A body with mass I kilogram (kg) is attached to the end of a spring that is stretched 4 meters (m) by a force of 105 newtons (N). It is set in motion with initial position x(0)-1m and initial velocity v(0)-5 (m/s). (Note that these initial conditions indicate that the body is displaced to the right and is moving to the left at time.) Find the value of the position function x(t) of the body at t-2.
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- 2.3. A train car is sitting on a level track when a second car moves in. The second car hits the first, their hitches engage, and they move together. Both cars have equal masses of about 120 000 kg, and the second car initially has a velocity of 1.5 m/s. (a) Draw a diagram that illustrates the situation and include an arrow representing the velocity vector of the second car and a separate arrow representing ĉ, the unit vector for the coordinate system along the tracks. (b) Write vector expressions for both the velocity and momentum of the second car using at least two forms of vector notation that have been covered in class. (c) Just before the collision, what is the velocity of the center of mass of the system that includes both cars? Again, express this as a vector. (d) Just before the collision, what is the total kinetic energy of the system that includes both cars?At a particular instant, a hot air balloon is 48.7m above a horizontal field and descending at a rate of 2.67m/s. At this instant, a girl who is riding in the gondola of the balloon throws a ball with a speed of 14.7m/s with a direction that is horizontal in the frame of the gondola. When the balloon lands on the ground, how far, in meters, is she from where the ball landed? Neglect air resistance.A horizontal force of 80.0 N is applied to a 5.00 kg block as the block slides a distance of 0.800 m along a horizontal floor. The coefficient of kinetic friction between the floor and the block is 0.500. If the block is initially at rest, how fast is it moving at the end of the displacement?
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- Consider the setup shown below: a block with mass m1 sits on a table with friction coefficient ? between the table and itself, attached on one side to a spring with stiffness k, and on the other side to a cord with negligible mass that wraps over a frictionless pully and supports a second block with mass m2 that’s suspended in the air over the edge of the table. If the friction between block 1 and the table is not enough to hold up block 2 (so that the spring has to stretch), how far is the spring stretched when the system comes to rest?∆? = __________________________________________________________________??1?2 *Please write solution and process as much as possible like detail.A bowling ball weighing 46.5 N initially moves at a speed of 5.10 m/s. How long must a force of 44.5 N be applied to the ball to stop it?Which of the following differential equations is the correct model if up is the positive direction? Consider an object of mass m that was thrown upwards and the magnitude of the force due to air resistance is 2v where v is the speed of the object in meters per second. pick (1) mv′=−mg−2v mv′=−mg+2v mv′=mg+2v mv′=mg−2v
- The y-coordinate of a particle varies at a constant speed of 4.2 m/s. At t=0, the y-coordinate was found to be 2.7 m. Find an analytic expression for the function y(t).A block of mass m = 3.59kg moves along the x-axis subject to a net force which depends on position. The force is Fner (x) = (-3.92x-1.49x³) î. The block is initially at x = Om moving with velocity = -3.73. (The input below will accept answers with no more than 1% variation from the correct value.) What is the smallest value of x the block reaches? m Hint: Calculate the work done as a function of x, and then solve the resulting quadratic expression for x². What is the block's speed when it reaches x = 1.62m? Ev