On a farm, a two-wheel rope pulley is used to lift buckets of water from a well. Ignoring friction, what is the maximum weight of water that can be lifted if a force equivalent to 8 kg is used to pull on the rope? A B 4 kg C D E 10 kg 12 kg 16 kg
A block of mass of 4 kg starts at rest. It is then is pushed by a force of F = 100 N at an angle of θ = 10∘ to the horizontal. The coefficient of kinetic friction between the block and the ground is μk = 0.4. What is the power of force F at time t = 3 s? P = W
A trebuchet uses a falling counterweight to launch a projectile. It can be thought of as a machine that converts the gravitational potential energy of the counterweight into kinetic and gravitational potential energy of the projectile. The counterweight has a mass of 170 kg and drops 5 m. The projectile has a mass of 4 kg, and starts on the ground. When it leaves the sling, it has a height of 6 m speed of 22 ms. If the average power used in lifting the counterweight is 34 W, find the time it takes to lift it from the ground to its full height. tlifting = s If the projectile goes from rest to its maximum speed in 1 s. find the average power used in launching the projectile in this time period. Pprojectile = W Find the efficiency of the trebuchet when it launches. Efficiency = %
A block of mass m = 5.78 kg is attached to a spring that is resting on a horizontal, frictionless table. The block is pushed into the spring, compressing it by 5.00 m, and is then released from rest. The spring begins to push the block back toward the equilibrium position at x = 0 m. The graph shows the component of the force (in newtons) exerted by the spring on the block versus the position of the block (in meters) relative to equilibrium. Use the graph to answer the questions. How much work W is done by the spring in pushing the block from its initial position at x = −5.00 m to x = 2.86 m? W = J What is the speed v of the block when it reaches x = 2.86 m? v = m/s What is the maximum speed vmax of the block? vmax = m/s
A uniform ladder of mass mL = 12.3 kg and length L = 3.80 m is leaned against a frictionless wall at an angle of θ = 23.4∘, as shown in Figure 2. A human, of mass mh = 83.8 kg, stands a distance d = 1.10 m up the ladder as shown. What is the minimum coefficient of static friction between the ladder and the ground that will prevent the ladder from slipping?
A block of mass m = 2.40 kg initially slides along a frictionless horizontal surface with velocity v0 = 4.00 m/s. At position x = 0, it hits a spring with spring constant k = 39.00 N/m and the surface becomes rough, with a coefficient of kinetic friction equal to μ = 0.350. Assume the positive direction is to the right. How far Δx has the spring compressed by the time the block first momentarily comes to rest? Δx = m
A 1.40−kg ball, moving to the right at a velocity of +3.84 m/s on a frictionless table, collides head-on with a stationary 6.20−kg ball. Find the final velocities of (a) the 1.40−kg ball and of (b) the 6.20−kg ball if the collision is elastic. (c) Find the magnitude and direction of the final velocity of the two balls if the collision is completely inelastic. (a) Number Units (b) Number Units (c) Number Units
A solid sphere with a mass of 13.2 kg and a radius of 0.29 m spins about its center with an initial angular velocity of 51.2 rad/s. If it slows at a rate of −2.6 rad/s2. what is its rotational kinetic energy after 6.09 seconds? The moment of inertia of a solid sphere is I = 0.4 MR2
In 0.628 s, a 14.8-kg block is pulled through a distance of 4.77 m on a frictionless horizontal surface, starting from rest. The block has a constant acceleration and is pulled by means of a horizontal spring that is attached to the block. The spring constant of the spring is 428 N/m. By how much does the spring stretch? Number Units
Block A has a weight of 10 lb and block B has a weight of 20 lb. Determine the speed of block A after it moves down a distance of 2 ft, starting from rest. The coefficient of kinetic friction between block B and the plane is μk = 0.2. Use the principle of work and energy to solve the problem. Neglect the mass of the cord and pulley. (45 pts.)
