Consider a ball rolling around in a circular path on the inner surface of a cone. The weight of the ball is shown by the vector W. Withoutfriction, only one other force acts on the ball-a normal force, (a) Draw in the vector for the normal force. (The length of the vector dependson the next step, b.) (b) Using the parallelogram rule, show that the resultant of the two vectors is along the radial direction of the ball'scircular path. (Yes, the normal is appreciably larger than the weight!)

While moving along the circular path on the frictionless wall inside the cone, the only normal force…

Answered: Consider a ball rolling around in a…

Similar questions

(a) The magnitude of the angular momentum about the origin of a particle of mass m moving with velocity v on a path that is a perpendicular distance d from the origin is given by m/v|d. Show that if r is the position of the particle then the vector J =r × mv represents the angular momentum. (b) Now consider a rigid collection of particles (or a solid body) rotating about an axis through the origin, the angular velocity of the collection being represented by w. (i) Show that the velocity of the ith particle is Vi = w X ri and that the total angular momentum J is J = Σm₁ [r}w - (r; · w)r;]. (ii) Show further that the component of J along the axis of rotation can be written as Iw, where I, the moment of inertia of the collection about the axis or rotation, is given by 1 = Σm₁p². Interpret pi geometrically. (iii) Prove that the total kinetic energy of the particles is 1².
As shown in the figure below, we have a square one meter on a side that is free to rotate about an axis perpendicular to the plane of the square, a distance a from one side and a distance b from the other side. a = b = b (i) Two forces, and F2, are applied to diagonally opposite corners, and act along the sides of the square, first as shown in case (i) and then as shown in case (ii) of the drawing. In each case the net torque produced by the forces is zero. If the magnitude of F2 is 4 times that of F₁, find the distances a and b that locate the axis. It should be noted that a and b are not drawn to scale. m m b a
Consider a disc of mass 0.44kg, with radius 0.5 m on a slope with angle 45 degrees to the horizontal. It has a good grip on the slope and does not slip. The disc is constructed so that its mass per unit area, ρ(r) = r1/2 kg m−2, with r being the radial distance in metres from the axis of the disc. What is the acceleration of the disc down the slope?
Problem 5: Two blocks are connected with a rope as shown. The surfaces and the pulley are frictionless. The pulley is a disk with radius r and mass m,. A force F is applied to Mass 1 as F m1 shown so that Mass 1 accelerates to the left and Mass 2 accelerates upward. Take the positive direction to the be the direction of accelerations of the masses. (That is, the positive direction for Mass 1 is to the left, and the positive direction for Mass 2 is upward.) mp m2 In the space below, show how you would find the acceleration of the masses. Start with equations from the equation sheet and show your steps to the point where you would calculate the results. You do not need to calculate any numerical result. Just show how you would solve the problem. Be sure your equations reflect the positive direction as described above. Max characters allowed 3000. 0/3000
Engineering Dynamics need help from 4,5,6,7 thank you A ball of mass m is moving along a vertical semi-cylinder of radius R as it is guided by the arm OA. The arm moves in a clockwise direction with a constant angular velocity ω. Assume 0° ≤ Φ ≤ 90°. Neglect any friction. Neglect also the size of the ball and the thickness of the arm. Find the relationship between r, R and θ where r is the distance between O and the ball. Draw a free body diagram of the ball assuming that it is in contact with the cylinder and the arm OA. Write the equations of motion in the (r, θ) coordinate system. Find the normal force acting on the ball by the cylinder for Φ = Φ0. Find the normal force acting on the ball by the bar for Φ = Φ0. Determine the angle Φ at which the ball loses contact with the cylinder. Take m = 1 kg, R = 1.4 m, ω = 0.5 rad/s, and Φ = 60°