Two particle of mass m, = 1.0 g and m, = 2.0 g had a head-on collision and after collision the two moves together with the same velocity. If m, moves with velocity v, = 3. 0i – 2.0j and m2 on the other hand moves with velocity v, = 4. 0j – 6.0k, find the velocity of the formed particle (both the vector v and its modulus/magnitude), if the components of the vectors v, and v2 are given in the SI units.
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- A 15-gram rifle bullet moving at 200 m/s hits a 3 kg block suspended from a 1:5 m long rope. If the bullet remains lodged inside the block, what will be the maximum angle reached by the ballistic pendulum after the collision?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.A ball with mass m travels with speed v perpendicular to a uniform stick with mass m and length l, which is initially lying at rest on a frictionless table. where along the stick shoudl the ball collide elastically with it, so that the ball and the center of the stick move with equal velocities after the collision?
- The following figure shows two particles of masses m1 and m2, with velocities before the collision of magnitude v1 and v2. If the collision is perfectly elastic, find the magnitude of the velocities v1' and v2' after the collision and the angle of incidence θ (theta), as a function of the masses and velocities before the collision.The sphere of mass m1 = 5 kg falls from a height H = 1.4 m onto the homogeneous board of negligible mass. The board can rotate around a horizontal axis passing through point O, and a body of mass m2 = 3.9 kg is placed on it at a distance b = 1 m from the axis of rotation. The collision is perfectly inelastic. How high does the body of mass m2 rise after the collision (in m) if a = 0.5 m?A 9.50-g bullet, moving horizontally withan initial speed v0, embeds itself in a 1.45-kg pendulum bob that isinitially at rest. The length of the pendulum is L = 0.745 m. Afterthe collision, the pendulum swings to one side and comes to restwhen it has gained a vertical height of 12.4 cm. (a) Is the kineticenergy of the bullet–bob system immediately after the collisiongreater than, less than, or the same as the kinetic energy of thesystem just before the collision? Explain. (b) Find the initial speedof the bullet. (c) How much time does it take for the bullet–bobsystem to come to rest for the first time?
- Four bricks of length L, identical and uniform, are stacked on top of one another in such a way that part of each extends beyond the one beneath. Find, in terms of L, the maximum values of (a) a1, (b) a2, (c) a3, (d) a4, and (e) h, such that the stack is in equilibrium, on the verge of falling.4.12). As given in Figure 4, a thin uniform rod with mass M 3 kg and length I=0.4 m isfixed at one end and positioned horizontally. It swings after being released and collides with astationary block of mass m=1 kg at the lowest point of its swing. Then the block sticks to the lowerend of the rod and they keep swinging together until the rod makes an angle θ with the vertical. Findthe maximum value of θ that the rod block system can move up to. The moment of inertia of the rodabout its center is I rod=1/12mRod L^2Consider a large but thin sheet of plastic with a uniform −3.3 × 10-6 C/m2that is being held parallel to the xz-plane and passing through the origin. At some time a small glass bead with 0.14 kg and 6.5 × 10-6 C is released from rest at 0.9 m on the y-axis. What will be the acceleration of the bead immediately after being released?
- A uniform density sheet of metal is cut into the shape of an isosceles triangle, which is oriented with the base at the bottom and a corner at the top. It has a base B = 13 cm, height H = 19 cm, and area mass density σ. e) Set up an integral to calculate the vertical center of mass of the triangle, assuming it will have the form C ∫ f(y) where C has all the constants in it and f(y) is a function of y. What is f(y)? f)Integrate to find an equation for the location of the center of mass in the vertical direction. Use the coordinate system specified in the previous parts, with the origin at the top and positive downward. g) Find the numeric value for the distance between the top of the triangle and the center of mass in cm.A 4.00 kg mass (mass 1) moves to the right with a speed of 3.00 m/s and collides with a 2.50 kg mass (mass 2) moving to the left with a speed of 1.50 m/s. Assuming the col- lision is elastic, what are the velocities of the first and second masses following the collision? A. mass 1: 2.01 m/s to the right, mass 2: 1.43 m/s to the right B. mass 1: -0.46 m/s, mass 2: 4.04 m/s to the right C. mass 1: -1.05 m/s to the left, mass 2: 2.05 m/s to the right D. mass 1: 1.81 m/s to the right, mass 2: 1.24 m/s to the rightA bullet, having a mass of 0.04 kg moving with a velocity of 450 m/s penetrates a distance of 0.08 m into a wooden block firmly attached to the earth. Assuming a constant accelerating force, compute the following: a) the acceleration of the bullet, b) the accelerating force, c) the time of acceleration, and d) the impulse of the collision.