Two forces, F1 and F2, act on the m = 6.95 kg block, which rests without friction on the floor, shown in the figure below. The magnitudes of the forces are F1 = 59.5 N and F2 = 32.5 N. θ = 74.9∘. What is the magnitude of the horizontal acceleration of the block?
Figure below shows a small sphere with mass 1.50 g hangs by a thread between two very large parallel vertical plates 5.00 cm apart. The plates are insulating and have uniform surface charge densities +σ and −σ. The charge on the sphere is q = 8.90×10−6 C. If the thread to remain at an angle of 30.0∘ with the vertical, calculate: (a) the potential difference between the plates. [8] (b) the uniform surface charge density. [2]
A pendulum bob of mass m = 1.3 kg hangs from a ceiling as shown below. The length of the pendulum L = 4.1 m. Initially, it is held at a position h = 0.01 m high from the lowest position. Once released, the pendulum will start oscillating. What is the oscillation period (in s)?
In reaching her destination, a backpacker walks with an average velocity of 1.05 m/s, due west. This average velocity results, because she hikes for 6.47 km with an average velocity of 2.98 m/s due west, turns around, and hikes with an average velocity of 0.485 m/s due east. How far east did she walk (in kilometers)?
Assuming that the Earth has a uniform density ρ = 5540.0 kg/m3, what is the value of the gravitational acceleration gd at a distance d = 300.0 km from the Earth's center? gd = m/s2
The diagram shows a box sliding to the right along a wall with an initial speed, u, at Point (a). What is the speed, v, of the box at Point (b)? Assume the top of the wall is frictionless and ignore air resistance. Use g = 9.81 m/s2. Give your answer in units of metres per second to two significant figures.
A spring hangs from the ceiling with an unstretched length of x0 = 0.95 m. A m1 = 8.7 kg block is hung from the spring, causing the spring to stretch to a length xs = 1.14 m. Find the length Δx of the spring when a m2 = 3.7 kg block is hung from the spring. For both cases, all vibrations of the spring are allowed to settle down before any measurements are made.
Two crates, of mass 65 kg and 125 kg, are in contact and at rest on a horizontal surface (Fig. 4-57). A 650-N force is exerted on the 65−kg crate. If the coefficient of kinetic friction is 0.18 , calculate (a) the acceleration of the system, and (b) the force that each crate exerts on the other. (c) Repeat with the crates reversed. FIGURE 4-57 Problem 49.
Calculate the magnitude of the normal force on a 12.7 kg block in the following circumstances. (Enter your answers in N.) (a) The block is resting on a level surface. N (b) The block is resting on a surface tilted up at a 35.8∘ angle with respect to the horizontal. N (c) The block is resting on the floor of an elevator that is accelerating upward at 5.03 m/s2. N (d) The block is on a level surface and a force of 155 N is exerted on it at an angle of 35.8∘ below the horizontal. N
The diagram shows a box sliding to the right along a wall with an initial speed, u, at Point (a). What is the speed, v, of the box at Point (b)? Assume the top of the wall is frictionless and ignore air resistance. Use g = 9.81 m/s2. Give your answer in units of metres per second to two significant figures. (a) (a) (b)
A ball A with a mass of 3 kg is thrown with a velocity of 4 m/s horizontally at a block B with mass 25 kg that is suspended from ropes. If the coefficient of restitution between the ball and block is e = 0.8, determine the height h that the block reaches before momentarily stopping. HINT: Determine the state of the block immediately after the collision and then use that information to determine the height h.
On a levelled and frictionless table lay two identical flat and circular disks of mass M = 4 kg and radius R = 0.6 m. The disks touching each other at one point and glued to each at this point. A point mass m = 1.2 kg moves with velocity v = 5 m/s to the positive x axis. The point mass collides with the upper disk and recoils back with half of its initial speed, as seen in the figure. After: As a result of the collision the two disks system begins to move. What is the magnitude of the angular velocity (in radians per second) of the rotation of the two disks system?
