(a) Find the escape speed of a projectile from the surface of the Moon. (See the front of the test for some numbers you may need here.) (b) Imagine you want to launch a package of mass 3kg from the surface of the Moon in such a way that it will never come back, and when it is very far from the Moon it will still be traveling with a speed of 50 m/s. You have a large and powerful spring whose stiffness is 6 x 10° N/m. How much do you have to compress the spring?

A Hooke's law spring is compressed a distance d and is used to launch a particle of mass m vertically to a height h above its starting position. Under double the compression, the spring is now used to launch a particle of mass 2m. How high does the second mass rise above its starting position?

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A ball of unknown mass m is tossed straight up with initial speed v. At the moment it is released, the ball is a height h above a spring-mounted platform, as shown in the figure. The ball rises, peaks, and falls back toward the platform, ultimately compressing the spring a maximum distance d from its relaxed position. Assume that the spring is perfectly ideal, with spring constant k, and that the mass of the spring and platform is negligible. What is the mass of the ball, m, assuming that there is no friction or air resistance? Using g to represent the acceleration due to gravity, enter an expression for m in terms of g, h, d, k, and v. kg m = m h www d

A 1.8kg physics cart is initially traveling 2.8m/s when it collides with an ideal spring (with a spring constant of 710N/m and natural length shown. The final time is defined as when the spring at maximum compression and the cart is about to rebound backwards. Neglect loss. List the energy types at the initial and final time and whether work and loss (due to non- conservative forces) occur as well as the corresponding amounts of energy. 0.335m reference level initial: unit v wwww work? unit loss? unit final: unit wwww reference level How much did the spring's length change during the compression? unit What is the length of the spring at maximum compression? unit What is the spring force at this time? unit

Say we have a mass, m, situated at a height, h, above an ideal spring with force constant k.  The mass is dropped vertically onto the spring. Derive an expression for the compression of the spring from equilibrium (x) as a function of m, k, and h. By what factor is the compression changed if the mass is dropped from a height of 3h? What is the speed of the mass just as it contacts the spring?

A new event has been proposed for the next Winter Olympics. As seen in the figure below, an athlete will sprint 100 m, starting from rest, then leap on a 25.0 kg bobsled. The person and bobsled will then slide down a 50.0 m long ice-covered (frictionless) ramp, sloped at 20.0°, and into a spring with a carefully calibrated spring constant of 2000.0 N/m. The athlete who compresses the spring the farthest wins the gold medal. Lisa, whose mass is 40.0 kg, has been training for this event. She can reach a maximum speed of 12.0 m/s in the 100 m dash. How far will Lisa compress the spring? 20°

A ball of mass m = 1.95 kg is released from rest at a height h= 76.0 cm above a light vertical spring of force constant k as in Figure [a] shown below. The ball strikes the top of the spring and compresses it a distance d = 9.20 cm as in Figure [b] shown below. Neglecting any energy losses during the collision, find the following. Hake www (a) Find the speed of the ball just as it touches the spring.. m/s (b) Find the force constant of the spring. kN/m

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Pick out the only vector quantity in the following list:  Temperature, pressure, impulse, time, power, total path length, energy, gravitational  potential, coefficient of friction, charge.