A small sphere of charge q = +65 µC and mass m = 5.1 g is attached to a light string and placed in a uniform electric field E that makes an angle θ = 31° with the horizontal. The opposite end of the string is attached to a wall and the sphere is in static equilibrium when the string is horizontal as in the figure shown below. (a) Construct a free body diagram for the sphere. (Submit a file with a maximum size of 1 MB.) Choose File No file chosen This answer has not been graded yet. (b) Find the magnitude of the electric field. N/C (c) Find the tension in the string. (Enter the magnitude of the tension in the string.) N
Determine the speed v which the 650-kg four-man bobsled must have in order to negotiate the turn without reliance on friction. Also find the net normal force N exerted on the bobsled by the track. Answers: v = m/s N = kN
Q2 (Ch7/8) (Solve this with the concept of energy and force) Object of mass M = 15.0 kg moving on horizontal surface. Object velocity at point A is VA = 8.50 m/s. There is μ = 0.350 kinetic friction on horizontal plane. AB = 5.50 m and BC = d = unknown. The acceleration due to gravity is g. a) Consider AB motion and find an algebraic equation for the velocity of the object when it reaches point B and then find the numerical value? (4 points) b) Object touches the spring with spring constant k = 195 N/m at point B. Then the object compresses the spring from B to C(BC = d = unknown) and finally object comes to rest at C. By considering BC motion build a quadratic equation for distance d. (3 points) c) By applying general solution find numerical value for spring compress distance d. (3 points)
A worker develops a tension T in the cable as he attempts to move the 50−kg cart up the 21∘ incline. Determine the resulting acceleration a of the cart if (a) T = 129 N and (b) T = 206 N. Neglect all friction, except that at the worker's feet. The acceleration a is positive if up the slope, negative if down the slope. Answers: (a) T = 129 N, a = m/s2 (b) T = 206 N, a = m/s2
a 0.075 kg projectile strikes and becomes embedded in 0.6 kg block wich is initially at rest. Determine the final velocity of both masses. Select one: a. 31.58 m/s b. 54.55 m/s C. 26.09 m/s d. 22.22 m/s
The figure shows an 8.2 kg stone at rest on a spring. The spring is compressed 11 cm by the stone. (a) What is the spring constant? (b) The stone is pushed down an additional 31 cm and released. What is the elastic potential energy of the compressed spring just before that release? (c) What is the change in the gravitational potential energy of the stone-Earth system when the stone moves from the release point to its maximum height? (d) What is that maximum height, measured from the release point? (a) Number Units (b) Number Units (c) Number Units (d) Number Units
The figure shows a thin rod, of length L = 2.30 m and negligible mass, that can pivot about one end to rotate in a vertical circle. A heavy ball of mass m = 15.0 kg is attached to the other end. The rod is pulled aside to angle θ0 = 14.0∘ and released with initial velocity v→0 = 0. As the ball descends to its lowest point, (a) how much work does the gravitational force do on it and (b) what is the change in the gravitational potential energy of the ball-Earth system? (c) If the gravitational potential energy is taken to be zero at the lowest point, what is its value just as the ball is released? (a) Number Units (b) Number Units c) Number Units
You drop a 2.40 kg book to a friend who stands on the ground at distance D = 13.0 m below. If your friend's outstretched hands are at distance d = 1.70 m above the ground (see the figure), (a) how much work Wg does the gravitational force do on the book as it drops to her hands? (b) What is the change ΔU in the gravitational potential energy of the book-Earth system during the drop? If the gravitational potential energy U of that system is taken to be zero at ground level, what is U (c) when the book is released and (d) when it reaches her hands? Now take U to be 100 J at ground level and again find (e) Wg, (f) ΔU, (g)U at the release point, and (h) U at her hands.
Tarzan (73.2 kg) is standing on a tree branch above the ground. He grabs the end of a vine that is 7.5 m long, He then jumps off his tree branch and swings down. While he swings, air resistance is acting. If he falls short of his original position on the other side of the swing by 1.21 m, how much work did air resistance do on Tarzan?
The mass of the blue (lower) puck in the figure below is 18.6 percent greater than the mass of the green (upper) one. Before colliding, the pucks approach each other with equal and opposite momenta, and the green puck has an initial speed of 10.7 m/s. The angle θ = 29.7∘. Calculate the speed of the blue puck after the collision if half the kinetic energy is lost during the collision. What is the speed of the green puck after the collision. Submit Answer Tries 0/10
Block 1 , mass m1, is at the top of a frictionless hill of height H moving with a velocity of magnitude v1. At the bottom of the hill is block 2, mass m2, which is attached to a spring with spring constant k. If block 1 hits and sticks to block 2, find the maximum amount the spring is compressed. Assume the collision takes place over a very small time so the spring does not compress during the collision.