The figure shows a cord attached to a cart with mass = 1.2 kg that can slide along a horizontal rail aligned along an x axis with μk = 0.10. The left end of the cord is pulled over a pulley, of negligible mass and friction and at cord height h = 1.4 m, so the cart slides from x1 = 4.0 m to x2 = 1.0 m. During the move, the tension in the cord is a constant 27 N. What is the change in the kinetic energy of the cart during the move?
The two blocks A and B have a mass mA and mB′, respectively, where mB > mA. If the pulley can be treated as a disk of mass M and radius r, determine the acceleration of block A. Neglect the mass of the cord and any slipping on the pulley. Hint: treat the pulley and the two blocks as a system. a. (10 points) Establish a coordinate system, specify the direction and sense of the accelerations aA and aB and the angular acceleration of the disk α. Draw the free-body-diagram and the kinetic diagram. b. (10 points) List the external forces acting on the system (the pulley and the two blocks) and calculate their moments about point O. c. (10 points) Calculate the mass moment of inertia of the pulley about point O. d. (10 points) Use kinematics to find the relation between aA, aB and α. e. (20 points) Establish the equation of motion and solve for aA. Hint: only consider the equation about the sum of moments about point O.
The block has a mass of 0.5 kg and moves within the smooth vertical slot. If the block starts from rest when the attached spring is in the unstretched position at A, determine the constant vertical force F which must be applied to the cord so that the block attains a speed vB = 5 m/s when it reaches B; sB = 0.25 m. Neglect the mass of the cord and pulley. a. (5 points) Establish a coordinate system, specify the direction and sense of the forces, displacement, velocity, etc. b. (10 points) Select a position between A and B. Draw the free-body-diagram. c. (10 points) List the forces doing work on the block when it moves from A to B. d. (5 points) Calculate the kinetic energy of the black when it arrives at B. e. (20 points) Use the principle of work and energy to solve for the constant vertical force F. Hint: when the block moves from A to B, how far does F travel in its direction? How much work does it do?
A woman at an airport is towing her 23.5 kg suitcase at constant speed by pulling on a strap at an angle of θ above the horizontal. She pulls on the strap with a 25.0 N force, and the friction force on the suitcase is 20.0 N. (a) Draw a free-body diagram of the suitcase. (Do this on paper. Your instructor may ask you to turn in this work.) (b) What angle does the strap make with the horizontal? (c) What normal force does the ground exert on the suitcase? N
The string in Fig. 8-27 is L = 140 cm long, has a ball attached to one end, and is fixed at its other end. The distance d from the fixed end to a fixed peg at point P is 80.0 cm. When the initially stationary ball is released with the string horizontal as shown, it will swing along the dashed arc. What is its speed when it reaches (a) its lowest point and (b) its highest point after the string catches on the peg? Figure 8-27 Problems 25 and 80 .
Objects with masses of 270 kg and a 570 kg are separated by 0.350 m. (a) Find the net gravitational force exerted by these objects on a 42.0 kg object placed midway between them. magnitude N direction (b) At what position (other than infinitely remote ones) can the 42.0 kg object be placed so as to experience a net force of zero? m from the 570 kg mass
The string in Figure 6-44 is wound around the nail as shown. The end of the string is attached to a mass, m, that is released from the horizontal position, starting from rest. Derive an expression for (a) the tension in the string when it makes an angle of 23∘ with the vertical (b) the total work done to bring the string to the position in part (a) (c) the work done by the tension
suitcase is 20.0 N. (a) Draw a free-body diagram of the suitcase. Choose File No file chosen This answer has not been graded yet. (b) What angle does the strap make with the horizontal (in degrees)? (c) What is the magnitude of the normal force that the ground exerts on the suitcase (in N)? N rolling friction is independent of the angle of the strap. (e) What is the maximum acceleration of the suitcase if the woman can exert a maximum force of 38.7 N ? (Enter the magnitude in m/s2.) m/s2
A projectile is launched from the ground with velocity |v→| = 5 m/s, at an angle θ = 63∘ from the horizontal direction. The projectile would have landed on the ground at the horizontal distance d1 away from the launch point, but instead it hit the top of a platform of height h in the way. The platform was hit at a horizontal distance d2 away from the launch point. If the projectile took t = 0.6 seconds to reach the top of the platform from its launching point, calculate the height of the platform, h. Use g = 9.8 m/s2 and retain 2 decimal places in your answer.
