Samus Aran from the Metroid series of video games has the ability to roll into a ball to get into smaller areas. Samus rolls down a path which drops down 22.0 m. If she was at rest when she started at the top, what is her linear velocity at the bottom of the path? Treat her as a solid sphere with a moment of inertia of 2/5 mr^2 .

Moon Knight, from both comics and the show of the same name, has crescent shaped daggers he throws at enemies. To throw a crescent dagger he applies a force of 0.918 N at an angle of 75.0° relative to the dagger’s center of mass at a point 0.0690 m away from the dagger’s center of mass. If the crescent dagger has a moment of inertia of 2.57⋅10^−5 kg⋅m^2 , what is the angular acceleration of a crescent dagger as it is thrown?

Because you are taking physics, your friend asks you to explain the detection of gravity waves that was made by LIGO in early 2016. (See the section that discusses LIGO.) To do this, you first explain about Einstein's notion of large masses, like those of stars, causing a curvature of spacetime. (See the section on general relativity.) To demonstrate, you put a bowling ball on your bed, so that it sinks downward and creates a deep depression in the mattress. Your sheet has a checked pattern that provides a nice coordinate system, as shown in the figure below. This is an example of a large mass (the bowling ball) creating a curvature of a flat, two-dimensional surface (the mattress) into a third dimension. (Spacetime is four dimensional, so its curvature is not easily visualized.) Then, you are going to amaze your friend by projecting a marble horizontally along a section of the sheet surface that is curved downward by the bowling ball so that the marble follows a circular path, as…

An artificial satellite circling the Earth completes each orbit in 136 minutes. (a) Find the altitude of the satellite. m (b) What is the value of g at the location of this satellite? m/s²

A car is traveling on a banked curve as shown in the figure below. The radius of curvature of the road is R, the banking angle is 0, and the coefficient of static friction is μs. nx R A ny (a) Determine the range of speeds the car can have without slipping up or down the road. (Use any variable or symbol stated above along with the following as necessary: g. Note that the subscript of V min = Vmax = (b) Find the minimum value for μ such that the minimum speed is zero. (Use the following as necessary: R, 0, and g.) μs = μs is lowercase.)

Use the data of this table to find the point between Pluto and the Sun at which an object can be placed so that the net gravitational force exerted by Pluto and Sun on that object is zero. m from the center of Pluto

(a) Imagine that a space probe could be fired as a projectile from the Earth's surface with an initial speed of 5.78 × 104 m/s relative to the Sun. What would its speed be when it is very far from the Earth (in m/s)? Ignore atmospheric friction, the effects of other planets, and the rotation of the Earth. (Consider the mass of the Sun in your calculations.) m/s (b) What If? The speed provided in part (a) is very difficult to achieve technologically. Often, Jupiter is used as a "gravitational slingshot" to increase the speed of a probe to the escape speed from the solar system, which is 1.85 x 104 m/s from a point on Jupiter's orbit around the Sun (if Jupiter is not nearby). If the probe is launched from the Earth's surface at a speed of 4.10 × 104 m/s relative to the Sun, what is the increase in speed needed from the gravitational slingshot at Jupiter for the space probe to escape the solar system (in m/s)? (Assume that the Earth and the point on Jupiter's orbit lie along the same…

A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1 860 kg. It has strayed too close to a black hole having a mass 98 times that of the Sun. The nose of the spacecraft points toward the black hole, and the distance between the nose and the center of the black hole is 10.0 km. H 100 m- Black hole //10.0 km/ i (a) Determine the total force on the spacecraft. N (b) What is the difference in the gravitational fields acting on the occupants in the nose of the ship and on those in the rear of the ship, farthest from the black hole? (This difference in acceleration grows rapidly as the ship approaches the black hole. It puts the body of the ship under extreme tension and eventually tears it apart.) N/kg

Three uniform spheres of masses m₁ = 3.00 kg, m₂ = 4.00 kg, and m3 = 6.50 kg are placed at the corners of a right triangle (see figure below). Calculate the resultant gravitational force on the object of mass m2, assuming the spheres are isolated from the rest of the Universe. Ĵ) × 10-11 N Î + (0, 3.00) m 1)x m₁ (-4.00, 0) m F12 m3 32 0 x m2