A 4.30 kg block is released from point A in the figure below. The track is frictionless except for the portion between points B and C, which has a length of 6.00 m. The block travels down the track, hits a spring (with a spring constant of 2210 N/m ), and compresses the spring 19 cm from its equilibrium position before coming to rest momentarily. a. What is the potential energy of the system at point A? (2) b. What is the potential energy stored in the spring when it is compressed by 19 cm? (2) c. How much non-conservative work was done by the system? (2) d. Determine the coefficient of kinetic friction, μk, between the block and the rough surface. (3) e. What happened to the lost mechanical energy? (1) (B) (c)
A 1-kilogram mass is attached to a spring whose constant is 18 N/m, and the entire system is then submerged in a liquid that imparts a damping force numerically equal to 11 times the instantaneous velocity. Starting at t = 0, an external force equal to f(t) = 2sin(3t) is applied to the system. Determine the equations of motion if the mass is initially released from a point 1 meter below the equilibrium position with an upward velocity of 11 m/s.
Q1 (Ch7/8) (Solve this with concept of energy and force. ) An object of mass m = 865 g moves on horizontal plane with velocity (v = 12.0 m/s) of the object at point A. Horizontal surface (AB) has μ1 = 0.550 of kinetic friction coefficient and inclined plane (BC) has μ2 = 0.350 of kinetic friction coefficient. Object reaches maximum height of h on inclined plane. At point C object velocity is zero. Inclined angle θ = 32∘. The acceleration due to gravity is g. a) Find an algebraic equation for the work done due to friction from A to B (AB = d = 7.0 m) and then find the numerical value? (2 points) b) Find an algebraic equation for the velocity of the object at point B and then find the numerical value (AB = d = 7.0 m)? ( 4 points) c) Find an algebraic equation for height h when the object reaches point C on inclined plane and then find the numerical value? ( 4 points)
(1) For the following free body diagrams and assuming initial momentum is zero (i. e. initial velocity is zero and the person is not moving), if these forces were to be applied over time (thus generating linear and/or angular impulse), what effect would there be at the total body level (i. e. will the person move forwards/backwards/neither, upwards/downwards/neither, and will they rotate forwards/backwards/neither)? Fully explain your answer for each diagram. (1.5 pts each) (a) (b) (c)
(2) Use the following graph to answer the questions for this problem. Make sure to show all of your work to receive full credit. The total time is 0.2 seconds. (a) The subject has a body weight of 500 N. What is the horizontal impulse generated, total vertical impulse generated, and net vertical impulse generated? (3 pts) (b) If mass is 50 kg, what is the change in horizontal and the change in vertical velocity? (1 pt) (c) List the 3 different ways the subject could increase their change in velocities. (1.5 pts)
The drawing shows a parallel plate capacitor that is moving with a speed of 42 m/s through a 4.8−T magnetic field. The velocity v is perpendicular to the magnetic field. The electric field within the capacitor has a value of 230 N/C, and each plate has an area of 7.8×10−4 m2. What is the magnitude of the magnetic force exerted on the positive plate of the capacitor? Number Units
The spring in the figure below is stretched from its equilibrium position at x = 0 to a positive coordinate x0. The force on the spring is F0 and it stores elastic potential energy PEs0. If the spring displacement is quadrupled to 4x0, determine the ratio of the new force to the original force, Fn F0, and the ratio of the new to the original elastic potential energy, PEsn PEs0. HINT (a) the ratio of the new force to the original force, Fn F0 (b) the ratio of the new to the original elastic potential energy, PEsn PEs0
A person of mass 70.0 kg stands on the floor of a lift which is accelerating downwards at 2.00 ms−2. The person exerts a force on the floor and the floor exerts an equal and opposite force R on the person. Calculate R.
A ball of mass m = 17.5 kg is located at a position r→ = −3.6x^ − 2.8y^ m relative to the origin. The velocity of the ball is v→ = −9.62x^ − 7.58y^ m/s. What is the magnitude of the angular momentum of the ball about the origin, in units of J⋅s?
A motorcycle with a mass of 250 kg makes a turn of radius 60 m on a banked road. The road is banked at an angle of 30. Calculate the speed at which no friction is required for the turn.
