a) Material point P(m) writes the flat curve, where r(0+1)² =α a is constant, under influence of central force. Find the power law. b) At the moment when the particle passes through the position 8 = 0, receives an impulse in direction of its movement, which zeros the radial component of its velocity and doubles transverse. Prove that the mobile will write the curve 3α 2 + cos √√3 2 0

if A⃗ =2i+3j+6kA→=2i+3j+6k and A⃗ =3i−4j+2kA→=3i−4j+2k, then the angle between the two vectors is

Consider the schematic of the molecule shown, with two hydrogen atoms, H, bonded to an oxygen atom, O. The angle between the two bonds is 106°. If the bond length r= 0.110 nm long, locate the center of mass of the molecule. The mass m, of the hydrogen atom is 1.008 u, and the mass mo of the oxygen atom is 15.9999 u. (Use a coordinate system centered in the oxygen atom, with the x-axis to the right and the y-axis upward. Give the coordinates of the center of mass in nm.) 53 nm YCH nm Submt Answer

In a ballistic pendulum an object of mass m is fired with an initial speed v0 at a pendulum bob. The bob has a mass M, which is suspended by a rod of length L and negligible mass. After the collision, the pendulum and object stick together and swing to a maximum angular displacement θ theta as shown (Figure 1). Find an expression for v0, the initial speed of the fired object. (Express your answer in terms of some or all of the variables m, M, L, and θ theta and the acceleration due to gravity, g.)   An experiment is done to compare the initial speed of bullets fired from different handguns: a 9.0 m and a .44 caliber. The guns are fired into a 10-kg pendulum bob of length L. Assume that the 9.0-m bullet has a mass of 6.0 g and the .44-caliber bullet has a mass of 12 g . If the 9.0-m bullet causes the pendulum to swing to a maximum angular displacement of 4.3 degree and the .44-caliber bullet causes a displacement of 10.1 degrees , find the ratio of the initial speed of the 9.0-m…

Consider a frictionless track as shown in the figure below. A block of mass m, = 2.00 kg is released from point O from a height of h = 1.15 m. It makes a perfectly inelastic collision at point ® with a block of mass m, = 2.00 kg that is initially at rest. After the collision, the block of mass m, moves to the right and collides with a spring at point ©. The spring is attached to a wall and has a spring constant of 8.81 kN/m. A m h m2 B (a) Calculate the energy loss during the collision. Enter the magnitude. 4.0 (b) Calculate the maximum compression of the spring. 4.0 cm (c) Instead of an inelastic collision, consider a head-on elastic collision at point ®. During this specific elastic collision when the masses are equal, m, transfers its kinetic energy to m, and as a result, m, comes to rest. Calculate the maximum compression of the spring. 4.0 cm

In a hydroelectric dam, water falls 30.0 mm and then spins a turbine to generate electricity. What is ΔUΔU of 1.0 kg of water? Express your answer with the appropriate units.

The 5.9-KN force F is applied at point A. (a) Compute the moment of F about point O, expressing it both as a scalar (positive if CCW, negative if CW) and as a vector quantity. (b) Determine the coordinates of the points on the x- and y-axes about which the moment of F is zero. Assume XA = 1.2 m, YA-1.8 m, a-6, b = 12. y, m A(x, y) j+ k) kN-m Answers: (a) Scalar: Vector: On the x axis: On the y axis: (6) Mo i Moi y= i -x, m m E kN-m i+ i

As the drawing illustrates, two disks with masses m₁ and m2 are moving horizontally to the right at a speed of vo. They are on an airhockey table, which supports them with an essentially frictionless cushion of air. They move as a unit, with a compressed spring between them, which has a negligible mass. Then the spring is released and allowed to push the disks outward. Consider the situation where disk 1 comes to a momentary halt shortly after the spring is released. Assuming that m₁ = 1.3 kg, m₂ = 2.4 kg, and vo = +4.9 m/s, find the velocity of disk 2 at that moment. Vf2 = i Save for Later m₁ m2 VO. Attempts: 0 of 3 used Submit Answer

As the drawing illustrates, two disks with masses m₁ and m2 are moving horizontally to the right at a speed of vo. They are on an airhockey table, which supports them with an essentially frictionless cushion of air. They move as a unit, with a compressed spring between them, which has a negligible mass. Then the spring is released and allowed to push the disks outward. Consider the situation where disk 1 comes to a momentary halt shortly after the spring is released. Assuming that m₁ = 1.3 kg, m₂ = 2.5 kg, and vo= +5.1 m/s, find the velocity of disk 2 at that moment. Vf2 = i m1 m2 VO

Two masses hang next to each other from a support. Each mass has a pendulum length R = 30 cm. Object A is raised to a 66 degree angle with respect to vertical and allowed to fall as a pendulum, eventually colliding elastically with object B. Let object A have a mass ma=45g and object B have mass mb=65g. For all answers, work symbolically and then plug in numbers at the end. (a) What is the velocity of the object A before the collision? (Ignore the physical size of A and B, that is, assume y = 0 for both during the collision) (b) What quantities are conserved during the collision? (c) What are the maximum heights of each object after the collision?