A student performs a ballistic pendulumexperiment using an apparatus. Initially the bullet is fired at the block while the block is at rest (at its lowest swing point).After the bullet hits the block, the block risesto its highest position, and continues swinging back and forth.The following data is obtained: the maximum height the pendulum rises is2.9 cm, the mass of the bullet is 67 g, and the mass of the pendulum bob is 822 kg. Find the final velocity of the system (m1 + m2) immediately after the collision and before the pendulum starts to swing upward. The acceleration of gravity is 9.8 m/s^2.Answer in units of m/s.

Question 5: Balls A and B have a mass of 600 g and 1 kg, respectively. If they are sliding on a smooth horizontal plane with the velocities shown, determine their speeds just after impact. The coefficient of restitution between them is e = 0.8. DA= 6 m/s 40° 50° B Ug = 4 m/s

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?

A toy rocket operates by having a spring-loaded tube which ejects a small model rocket when released. The spring inside has a spring constant k = 625N/m, the rocket has a mass of 0.100 kg, and the maximum compression of the spring is 0.18 m.  Consider the system of the rocket, spring, and the earth. Consider the interval of time between t1, when the rocket is released from the point of maximum spring compression, and t2, the moment when the spring is fully released and the rocket leaves the launcher. List below the types of energy that are changing during this interval and whether the changes are positive or negative. Please explain how you know.

Explorers in the jungle find an ancient monument in the shape of a large isosceles triangle as shown. The monument is made from tens of thou- sands of small stone blocks of density = 800 kg/m3 . The monument is 15.7 m high and 64.8 m wide at its base and is everywhere 3.60 m thick from front to back. Before the monument was built many years ago, all the stone blocks lay on the ground. (a) Choosing a coordinate system with x = 0 at the center of the pyramid, y = 0 at the base of the pyramid, and z = 0 at the face of the pyramid shown in the diagram, determine the coordinates of the center of mass of the pyramid in the x, y, and z directions. (b) How much work did laborers do on the blocks to put them in position while building the entire monument? Note: The gravitational potential energy of an object–Earth system is given by Ug = MgyCM, where M is the total mass of the object and yCM is the elevation of its center of mass above the chosen reference level.

A lunar landing craft is hovering over the Moon's surface. One-third of its mass is fuel, while the exhaust velocity u is 1200 m/s. How long will it take before the craft runs out of fuel? Assume that the acceleration due to gravity on the surface of the Moon is one-sixth of that on Earth.

Assume that the mass of the bullet, m1, is 4.97 g, the mass of the pendulum, m2, is 1.029 kg, and h is 4.71 cm. (a) Find the velocity of the system after the bullet embeds in the block. m/s(b) Calculate the initial speed of the bullet. m/s

k 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…

Spheres A (mass 0.040 kg), B (mass 0.060 kg) and C (mass 0.080 kg) are approaching the origin as they slide on a frictionless air table. The initial velocities of A and B are v₁ = 1.60 m/s in the negative x direction and VB = 0.90 m/s at an angle 08 = 60°, as shown. All three spheres arrive at the origin at the same time and stick together. After the collision, the masses move at a speed of 0.50 m/s in the -x direction. UC y OB B UB VA A X C a. What is the x-component of the initial velocity of C? b. What is the y-component of the initial velocity of C? c. Calculate the change in mechanical energy of the collision. d. What type of collision is this? Explain.

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