Suppose a cart of mass 2 kg is attached by a spring of constant k = 1 to a cart of mass 3 kg, which is attached to the wall by a spring also of constant k = 1. Suppose that the initial position of the first cart is 6 meters in the positive direction from the rest position, and the second mass starts at the rest position. The masses are not moving and are let go. Find the position of the second mass as a function of time.
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- A rod of length 3 meters with density 8(x) = 1.1 + 1.1x4grams/meter is positioned along the positive x-axis, with its left end at the origin. Find the total mass and the center of mass of the rod. Round your answers to four decimal places. The total mass of the rod is i The center of mass of the rod is i grams. meters.This is a two-part problem. A rocket, fired from rest at time t = 0, has an initial mass of m0 (including fuel). Assuming the fuel is consumed at a constant rate k, the mass m of the rocket, while fuel is being burned, will be given by m0 - kt. It can be shown that if air resistance is neglected and the fuel gases are expelled at a constant speed c relative to the rocket, then the velocity v of the rocket will satisfy the equation m(dv/dt) = ck - mg. In this equation, g is the acceleration due to gravity. I) Find v(t) keeping in mind that the mass m is a function of t. II) Suppose that the fuel accounts for 70% of the initial mass of the rocket and that all of the fuel is consumed at 130 s. Find the velocity of the rocket in meters per second at the instant the fuel is exhausted.A rocket accelerates by burning its onboard fuel, so its mass decreases with time. Suppose the initial mass of the rocket at liftoff (including its fuel) is m, the fuel is consumed at rate r, and the exhaust gases are ejected with constant velocity ve (relative to the rocket). A model for the velocity of the rocket at timet is given by the equation m - rt v(t) = -gt - Ve In where g is the acceleration due to gravity and t is not too large. If g = 9.8 m/s2, m = 32,000 kg, r = 190 kg/s, and ve = 3,000 m/s, find the height of the rocket one minute after liftoff. (Round your answer to the nearest whole meter.)
- A 2 kg block is moving at v= 3 m/s along a frictionless table and collides with a second 2 kg block that is initially at rest. After the collision, the two blocks stick together and then slide up a 45∘frictionless inclined plane a)Calculate the maximum distance LL that the two blocks travel up the incline.At an amusement park, the bumper cars each have a mass of 218kg. The riders have masses of 48kg and 60kg respectively. Car A is moving to the right with a velocity of (va)=3 m/s to the right while Car B has a velocity of (va), = 2 m/s to the left. 2. A.If the coefficient of restitution between each car is 0.8, determine the velocity of each car after impact. b. If the collision occurred in 0.06 s, determine the impulsive force, Fs, of Car B on Car A PIM: include direction of the force] c. The impulse force, FA, of Car A on Car B. ; include direction of the forceThe NASA Space Launch System rocket that will carry the Artemis mission to the Moon travels 500 feet (152 m) straight up in the first 7 seconds of flight. It weighs 5.75 million pounds (mass of 2.61e6 kg). In this problem, we'll calculate the acceleration and the net force on a similar rocket. The numbers will be randomized slightly for our question. Since the rocket is using fuel, this is an approximation anyway. The SLS starts from rest and reaches a final velocity of 36.2 m/s in 7.30 seconds. What is its average acceleration? m/s² What is the net upward force on the rocket providing that acceleration, if it has mass 2.69E+6 kg? N
- A rocket accelerates by burning its onboard fuel, so its mass decreases with time. Suppose the initial mass of the rocket at liftoff (Including its fuel) is m, the fuel is consumed at rate r, and the exhaust gases are ejected with constant velocity v. (relative to the rocket). A model for the velocity of the rocket at time t is given by the equation m v(t) = -gt - v, In m where g is the acceleration due to gravity and t is not too large. If g = 9.8 m/s2, m = 27,000 kg, r = 160 kg/s, and v = 3,100 m/s, find the following. (a) the height of the rocket (in meters) one minute after liftoff (Round your answer to the nearest meter.) (b) the height of the rocket (in meters) after it has consumed 5,000 kg of fuel (Round your answer to the nearest meter.) mA cat (mass of 3.63 kg) is on a sled (mass of 22.7 kg) which rests on an icy surface... so no friction. In front of this sled, there is another identical sled. The cat jumps from the first sled to the second AND immediately back to the first. Both jumps are made at a relative speed of 3.7 m/sec between the cat and the sled it is on. Calculate the final speeds of the two sleds!An 8.00-kg point mass and a 15.0-kg point mass are held in place 50.0 cm apart. A particle of mass m is released from a point between the two masses 20.0 cm from the 8.00-kg mass along the line connecting the two fixed masses. Find the magnitude and direction of the acceleration of the particle.
- In a good hit, a baseball and bat are in contact with each other for about 1 millisecond. In the first game of the 2012 World Series, Tigers pitcher Justin Verlander threw a 90-mph pitch to the Giants’ Pablo Sandoval. Sandoval’s hit returned the ball directly back at Verlander at 70 mph. Calculate the average force of the bat on the ball, during the contact. Round the final answer to the nearest whole number.Assume that the origin goes through the place marked in the diagram. The three masses are connected by massless, rigid rods of 30 cm length (center-to-center). If the mass of A is 100 g, the mass of B is 150 g and the mass of C is 400 g, what is the x-coordinate (in cm) of the center of mass? What is the y-coordinate (in cm) of the center of mass?A block of mass m = 2.40 kg starts from the rest and slides down a 30.0∘ incline which is 3.60 m high. At the bottom, it strikes a block of mass M = 7.20 kg which is at rest on a horizontal surface (Figure 1). (Assume a smooth transition at the bottom of the incline.) The collision is elastic, and friction can be ignored. Determine the speed of the block with mass m = 2.40 kg after the collision. Determine the speed of the block with mass M = 7.20 kg after the collision. Determine what distance along the incline will the smaller mass climb back after the collision.