2. A skateboarder with his board can be modeled as a particle of mass 76.0 kg, located at his center of mass 0.500 m above the ground. As shown in figure, the skateboarder starts from rest in a crouching position at one lip of a cylinder of radius 6.80 m with its axis horizontal. On his descent, the skateboarder moves without friction and maintains his crouch so that his center of mass moves through one quarter of a circle. Find his speed at the bottom of the half-pipe (point B). Answer: VB 11.22 m/s Solution
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- A person of mass 86.5 kg is initially at rest on the edge of a large stationary platform of mass 190 kg, supported by frictionless wheels on a horizontal surface. The person jumps off the platform, traveling a horizontal distance of 1.00 m while falling a vertical distance of 0.500 m to the ground. What is the final speed of the platform? please solveAs part of a carnival game, a my = 0.653 kg ball is thrown at a stack of 23.8 cm tall, mo = = 0.363 kg objects and hits with a perfectly horizontal velocity of Ubi = 10.8 m/s. Suppose that the ball strikes the topmost object. Immediately after the collision, the ball has a horizontal velocity of bf = 3.10 m/s in the same direction, the topmost object has an angular velocity of @= 1.63 rad/s about its center of mass, and all the remaining objects are undisturbed. Assume that the ball is not rotating and that the effect of the torque due to gravity during the collision is negligible. If the object's center of mass is located r = 16.7 cm below the point where the ball hits, what is the moment of inertia I, of the object about its center of mass? What is the center of mass velocity Uo.cm of the tall object immediately after it is struck? (1) 0 Io = b.J Vo.cm = kg-m² m/sA woman weighing 61.5 kg stands at one end of a 120-kg raft that is 6.00 m long. The other end of the raft is 0.500 m from a pier. So, before the woman moves, she is at a total distance of 6.50 m away from the pier. The woman walks toward the pier until she gets to the other end of the uniform raft and stops there. What is the distance between the uniform raft and the pier?
- In the instant of the figure, two particles move in an xy plane. Particle P₁ has mass 7.40 kg and speed v₁ = 1.91 m/s, and it is at distance d₁ = 9.52 m from point O (the figure is not drawn to scale). Particle P₂ has mass 2.73 kg and speed v2 = 2.37 m/s, and it is at distance d₂ = 8.89 m from point O. What is the magnitude of the net angular momentum of the two particles about O? P₁O Number i Units ས། ྋ P2Far out in space, a mass m1=143300.0 kg rocket and a mass m2= 230500.0 kg rocket are docked at opposite ends of a motionless 89.0m long connecting tunnel. The tunnel is rigid and has a mass of 10300.0kg.a) How far from the 143300.0-kg rocket is the center of mass? 5.46×101 m b) The rockets start their engines simultaneously, each generating 54680.0N of thrust in opposite directions. What is the structure's angular velocity after 25.7s?A man with mass m1 = 51 kg stands at the left end of a uniform boat with mass m2 = 168 kg and a length L = 3.3 m. Let the origin of our coordinate system be the man’s original location as shown in the drawing. Assume there is no friction or drag between the boat and water. 1) If the man now walks to the right edge of the boat, what is the location of the center of mass of the system? 2) After walking to the right edge of the boat, how far has the man moved from his original location? (What is his new location?) 3) After the man walks to the right edge of the boat, what is the new location the center of the boat? 4) Now the man walks to the very center of the boat. At what location does the man end up?
- A merry-go-round at an amusement park consists of an outer ring of horses and an inner ring of elephants. The ring of eight horses has a radius of rh = 8.9 m. Each of the eight horses has a mass mh = 110 kg. The ring of four elephants has a radius of re = 6.5 m and each of the four elephants has a mass me = 195 kg. The platform of the merry-go-round itself has a mass of mp = 1500 kg and a radius of rp = 10.5 m. At it’s operating speed, the merry-go-round makes one revolution every t = 11 s.Enter an expression for the total moment of inertia of the carousel about its axis, in terms of the defined quantities. I =Calculate the moment of inertia of the carousel about its axis, in units of kilogram meters squared. I =Enter an expression for the angular speed of the carousel, in terms of the defined quantities. ω = Calculate the carousel’s angular speed, in radians per second. ω =A skateboard of mass m rests on the top of a hemispheric dome of radius R. After giving the skateboard a small kick, imparting an initial speed of vo, it begins rolling down the dome. Let the angle 0 indicate the location of the skateboard as it rolls down the surface of the dome. R 1. Eventually, the skateboard will lose contact with the dome. Given m, R, vo, and g, find the angle 0. at which the skateboard loses contact. Express your answer symbolically (i.e. without numbers). Check your work. Suppose you choose m = 1.5 kg, vo = g = 9.81 m/s. In this case, your answer should evaluate to 0. = 34.2°. 4.5 m/s, R = 4.3 m, and 2. Given m, R, and g, determine the range of speeds for which it is impossible to remain in contact with the wall at all.A hammer is made of a solid sphere and a solid rod of negligible mass attached to the sphere. The radius of the sphere is R=25.0 cm and its mass is m=0.100 kg. The distance from the center of the sphere to the pivot is l=1.00 m. The hammer is released from it is initial position at the angle ϕ=30° with the vertical direction (see Figure below). Find the velocity of its center of mass at the lowest point. The moment of inertia of a solid sphere is 2mR2/5 about the axis through any diameter.
- A woman weighing 57.1 kg stands at one end of a 120-kg raft that is 6.00 m long. The other end of the raft is 0.500 m from a pier. So, before the woman moves, she is at a total distance of 6.50 m away from the pier. The woman walks toward the pier until she gets to the other end of the uniform raft and stops there. What is the distance between the uniform raft and the pier?8. A 50.0 kg cart is rolling to the left on a frictionless surface at 5.00 m/s. A 15.0 kg package slides down a chute inclined at 37° and leaves the end of the chute with a speed of 3.00 m/s. The package lands in the cart and they roll off together. The lower 37 end of the chute is a vertical distance of 4.00 m above the bottom of the cart. 4,00 m (a) What is the speed of the package just before it lands in the cart? (b) What is the velocity of the cart after the package lands in it?Use g = 10 m/s/s in the following problems. A). A 250 gram meter stick has a center of mass at the 50 cm mark. You place a pivot at the 50 cm mark and hang 100 grams at the 40 cm mark. How much mass must you hang at the 90 cm mark to balance the system? B). A 250 gram meter stick has a center of mass at the 50 cm mark. You place a pivot at the 50 cm mark, hang 100 grams at the 40 cm mark and hang 200 grams at the 30 cm mark. How much mass must you hang at the 90 cm mark to balance the system?