A simple pendulum consists of a particle of mass m on an inextensible massless string of length l. The kinetic energy of the system in Cartesian coordinates is given by
Q: The drawing shows a top view of a frictionless horizontal surface, where there are two springs with…
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Q: A 2.00-kg pendulum ball is attached to a light-uniform cable of length 1.20 m that is hanging from…
A: Given Information:- Mass of the pendulum ball is mP=2.00 kg. Length of the cable is l=1.20 m. The…
Q: A ball of mass 0.30 kg is fired with velocity 120 m/s into the barrel of a spring gun of mass 1.8 kg…
A: Apply the conservation of momentum. 0.3*120 = (0.3+1.8)*vv= 17.14 m/s
Q: x Initially h is 268mm, Mass = 11 kg, k= 242 N/m and has unstretched length= 135 mm. Find the…
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Q: A spring with a spring constant of 301 N/m is initially compressed by a distance of 0.065 m from its…
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Q: A mass of 0.83 kg is initially traveling at 6.1 m/s across a horizontal, frictionless surface. It…
A: Since the mass comes to rest, the final kinetic energy of the mass is zero. Apply conservation of…
Q: A spring with a spring constant of 335 N/m is initially compressed by a distance of 0.045 m from its…
A: Given data: k = 335 N/m x= 0.045 m m=0.045 kg Need to determine the speed of the block.
Q: The drawing shows a top view of a frictionless horizontal surface, where there are two springs with…
A: Given data: The spring constant, k=150 N/m. a). The mass, m1=m2=2.0 kg b). The mass,m1=2.0 kg and…
Q: In the figure, a block of mass m = 3.30 kg slides from rest a distance d down a frictionless incline…
A: Mass (m) = 3.3kg θ = 35.0 ˚ ( Angle of inclination) Spring constant (k)= 450N/m Compression (x)…
Q: A spring-mass system has a spring with spring constant k=65.0 N/m and a 800.0 gram mass on the end…
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Q: A 6 kg mass slides to the right on a surface having a coefficient of friction 0.48 as shown in the…
A: Mass m = 6 kg Coefficient of friction μ = 0.48 Initial speed v= 8 m/s spring constant k = 145 N/m…
Q: A pendulum is made by tying a 520 gg ball to a 45.0 cmcm -long string. The pendulum is pulled 21.0…
A: Given quantities: mass of the ball (m) = 520 grams length of the string (L) = 45 cm angle made by…
Q: Consider a block of mass 0.220 kg attached to a spring of spring constant 120 N/m. The block is…
A: m = 0.220 kg K = 120 N/m x1 = 11.2 cm = 0.112 m
Q: A 2.00-kg pendulum ball is attached to a light-uniform cable of length 1.20 m that is hanging from…
A: Mass of pendulum, m1=2.00 kgAngle with the vertical, θ=50.0°Length of cable, L=1.20 mMass of block,…
Q: A spring with a spring constant of 303 N/m is initially compressed by a distance of 0.056 m from its…
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Q: A pitcher bestows a power of P = 206 W to a baseball of mass m = 0.095 kg for a period of t = 0.28…
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Q: A point-like mass m is constrained to move along the z-axis only. It is attached to two springs,…
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Q: The figure below shows a vertical, massless spring which is attached to the ground at one end. A…
A: Given:- Vertical distance h=5 cm =0.05 m velocity v = 0.7 m/s mass of the sphere m= 3 kg Find:-…
Q: In this question you will use an energy approach to determine how the mass of a spring affects its…
A: Note: as per the policy, only the first three subparts of the question will be solved. If you want…
Q: A 0.150kg bullet is initially at rest 1.50m above the earth in a rifle which is aimed horizontally…
A: GIVEN mass of bullet=m= 0.150 kg height above earth = h = 1.5 m…
Q: Let's say we have a spring with a constant of K= 300 N/m and this spring is attached to the incline…
A: Spring constant (k) = 300 Nm θ = 44od = 1.3 m m = 1 kg
Q: An ideal spring is attached to the ceiling. While the spring is held at its relaxed length, a wooden…
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- A block of mass M = 8 kg rests on a horizontal frictionless floor, and is connected to a vertical wall by a spring of force constant k = 200 N/m. When the spring is in its equilibrium position (neither stretched nor compressed), the block just touches a second lighter block of mass m = 4 kg at rest on the frictionless floor. The spring with mass M attached is now compressed by 0.1 m and released. The two blocks undergo a completely inelastic collision, i.e., they stick together after collision. Draw a diagram and define all relevant variables. Just before the collision, what is the velocity of mass MT Just after the collision, what is the common velocity of the two blocks? (What is the maximum stretching of the spring after the collision?: How long after the collision do the masses reach their first maximum stretch?Consider the following system: A spring has stiffness 598 N/m and is initially uncompressed. It is oriented vertically and placed on hard surface. A mass of size 2.3 kg is released from rest 9 m above the spring. Calculate the speed of the mass at the moment when the spring is compressed 0.5 m. Use g = 10 m/s2. (Please answer to the fourth decimal place - i.e 14.3225)Apollo and Artemis are playing on the teeter‑totter in their school's playground. They both have approximately the same mass. They are sitting on either side of the teeter‑totter at about the same distance from the teeter‑totter's pivot point. The teeter‑totter is going up and down and they are having a great time! Mercury, the new kid in school, wanders by. Since they are very friendly kids, Apollo and Artemis ask Mercury to join them. Mercury joins Apollo on his side of the teeter‑totter and sits next to him. What should Artemis do in order to keep the fun going? 1)Move farther from the teeter‑totter's pivot point in order to balance out the new smaller torque provided by Mercury and Apollo. 2)Move closer to the teeter‑totter's pivot point in order to balance out the new larger torque provided by Mercury and Apollo. 3)Move farther from the teeter‑totter's pivot point in order to balance out the new larger torque provided by Mercury and Apollo. 4)Move closer to the…