The truck with a ladder plotted in Fig. 5 starts from rest (and accelerates to the left) with an acceleration of 7 m/s2. The ladder of mass m = 10 kg, which is the rigid body of interest in this problem, can be modeled as a uniform slender rod that is hinged at point A and supported at point B. As a consequence, the center of mass G of the ladder is located at the midpoint of the rod. Any friction in this problem is supposed to be small enough to be neglected. a) Determine the minimum linear acceleration amin of the truck such that the ladder loses contact at point B, i. e. the normal force NB at B vanishes, and starts to rotate about point A. Do so by determining the sum of the moments about point A, and verify that for the given acceleration of the truck, the ladder will in fact lose contact at point B. b) Determine the mass moment of inertia I¯ of the ladder associated with its center of mass G. c) Use the result found in Part b) and employ the concept of relative acceleration expressed in terms of a normal-tangential coordinate system to determine the initial angular acceleration vector α of the ladder. Figure 5: A truck with a ladder accelerating from rest to the left and measurements.
Practice only: Instead of using the Electrostatic Analyzer to pick particles with a standard velocity, one may instead use a velocity selector depicted below. It uses both an electric field and a magnetic field together to provide a stream of particles with a particular velocity. The potential difference between the plates is 100 V and the distance between plates is 5 cm. If we want a positive point charge to pass through un-deflected and exit the plates with a velocity of 2 km/s, what strength magnetic field should we use (in T)? ( Draw all the forces on the particle when it's between the plates and use those forces to determine the answer)
The system shown in the following figure is in static equilibrium and the angle θ = 31∘. Given that the mass m1 is 8.10 kg and the coefficient of static friction between mass m1 and the surface on which it rests is 0.31 , what is the maximum mass that m2 can have for which the system will still remain in equilibrium? kg
Two forces are applied to a 12.0 kg mass block on a friction-free surface. Find the acceleration of the block. A block with two forces applied on a friction-free surface. 1.21 m/s2 1.06 m/s2 0.99 m/s2 1.03 m/s2
An m = 2.36−kg ball tied to a string fixed to the ceiling is pulled to one side by a force F at an angle of θ = 28.2∘. Just before the ball is released and allowed to swing back and forth, how large is the force F that is holding the ball in position? What is the tension in the string? Submit Answer
A block of mass m1 = 3.10 kg on a frictionless plane inclined at angle θ = 25.9∘ is connected by a cord over a massless, frictionless pulley to a second block of mass m2 = 2.55 kg hanging vertically (see the figure). (a) What is the acceleration of the hanging block (choose the positive direction down)? (b) What is the tension in the cord? (a) Number Units (b) Number Units
(a) A tennis ball of mass 0.08 kg and speed 20 m/s strikes a wall at a 45∘ angle and rebounds with the same speed at 45∘. (a) What is the impulse (magnitude and direction) given to the ball? (b) If the same ball, with the same initial velocity, hits an identical ball with v = 0 dead on in an elastic collision, what will the final velocity (just after the collision) of each ball be? (assume the collision is instantaneous). (b)
A box slides from rest down a frictionless ramp inclined at 30.0∘ with respect to the horizontal and is stopped at the bottom of the ramp by a spring with a spring constant of k = 4.00×104 N/m. If the box has a mass of 12.0 kg and slides 3.00 m from the point of release to the point where it comes to rest against the spring, determine the compression (in m ) of the spring when the box comes to rest. m
The coefficient of kinetic friction for a 21-kg bobsled on a track is 0.10. Part A What force is required to push it down a 4.0∘ incline and achieve a speed of 64 km/h at the end of 75 m? Express your answer using two significant figures. Fp = N Submit Request Answer
A pendulum of length L = 2.0 m and mass m = 1.0 kg is deflected through an angle ϑ. When the pendulum arrives in the vertical position, it hits a block of M = 3.0 kg resting on a frictionless table. The height of the table is equal to the flight distance of the mass after the collision h = Δx = 1.8 m. Let g = 10 m/s2. (a) Determine the velocity of the block immediately after the collision. (b) Calculate the velocities of the pendulum immediately before and after the elastic collision. (c) Determine the magnitude of the angle ϑ by which the pendulum is deflected before and after the elastic collision. (d) What % of mechanical energy is transferred from the pendulum to the block during the collision? If you do not get a solution for (a), take the following value as a possible solution vM′ = 3.0 ms.
