The distance of B below the ring in terms of a, is (A) a (B) a/2 (C) a/3 (D) a/4 B A Particles A and B, of masses 3m and m respectively, are connected by a light inextensible string of length a that passes through a fixed smooth ring R. Particle B hangs in equilibrium vertically below the ring. Particle A moves in horizontal circles on a smooth horizontal surface with speed √ga. The angle between AR and BR is 0 (see diagram). The normal reaction between A and the surface is mg.

The distance of B below the ring in terms of a, is (A) a (B) a/2 (C) a/3 (D) a/4 B A Particles A and B, of masses 3m and m respectively, are connected by a light inextensible string of length a that passes through a fixed smooth ring R. Particle B hangs in equilibrium vertically below the ring. Particle A moves in horizontal circles on a smooth horizontal surface with speed √ga. The angle between AR and BR is 0 (see diagram). The normal reaction between A and the surface is mg.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter7: Gravity

Section: Chapter Questions

Problem 42PQ

See similar textbooks

Similar questions

4. A particle of mass m slides without friction along a wire bent into the shape of a circular helix whose equation is z=a0, r=R, where r, 0, and z are the usual cylindrical coordinates, and a is a constant. The particle is attracted to the origin with a force equal to k times the distance from the origin. Write and solve the equation of motion, using the constrains to reduce the problem to one involving a single variable.
A 200 kg mass hangs from a 300 m cable on Mars (g=3.71 m/s2). It is displaced left from equilibrium along an arc with length 30 m and released at t = 0. What is its position relative to equilibrium when t = 20 s? What is its acceleration?
A bead of mass m slides without friction along a curved wire with shape z = f(r) where r = Vr2 + y², i.e. the distance from the z-axis. The wire is rotated around the z-axis at a constant angular velocity w. Gravity acts downward along the z-axis with a constant acceleration g. a) Using Newton's second law in an inertial frame, derive an expression for radius ro of a fixed circular orbit (i.e. a solution with r = ro = const.). What is the normal force the wire applies to the bead to keep it in a circular orbit? b) Show that the equation of motion for r(t) (general equation not the circular motion) is F(1 + f'(r)²) + i² f'(r)f"(r) + gf'(r) – w?r = 0. Using this verify your answer to part (a). c) Consider small displacements from the circular orbit, r = ro+e(t). Derive a condition on the function f(r) such that a circular orbit at r = ro is stable. d) Find the force on the bead in the o direction, i.e. perpendicular to the plane of wire. The angular velocity is w = . Obtain the answer…
A particle of mass m is placed at a distance r away from the center of a thin circular hoop of mass M and radius R. The particle is in the plane of the hoop, and r < R. M. Find the gravitational force on the particle. Does your answer make sense in the limit r + 0? r + R? 2.
Problem 1) We consider the following system when placed in a uniform gravitational field (with acceleration g): An ordinary 2 dimensional pendulum of length l is placed at the edge of a disc of radius a. The disc rotates with constant angular velocity w. Neglect all masses apart from the mass m at the end of the 2D pendulum. mass n a) How many degrees of the freedom does the system have, after taking into account the presence of constraints? b) Find the Lagrangian for the system
I whirl John (mass 0.27 kg) over my head in a circle. There is a spring scale between my hand and the string, so I can measure the force of tension in the string, which I find to be 2.12 N. I measure the length of the string (the radius of the circle) and find it to be 1.34 m. Assuming that John's speed is not changing, how fast is he going?
An experiment is performed using the apparatus above. A small disk of mass m, on a frictionless table is attached to one end of a string. The string passes through a hole in the table and an attached narrow, vertical plastic tube. An object of mass m; is hung at the other end of the string. A student holding the tube makes the disk rotate in a circle of constant radius r, while another student measures the period P. m,r a. Derive the equation P= 2x that relates Pand m;. The procedure is repeated, and the period P is determined for four different values of m, where m, = 0.012 kg and r= 0.80 m. The data, which are presented below, can be used to compute an experimental value for g. m: (kg) 0.020 0.040 0.060 0.080 P (s) 1.40 1.05 0.80 0.75 b. What quantities should be graphed to yield a straight line with a slope that could be used to determine g? On the grid beklow, plot the quantities determined in part (b), label the axes, and draw the best-fit line to the data. You may use the blank…
If a particle executes uniform circular motion in the xy plane in clock wise direction, then the angular velocity is in the +z direction Select one: True O False
1.1 A thin uniform disk of radius a, mass m and A mass per unit length. Find the gravitational force that the ring exerts on a particle of mass M at distance d from the center of the ring, see figure below. of Note! Disk is in the ZX-plane and D is along the Y-axis 1.2 Given that A = Skgm", a = 50 cm and d 1.1 m. Determine the gravitational force that the disk exerts on a particle of mass M = 750 g.
3. A simple pendulum consists of a pendulum bob of mass M at the end of a "mass-less" string of length L. The pendulum bob oscillates back and forth and is moving at speed v when the string is oriented at a constant angle 0 from vertical. Give answers in terms of L, 0, v, M and/or g. This is similar to the vertical circle from the Circular Motion Experiment worksheet except that we are not going in a full circle. a. Draw the free body diagram of forces acting on the pendulum bob. Include a coordinate system on your diagram showing your choice for the +x and +y directions. b. Write out Newton's 2nd law EF = mã for each direction. X: y: c. What is the tangential acceleration of the pendulum bob? d. Determine the tension of the string. e. What is the magnitude of the total acceleration of the pendulum bob?
Suppose a teacher is riding a Ferris wheel. The maximum height they attain is 30 m and theminimum height is 6 m. The time it takes to make one full rotation is about 5 minutes. Determine:a/ The periodb/ The amplitudec/ A possible equation that models this situation, if the time starts at the minimum height.
A “semi-infinite” uniform rod occupies the nonnegative x-axis. The rod has a linear density δ, which means that a segment of length dx has a mass of δ dx. A particle of mass M is located at the point (−a, 0). The gravitational force F that the rod exerts on the mass is given by where G is the gravitational constant. Find F.