- A 0.2-kg pendulum bob A hangs from a 0.75 m cord attached to a fixed pivot. It is released from rest at point 1 when the cord is horizontal and without slack, and swings down to strike 0.2-kg bob B at point 2. The coefficient of restitution between the two bobs is e = 0.7. Neglect the size of the bobs and the mass of the cords. 0.75 m 1 For parts b-f below, consider bob A at the instant the cord is vertical, when it has reached point 2, and immediately before the collision: a) ) What is the tension in the cord of the stationary bob B? b) ( Draw a clear and complete free body diagram of bob A. с) ( Find the speed of bob A. d) Find the tangential acceleration of bob A. e) Find the normal acceleration of bob A. f) Find the tension in the cord of bob A. g) Find the speed of bob A immediately after the collision.A block A, of mass m = 10 Kg, compresses a spring of constant K = 1000 N / m in a length x = 3 cm. Starting from rest, the block is released, which moves from that moment on a horizontal surface without friction until it collides with another block B of mass m = 40 Kg, which was at rest. (Perfectly inelastic shock) and together they go up the channel (inclined surface) without friction, to later continue along a second horizontal plane without friction, at a height h with respect to the first (see Figure). Determine the energy variation that occurs in the collision .A block of mass m is at the top of an inclined plane of length L and angle 0. At the bottom of the plane there is a relaxed spring with spring constant k. (See the figure.) The block is released from rest and slides without friction down the plane. At the bottom of the plane, the block strikes the spring and momentarily comes to rest by compressing the spring by some amount D. (a) Find D in terms of m, k, L, g, and 0. (b) Describe in words what the motion will look like over time.
- A block with a mass m = 7.80 kg is attached to a lightweight spring with a spring constant k = 100 N/m that is attached to a wall. Initially the block is at rest and the spring is relaxed, as shown in figure (a). A second block with a mass mg = 7.00 kg is pushed up against block m, compressing the spring a distance A = 0.210 m, as shown in figure (b). The two blocks are released from rest, and both start moving to the right with negligible friction. IS a (a) When block m, reaches the equilibrium point, as shown in figure (c), block m, loses contact with block m,. Block m, continues to move right at a speed v. What is the speed v (in m/s)? m/s (b) Block m, continues to move right, reaching the point where the spring is at the maximum stretch (for the first time), as shown in figure (d). At this point, what is the distance D between the two blocks (in cm)? (Assume the widths of the blocks are much smaller than D.) cmThe pulley system below consists of two masses connected by a string of negligible mass through a massless pulley. A spring with constant k is placed so that its equilibrium position is located a distance h below the bottom of mass m2. There is no friction either in the pulley, or between the surfaces of the masses and the platform. When the two masses m₁ and m2 are released from rest, mass m2 begins falling and pulls mass m₁ up the ramp. Find an expression for the maximum compression of the spring d caused by mass m2 when it hits the spring. Your answer should be in terms of the variables given (and g). m2 MW my 0A 0.35 kg mass is held against a compressed spring with a spring constant of 89 N/m. The mass is initially at rest upon a horizontal surface and the spring force is directed parallel to the plane of the surface. If the coefficient of kinetic friction is 0.86, with what speed does the mass leave contact with the spring if the spring is initially compressed by 0.232 m?
- A ball is held at rest at some height above a horizontal surface. Once the ball is released it falls under gravity, hits the surface at time T1 , and starts bouncing vertically up and down. Suppose that with each bounce the ball loses a fixed fraction p (with 1>p>0) of its energy. This loss could be due to a number of reasons (inelasticity, drag, etc) that are left unspecified. How many times will the ball bounce before coming to rest? Provide a detailed explanation of your reasoning, not simply a one-line answer. How long will it take for the ball to come to rest (if at all), i.e., what is the stopping time Tstop? Give your answer for Tstop as a single formula that contains only two independent variables, namely p and the time T1 .A 10.0 gg rifle bullet is fired with a speed of 350 m/s into a ballistic pendulum with mass 10.0 kg , suspended from a cord 70.0 cm long. Compute the initial kinetic energy of the bullet. Compute the kinetic energy of the bullet and pendulum immediately after the bullet becomes embedded in the pendulum. Compute the vertical height through which the pendulum rises.