The rider in Fig A1 a takes off the 1 m high track at 30∘ to the horizontal as shown. If the total time taken from the point of take-off at A to the point of touch down at B is 1.5 seconds, the maximum height reached h is equal to: A) 8.23 m B) 2.38 m C) 3.28 m D) None of these
At point A in the figure shown below, a spring with spring constant 1000 N/m is compressed 50.0 cm by a 2.00 kg block. When released the block travels over the frictionless track until it is launched into the air at point B, and it lands at point C. The inclined part of the track makes an angle of θ = 55.0∘ with the horizontal and point B is a height h = 4.50 m above the ground. a. With what speed does the block leave the ramp at point B? (10 points) b. What is the maximum height reached by the block after it leaves the ramp? Be careful! The speed is not zero at the highest point. (10 points) c. With what speed does the block land at point C? (10 points)
For the situation shown in Figure calculate FL, the magnitude of the force exerted by the left hand. The hands are 0.906 m apart, and the CG of the pole is 0.560 m from the left hand. The mass of the pole is 4.17 kg. Input your answer in N using 3 significant figures. g = 9.80 m/s2 Center of gravity (CG) is the point where the total weight of the body is assumed to be concentrated.
A 2 kg object which is launched at a velocity of 8 m/s from point K, passes point L, which is at height of 3 m, at a velocity vL and compresses the spring. a) What is the velocity of the object at point L? b) If the spring constant is 200 N/m, what is the maximum amount of compression of the spring? (Neglect any friction effects)
A block of mass m = 0.24 kg is accelerated (from rest) by a constant applied force F. The block then slides through a region of friction of length d = 0.15 m and where μk = 0.1. Finally, the block climbs the curved ramp and momentarily stops at height h = 0.11 m above the original level. How much work did the force F do on the block? Give your answer in J but enter only the numerical part in the box.
A 65.0 kg person stands a distance d = 2.5 m from one end of a uniform plank of mass 25.0 kg and length 8.0 m suspended by ropes at each end. Determine the tension in the rope nearest to the person. 320 N 440 N 560 N 200 N
A cart of mass 5 kg is held on the ramp at a height of 1.8 m. Another cart of mass 5 kg is on a frictionless surface sitting next to a spring with spring constant 110 N/m. At some instant, the first cart starts sliding down and hits the second cart. If the collision between the carts is elastic in nature, find the compression in the spring caused by the second cart. [limit your answers within one decimal places].
A rope is used to pull a 5.33 kg block at constant speed 2.05 m along a horizontal floor. The force on the block from the rope is 4.17 N and directed 12.9∘ above the horizontal. What are (a) the work done by the rope's force, (b) the increase in thermal energy of the block-floor system, and (c) the coefficient of kinetic friction between the block and floor? (a) Number Units (b) Number Units (c) Number Units
A ski jumper starts with a horizontal take-off velocity of 27 m/s and lands on a straight landing hill inclined at 30∘. Determine the length d of the jump. (You must provide an answer before moving to the next part.) The length of the jump d, is m.
A uniform plank of length 2.00 m and mass 27.0 kg is supported by three ropes, as indicated by the blue vectors in the figure below. Find the tension in each rope when a 675−N person is d = 0.500 m from the left end. magnitude of T→1 N magnitude of T→2 N magnitude of T→3 N
In reaching her destination, a backpacker walks with an average velocity of 1.26 m/s, due west. This average velocity results, because she hikes for 5.81 km with an average velocity of 3.46 m/s due west, turns around, and hikes with an average velocity of 0.483 m/s due east. How far east did she walk (in kilometers)?
The cart of mass M is initially resting on a track, and an object of mass m is hanging by a massless string. When the hanging mass m is falling by the action of the gravity, the cart M is pulled and moves with an acceleration a as shown in the figure below. Choose all that are correct from the following. As the mass of the cart M increases to infinity so does the tension in the string If the cart moves with a greater acceleration, it means that the tension in the string is greater The absolute maximum acceleration that the cart can have does not depend on M or m As the mass of the object m increases to infinity so does the acceleration of the cart The tension in the string while the cart is moving does not depend on cart's mass M because it's on a horizontal track and is not supported by the string
A 3.1 kg mass attached to the end of a string swings in a vertical circle having a radius of 4.3 m. At an instant when the string makes an angle of 2 degrees above the horizontal as shown in the figure, the tension in the string is 2.5 N. What is the net force on the ball at this instant? < > N What is the speed of the ball at this instant? m/s
A mass spectrometer is a device that can sort ions based on their mass to charge ratio. Given the incoming particle is a proton with a horizontal speed of 1.5×108 m/s, and the magnetic field strength is 0.7 T, what would the radius of the proton's path be, in metres?
