If we release a ball of mass 2kg and radius 4cm from rest at the top of the ramp as shown: (a) What is its velocity when it reaches the bottom? (b) How many revolutions has it turned when it reaches the bottom? (c) What is its total kinetic energy, in Joules, when it reaches the bottom? 15m 30°
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- A recently patented pile driver pounds piles into the ground by launching 15 kg bowling balls from a spring loaded gun, up around a frictionless loop-de-loop of radius r= 8 m, and down onto the pile. When the spring is compressed by As = 2 m, the bowling balls have a speed of 20 m/s at the top of the loop, as shown. (You may v = 20 m/s r=8 m assume g = 10 m/s².) k ? As = 2 m Find the spring constant of the gun. pile A) Zero B) 100 N/m C) 2700 N/m D) 150 N/m E) 1300 N/m O A O B O D O ER R A mass m = 88 kg slides on a frictionless track that has a drop, followed by a loop-the-loop with radius R = 15.8 m and finally a flat straight section at the same height as the center of the loop (15.8 m off the ground). Since the mass would not make it around the loop if released from the height of the top of the loop (do you know why?) it must be released above the top of the loop-the-loop height. (Assume the mass never leaves the smooth track at any point on its path.) 1) What is the minimum speed the block must have at the top of the loop to make it around the loop-the-loop without leaving the track? m/s Submit 2) What height above the ground must the mass begin to make it around the loop-the-loop? m Submit 3) If the mass has just enough speed to make around the loop without leaving the track, what will its speed be at the bottom of the loop? m/s Submit +A car rounds a freeway exit turn of radius 40m at constant speed of 20m/s. The turn goes 3/4 around(not a full circle). How much work is done by the friction force on the car’s tires that allows it to turn?
- In the game of tetherball a rope with length ?=1.50 m connects a ball with mass ?=0.750 kg to the top of a vertical pole so that the ball can spin around the pole as shown in the figure. What is the speed ? of the ball as it rotates around the pole when the angle ? of the rope is 38.0∘ with the vertical?A planet orbits its star in an elliptical orbit. Which of these quantities do not change as the planet orbits? O None of these quantities change as the planet orbits. O All of these quantities change as the planet orbits. O The planet's angular momentum O The planet's potential energy O The planet's kinetic energyMaria sets up a simple track for her toy block (m 0.54 m Need Help? = (a) Neglecting friction, what is the speed of the block when it reaches the bottom of the curve (the beginning of the horizontal section of track)? 3.25 m/s 0.40 kg) as shown in the figure below. She holds the block at the top of the track, 0.54 m above the bottom, and releases it from rest. (b) If friction is present on the horizontal section of track and the block comes to a stop after traveling 0.82 m along the bottom, what is the magnitude of the friction force acting on the block? 2.11 X Your response differs from the correct answer by more than 10%. Double check your calculations. N Read It
- As shown below, a bullet of mass m and speed v is fired at an initially stationary sphere. The bullet goes through the sphere, and exits with a speed of. The sphere is attached to a rigid pole of 6 length L and negligible mass. What is the minimum value of v such that the sphere will barely swing through a complete vertical circle? (Use the following as necessary: m, L, g, and M for the mass of the sphere.) 12M√gl 5m v/6 Ⓡ Use conservation of energy to determine the speed of the sphere immediately after collision. Assume that at the top of the swing the sphere is momentarily at rest, so its kinetic energy is zero. Then apply conservation of momentum to find the initial minimum speed of the bullet.Consider the mechanical energy of a body in geostationary orbit above the Earth's equator, at rGS=42000 km. Consider the mechanical energy of the same body on Earth at the South pole, at re=6400 km. For this problem, we consider the Earth to be spherical. (Remember, the object at the equator is in orbit, the object at the Pole is not in orbit.) G=6.67×10−11 Nm2kg−2, and the mass of the Earth is M=5.97×1024 kg What is the difference in the mechanical energy per kilogram between the two? E =E= ___ MJ.kg−1 (to two significant figures, don't use scientific notation)A 74kg cyclist is riding in his 8.2kg moves in a circle of radius 8m. The road exerts a central force of 332N. What is the speed of the cyclist?