A package of mass 8 kg sits at the equator of an airless asteroid of mass 3.0 x 1020 kg and radius 1.3 x 105 m. We want to launch the package in such a way that it will never come back, and when it is very far from the asteroid it will be traveling with speed 208 m/s. We have a large and powerful spring whose stiffness is 2.7 x 105 N/m. How much must we compress the spring? Icompression] (a positive number) = m

A planet has a radius of 4.00 x 10^6 m, and rotates so rapidly that an object on the equator feels only 10% of the weight that it feels at the poles. What is the speed of an object at the equator?

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?

The figure shows a thin rod, of length L = 2.20 m and negligible mass, that can pivot about one end to rotate in a vertical circle. A heavy ball of mass m = 8.10 kg is attached to the other end. The rod is pulled aside to angle 00 = 8° and released with initial velocity V 0. (a) What is the speed of the ball at the lowest point? (b) Does the speed increase, decrease, or remain the same if %3D the mass is increased? 3.

A comet is in an elliptical orbit around the Sun. Its closest approach to the Sun is a distance of 4.9 x 1010 m (inside the orbit of Mercury), at which point its speed is 9.3 × 104 m/s. Its farthest distance from the Sun is far beyond the orbit of Pluto. What is its speed when it is 6 x 10¹2 m from the Sun? (This is the approximate distance of Pluto from the Sun.) speed= i ! m/s

At a post office truck loading station, a small 0.2 kg package is released from rest at point A on a track that forms a quarter circle with a radius of 1.60 m. The packet is so small relative to said radius that it can be treated as a particle. The package slides along the track and reaches point B with a speed of 4.80 m/s. From here, the package slides 3.0 m on a horizontal surface to point C, where it stops. 0.21 A: R=1.60 m a)- What coefficient of kinetic friction does the horizontal surface have? -0.7281 B -3.00 m B: 0.45 m = 0.200 kg C: -0.8321 b)- How much work does friction do on the package as it slides along the circular arc between A and B? 0.39 C D: 0.835 J 0.27 D: -3.821 E: 0.30 3.28 J

Zero, a hypothetical planet, has a mass of 4.5 x 1023 kg, a radius of 3.2 x 106 m, and no atmosphere. A 10 kg space probe is to be launched vertically from its surface. (a) If the probe is launched with an initial kinetic energy of 5.0 x 107 J, what will be its kinetic energy when it is 4.0 x 106 m from the center of Zero? (b) If the probe is to achieve a maximum distance of 8.0 x 106 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero?

A satellite is traveling around a planet in a circular orbit with radius R. It moves in a constant speed of v = 1.1 × 104 m/s. The mass of the planet is M = 6.04 × 1024 kg. The mass of the satellite is m = 1.2 × 103 kg. First, find an expression for the gravitational potential energy PE in terms of G, M, m, and R.  a)Calculate the value of PE in joules.  b)Enter an expression for the total energy E of the satellite in terms of m and v.  c)Calculate the value of the total energy E in joules.

An asteroid has a mass of m = 2.6 x 106 kg and is approaching Earth. When the asteroid is exactly 3 radii away from the Earth's centre,  it's speed relative to the Earth's centre is u = 8.7 x 103 ms-1. The asteroid then falls to the Earth's surface, but remains intact without dissipating any energy as it passes through the Earth's atmosphere. If the rotation of the asteroid and the Earth is ignored, what is the kinetic energy of the asteroid just before it hits the ground?

Two rigid bodies, A and B, both 1 kg in mass, are connected by a linear spring with a spring constant of 0.2 N/m.  Initially, the spring is unstretched and the bodies are at rest.  If multiple forces and moments are applied to the two bodies that result in the speed of body A increasing to 10 m/s, the speed of body B increasing to 4 m/s, and the stretch of the spring increasing by 10 m, then  -20 Nm of work was done by the spring on the body A, B system. Two rigid bodies, A and B, both 1 kg in mass, are connected by a linear spring with a spring constant of 0.2 N/m.  Initially, the spring is unstretched and the bodies are at rest.  If multiple forces and moments are applied to the two bodies that result in the speed of body A increasing to 10 m/s, the speed of body B increasing to 4 m/s, and the stretch of the spring increasing by 10 m, then  -20 Nm of work was done by the spring on the body A, B system. True False