In the ballistic pendulum shown below, the block has a mass of 2.9 kg, the bullet has a mass of 0.0057 kg, and the string has a length of 1.82 m. A bullet is shot directly at the block, lodging into the block, and causing the pendulum to swing forward 20∘. What was the initial speed of the bullet, in m/s?
A 50 kg tight rope walker takes a break when walking across a tight rope. The angle θ in the picture is 5∘. What is the tension in the rope, in newtons?
Someone standing on a hillside throws a ball up a hill with an initial speed of 11.0 m/s. The hill has a slope of θ = 17∘ with respect to the horizontal, and they throw the ball at an angle of ϕ = 23∘ above the slope of the hill. How far away from the person will the ball land, L, in m? Answers within 3% of the true answer will be considered correct. Attach your work for full marks.
A spaceship has a rotating compartment which gives its passengers artificial gravity. Suppose this compartment is a cylinder with a radius of 4.5 m. In order for the artificial gravity to be the same strength as what is experienced on Earth's surface, what would the period of rotation of this compartment need to be, in seconds?
Two bags of equal mass m are tied together with unstretchable, massless rope. One bag hangs vertically, while the other is free to slide on a frictionless slope of angle β. Treat the tip of the slope (which the rope is passing over) like a massless, frictionless pulley. Let g denote the magnitude of free-fall acceleration. Let down define the positive direction for the hanging bag. What is ay, the vertical component of the acceleration of the hanging bag? ay = Enter your expression in terms of given quantities and integers.
A block of known mass m is attached to one end of a massless spring with a spring constant ks and equilibrium length xeq. The other end of the spring is then attached to a device which will cause the whole system to rotate. The block follows a circular path of radius xeq + A during its orbit. a. Give an expression for the period of rotation in terms of A, xeq, ks, and m. b. Calculate the kinetic and potential energy of the system. Show that the system will never have less potential energy than kinetic energy for any values of the above parameters (A, xeq, ks, and m).
A uniform 50−kg scaffold of length 7.0 m is supported by two light cables, as shown below. A 62−kg painter stands 1.0 m from the left end of the scaffold, and his paint bucket is 1.5 m from the right end. If the tension in the left cable is twice that in the right cable, find the tensions in the cables and the mass of the bucket. As a hint, you have three unknowns, T1 (left cable), T2 (right cable), and the bucket's mass/weight. One way to do this is to set the axis at the bucket, so that the weight of the bucket is not part of the net torque equation (because the lever arm, the distance from the axis, is zero). Then use the fact that the net torque needs to be equal to zero for everything to be balanced. You should be able to solve for T1 and T2. Then, do a new problem where you sum all of the "y" forces, and equate them all to zero (that should allow you to calculate the mass or weight of the bucket). mbucket = kg Tleft = N Tright = N
A 2-kg object, moving at 1 m/s, collides with a 1-kg object that is initially at rest. After the collision, the two objects are found to move away from each other at 1 m/s. Assume they form an isolated system. (a) What are their actual final velocities in the Earth reference frame? (b) What is the velocity of the center of mass of this system? Does it change as a result of the collision?
A 2.30 kg thin, spherical shell of radius 0.160 m is released from rest at point A in the figure below, its center of gravity a distance of 1.80 m above the ground. The spherical shell rolls without slipping to the bottom of an incline and back up to point B where it is launched vertically into the air. The spherical shell then rises to its maximum height hmax at point C. HINT (a) At point B, find the spherical shell's translational speed vB (in m/s ). m/s (b) At point B, find the spherical shell's rotational speed ωB (in rad/s). rad/s (c) At point C, find the spherical shell's rotational speed ωC (in rad/s). rad/s (d) At point C, find the maximum height hmax of the spherical shell's center of gravity (in m ). m
A 4.540 kg block of wood rests on a steel desk. The coefficient of static friction between the block and the desk is μs = 0.505 and the coefficient of kinetic friction is μk = 0.205. At time t = 0, a force F = 13.8 N is applied horizontally to the block. State the force f(t) of friction applied to the block by the table at times t = 0 and t > 0. f(0) = N f(t > 0) = N Consider the same situation, but this time the external force F is 27.9 N. Again, state the force of friction acting on the block at times t = 0 and t > 0. f(0) = N f(t > 0) = N