A box of mass M=1980 g, filled with sand, is suspended from a 1=1.5 m long rope. The length of the rope is much larger than the dimensions of the box. A bullet with mass m=20 g flying with a velocity of v=500 m/s in the horizontal direction hits the box and gets stuck. Find the maximum deviation angle of the rope from the vertical. Neglect the drag force of the air. Take g=10m/s^2.
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A box of mass M=1980 g, filled with sand, is suspended from a 1=1.5 m long rope. The length of the rope is much larger than the dimensions of the box. A bullet with mass m=20 g flying with a velocity of v=500 m/s in the horizontal direction hits the box and gets stuck. Find the maximum deviation angle of the rope from the vertical. Neglect the drag force of the air. Take g=10m/s^2.
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- A box of mass m = 25 kg slides with an initial speed v0 = 7.0m/s up a slope which forms the angle = 12° relative to the horizontal. A strong wind is blowing with fixed horizontals force Fv = 50N to the right (see figure). The coefficient of friction in motion is uk = 0.18. (a) What is the transverse force acting on the box from the slope? (b) How far, L, does the box slide up the slope before it stops? (c) What must be the minimum coefficient of friction at rest, us, for the box to slide not back down the hill? F₁ m Vo L DA particle, which remains at rest, is acted on by three forces F, G and H. The force F has magnitude 55 N and is directed to the left and up making an angle of 45 degrees with the vertical The force G is directed vertically down and H is directed to the right and up making an angle of 60 degrees with the vertical. Find the magnitude of the vectors G and H, giving your answers to one decimal place. The magnitude of G is N (to 1 d.p.) The magnitude of H is N (to 1 d.p.)A child is playing on a hill with a cardboard box. The combined mass of child and box is ? = 120 kg. He climbs into box, which is initially at rest, at the top of the hill. The hill is inclined at an angle of 30 degrees with respect to the horizontal. The coefficients of static and kinetic friction between the box and the hill are mu s = 0.4 and mu k = 0.2. Consider that the box (with child inside) has begun to slide down the hill (you can assume that it has been given a brief push to get it started moving). What is the magnitude of the acceleration of the box? b. If the hill is 4 m tall, what is the child’s speed when he reaches the bottom? c. At the bottom of the hill, the ground becomes level (horizontal), but the coefficients of friction do not change. How far does the child slide before he comes to a stop? Thank you in advance, it's a lengthy question and I really need help :)
- A black aluminum glider floats on a film of air above a level aluminum air track. Aluminum feels essentially no force in a magnetic field, and air resistance is negligible. A strong magnet is attached to the top of the glider, forming a total mass of 240 g. A piece of scrap iron attached to one end stop on the track attracts the magnet with a force of 0.823 N when the iron and the magnet are separated by 2.50 cm. (a) Find the accelerationof the glider at this instant. (b) The scrap iron is now attached to another green glider, forming total mass 120 g. Find the acceleration of each glider when the gliders are simultaneously released at 2.50-cm separation.The figure shows a container of mass m₁ = 1.7 kg connected to a block of mass m₂ by a cord looped around a frictionless pulley. The cord and pulley have negligible mass. When the container is released from rest, it accelerates at 1.0 m/s² across the horizontal frictionless surface. What are (a) the tension in the cord and (b) mass m₂? (a) Number (b) Number i Units Units m₁ mq >Consider a conical pendulum with a bob of mass m = 58.0 kg on a string of length L = 10.0 m that makes an angle of 8 = 2.00° with the vertical. (Consider +î to be towards the center of the circular path and +j to be upward.) (a) Determine the horizontal and vertical components of the force exerted by the string on the pendulum. NI+ Nj (b) Determine the radial acceleration of the bob. m/s²
- Two carts, A and B, roll on inclined planes with negligible friction. Cart A has a mass of 1.3 kg and it is on a plane inclined at an angle of ? θ ? θ = 63 degrees. Cart B has a mass of 2.5 kg and it is on a plane inclined at an angle of ? ϕ ? ϕ = 14 degrees. The carts are connected by a (nearly) massless string that runs over a (nearly) massless and frictionless pulley. Find the tension (in newtons) in the string.In a two-dimensional tug-of-war, Alex, Betty, and Charles pull horizontally on an automobile tire at the angles shown in the picture. The tire remains stationary in spite of the three pulls. Alex pulls with force F A of magnitude 214 N, and Charles pulls with force F c of magnitude 183 N. Note that the direction of F c is not given. What is the magnitude of Betty's force F B if Charles pulls in (a) the direction drawn in the picture or (b) the other possible direction for equilibrium? Alex Charles 145° Betty (a) Number i Units (b) Number i Units >Students are performing an experiment with the setup shown above, where a block of mass M sits on a horizontal table. The coefficient of kinetic friction between the block and the table is μk. The block is connected to a hanging object over a pulley. The pulley has negligible mass and friction. The string connecting the two is very light and does not stretch. The students add mass to the hanging object so that its mass is m, where m < M, and the block-hanging object system is released from rest. The hanging object falls for a distance h, at which point it collides with the ground and comes to rest. The block on the table keeps sliding and travels a total distance d before coming to rest. It does not reach the pulley, and d > h. A student creates a data table (see image) for the net force exerted on the block during the speeding up and slowing down portions of the experiment. (d) Does the block of mass M spend more time speeding up or slowing down? Justify your answer.