Problem 3.50 An object of mass m is initially at rest at x = 2 m. Determine the time for it to reach x = 3 r if it is acted upon by a force F = kx. Express your answer in terms of k and m.
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- How to solve this?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?Question 1: A bullet of mass m hits a block of mass M on a table with velocity vo as shown in the figure below. The bullet embeds in the block. The friction coefficient between the block and the table poxez² where .2 is u = is a constant and 0There are two particles (1 and 2) that are moving around in space. The mass of particle 1 is 2.8 kg and the mass ofparticle 2 is 1.96 kg. The particles are isolated so that only the forces between the particles are significant. The forcethat 2 exerts on 1 is given by:~F21(t) = Fat ˆi + Fbt3 ˆjThe initial time is ti = 4.1 s and the final time is tf = 6.8 s.Use the following values for the parameters:Fa = -18.4 N/s , Fb = 11.2 N/s3, If the y component of the impulse from 1 on 2 is -5196 N s, what is the y component of the change in momentum forparticle 2?An ice skater with mass = mi goes skating while carrying a bag of sand with initial mass = m0 . At one point, she gives herself a constant initial velocity v0 , and then slowly pours the sand out of the bag at a constant rate κ. Is she speeding up or slowing down? Write out an expression for the velocity as a function of time. How long does it take for her velocity to change by a factor of 2? Your answer can include mi, m0, v0, and κ.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?Suppose you are navigating a spacecraft far from other objects. The mass of the spacecraft is 3.2 × 104 kg (about 32 tons). The rocket engines are shut off, and you're coasting along with a constant velocity of km/s. As you pass the location km you briefly fire side thruster rockets, so that your spacecraft experiences a net force of N for 23.0 s. The ejected gases have a mass that is small compared to the mass of the spacecraft. You then continue coasting with the rocket engines turned off. Where are you an hour later? (Think about what approximations or simplifying assumptions you made in your analysis. Also think about the choice of system: what are the surroundings that exert external forces on your system?) 7₁ = mk A 13.00 kg particle starts from the origin at time zero. Its velocity as a function of time is given by = 10t² + 1tj where is in meters per second and t is in seconds. (Use the following as necessary: t.) V (a) Find its position as a function of time. ŕ= esc 10/³1 + ²/2 2²; 3 (b) Describe its motion qualitatively. The particle starts from rest at the origin, starts moving in the y direction, and gains speed faster and faster while turning to move more and more nearly parallel to the x axis. Score: 0.06 out of 0.06 Comment: (c) Find its acceleration as a function of time. a = 20ti + lj m/s² (d) Find the net force exerted on the particle as a function of time. F= T= (e) Find the net torque about the origin exerted on the particle as a function of time. N m X X (f) Find the angular momentum of the particle as a function of time. Ľ Need Help? Read It F1 N x (g) Find the kinetic energy of the particle as a function of time. K= x kg m²/s X (h) Find the power injected into the particle as a…Asap plxxxxxA hockey puck of mass 100 g is sliding due east on a frictionless table with a speed (₂) of 11 m/s. Suddenly, a constant force (F) of magnitude 6.5 N and direction due north is applied to the puck for 1.7 s as shown below. Find the north and east components of the momentum at the end of the 1.7 s interval. Pnorth = Peast = ILL F 15 number (rtol=0.01, atol=1e-08) number (rtol=0.01, atol=1e-08) kg*m/s ? kg*m/sMichael fell asleep while driving home from school. His 1255 kg car hit a guardrail while moving at 15.98 m/s. The guardrail exerted a 6.110E4 N force on the car for 0.1233 s. After the car hit the guardrail, how fast was it moving?Problem 5: Rafael drops a hard rubber ball, of mass m = 310 g, onto the pavement. He drops it from a height h = 2.9 m, and it bounces back to a height h = 1.65 m. While the ball is in contact with the ground, the ground exerts a non-constant force on the ball as shown in the figure. During the time interval At¡ the force rises linearly to Fmax, and during the time interval At, the force returns linearly to zero as the ball leaves the ground. Refer to the figure. F Fmax Ati At2