A car is stopped at a traffic light. It then travels along a straight road such that its distance from the light is given by x(t) = bt2 − ct3, where b = 2.40 m/s2 and c = 0.120 m/s3. (a) Calculate the average velocity of the car for the time interval t = 0 to t = 10.0 s. (b) Calculate the instantaneous velocity of the car at t = 0, t = 5.0 s, and t = 10.0 s. (c) How long after starting from rest is the car again at rest? Section 2.2 Instantaneous Velocity 2.7 - CALC
A ball of clay of mass m1 = 10 kg and horizontal speed of V1 = +10 m/s collides head-on (that is they are traveling along the same line, but in opposite direction) with a ball of putty of mass m2 = 10 kg and a horizontal speed of V2 = −9. The two balls stick together. How fast and in which direction ("+" or "-") are they moving after the collision? Your Answer: Answer units
Romeo (78.5 kg) entertains Juliet (51.8 kg) by playing his guitar from the rear of their boat at rest in still water, 2.67 m away from Juliet who is in the front of the boat. After the serenade, Juliet carefully moves to the rear of the boat (away from shore) to plant a kiss on Romeo's cheek. How far does the 73.3 kg boat move toward the shore it is facing?
In the figure, block 1 of mass m1 slides from rest along a frictionless ramp from height h = 3 m and then collides with stationary block 2, which has mass m2 = 3m1. After the collision, block 2 slides into a region where the coefficient of kinetic friction μk is 0.4 and comes to a stop in distance d within that region. What is the value of distance d if the collision is (a) elastic and (b) completely inelastic? (a) Number Unit (b) Number Unit
Q7) A 20 kg box is at rest on the floor and you start to push on it. The graph below shows the force of friction between the box the floor as you apply more and more force. ( 9 MARKS)
The diagram shows a constant force (highlighted in red) that is applied to a box as it is dragged along the ground in a straight line from Point (a) to Point (b). What is the work done by this force between these two points? The distance between points (a) and (b) is shown in the diagram. Give your answer in units of joules to three significant figures.
The 2 kg box has a velocity of 3 m/s at point A while traveling on a smooth ramp towards point B as shown in Figure Q4. The box must arrive at point B with a velocity that does not exceed 8 m/s. a) Determine the maximum height h of the ramp. b) If there is friction between box and ramp, by using h calculated in (a), determine the work done by the friction.
The figure gives the speed v versus time t for a 0.997 kg object of radius 2.83 cm that rolls smoothly down a 25.1∘ ramp. What is the rotational inertia of the object?
Two blocks, M1 and M2, are connected by a massless string that passes over a massless pulley. M1 has a mass of 2.25 kg and is on an incline of angle θ1 = 47.5∘ that has a coefficient of kinetic friction μ1 = 0.205. M2 has a mass of 5.25 kg and is on an incline of angle θ2 = 32.5∘ that has a coefficient of kinetic friction μ2 = 0.105. The figure illustrates the configuration. The two-block system is in motion, with block M2 sliding down the ramp. Find the magnitude a2 of the acceleration of block M2. a2 = m/s2
In the figure a small, nonconducting ball of mass m = 1.2 mg and charge q = 2.2×10−8 C (distributed uniformly through its volume) hangs from an insulating thread that makes an angle θ = 24∘ with a vertical, uniformly charged nonconducting sheet (shown in cross section). Considering the gravitational force on the ball and assuming the sheet extends far vertically and into and out of the page, calculate the surface charge density σ of the sheet. Number Units