform 4.4 kg cylinder (moment of inertia I = 1 2 mR2 ) can rotate about an axis through its center at O. The forces applied are : F1 = 6.1 N, F2 = 5.4 N, F3 = 2.8 N, and F4 = 5.9 N. Also, R1 = 13 cm and R3 = 6.2 cm. 5 Find the magnitude (in rad/s2) and direction (+ denotes counterclockwise and - denotes clockwise) of the angular acceleration of the cylinder.
A puck of mass m = 1.60 kg slides in a circle of radius r = 15.0 cm on a frictionless table while attached to a hanging cylinder of mass M = 3.80 kg by a cord through a hole in the table. What speed keeps the cylinder at rest? Number Units
A merry-go-round rotates from rest with an angular acceleration of 1.59 rad/s2. How long does it take to rotate through (a) the first 1.13 rev and (b) the next 1.13 rev? (a) Number Units (b) Number Units
A hollow ball m = 20.0 g and radius r = 1.00 cm is placed on a ramp at height H. Assuming that it rolls without slipping and referring to the image below. If R = 10.0 cm and H = 59.0 cm, does the ball stay in contact with the top of the loop? Please show your work
A chain is attached to a boulder and pulled due north by a monster truck with a force of magnitude 2036 newtons. (A newton is about a quarter of a pound.) A second monster truck pulls on a chain pointed 20∘ west of north with a force of magnitude 3060 newtons. Find the resultant force on the boulder and its direction. (Use decimal notation. Give your answer for the force to one decimal place. Give your answer for the direction of the boulder to the nearest degree. Include the degree symbol in your answer where needed.) resultant force: newtons resultant direction: west of north
A belt connects a pulley of radius 8 centimeters to a pulley of radius 6 centimeters. Each point on the belt is traveling at 24 centimeters per second. Find the angular velocity of each pulley (see figure below). smaller pulley ω = rad/sec larger pulley ω = rad/sec
Figure below shows a ring of outer radius R = 13.0 cm and inner radius rinner = 0.200R. It has uniform surface charge density σ = 6.20 pC/m2. With V = 0 at infinity, find the electric potential at point P on the central axis of the ring, at distance z = 2.00 R from the center of the ring. (a) Start with the formula for the potential: V = k∫dQ |r→ − r→′| What is your dQ? What is your infinitesimal area element? What are your vectors r and r′ ? What is the distance to point P ? What is dV ? Potential due to a small ring of charge on the disk? (b) Write out the integral that you need to compute to get V. What are the bounds? (c) Once you get an expression for V, solve numerically. (d) Check to see if the units of your expression makes sense for V.
Amy is in a tuck and skiing straight down a 30∘ slope. Air resistance pushes backward on her with a force of 10 N. The coefficient of dynamic friction between her skis and the snow is 0.08, and the coefficient of static friction is 0.10 . Amy's mass is 50 kg. What is the component of her weight that is pushing Amy along (parallel to) the slope? What is the magnitude of the normal reaction force exerted by the snow on her skis? What is the magnitude of the frictional force between the skis and the snow? What is her acceleration along the slope? (assume that going down is positive)
The 20-cm diameter disk in (Figure 1) can rotate on an axle through its center. Express your answer in newton-meters to two significant figures. Figure 1 of 1 Submit Previous Answers Request Answer
A coil with 160 turns, a radius of 5.0 cm, and a resistance of 12 Ω surrounds a solenoid with 230 turns/cm and a radius of 4.5 cm (see Fig). The current in the solenoid changes at a constant rate from 0 to 2.0 A in 0.10 s. Calculate the magnitude and direction of the induced current through the resistor in the outer coil.