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- One hazard of space travel is the debris left by previous missions. There are several thousand objects orbiting Earth that are large enough to be detected by radar, but there are far greater numbers of very small objects, such as flakes of paint. Calculate the magnitude of the force, in newtons, exerted by a 0.085-mg chip of paint that strikes (and sticks to) a spacecraft window at a relative speed of 4.25 × 103 m/s, given the collision lasts 6.1 × 10– 8 s. F =You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors or windows. You decide to do some experiments to find out more about your strange situation. Your own body mass is 50.1 kg. You pick up an object and drop it from rest, starting at a height of 1.97 meters above the floor, and it hits the floor 0.380 seconds later. You can ignore air resistance. Based on the outcome of this experiment, when you step on the scale provided for you, what weight will it register for your body? 684 N 911 N 1,367 N 491.5 NAt the scene of an accident, two traffic experts appear to determine which of the drivers was at fault considering that it was a highway where the speed limit is 80 km / h. The data collected in the field indicate that the vehicles stuck and skidded together a length of 25 m on the pavement whose dynamic friction coefficient is μk = 0.30. Considering that the masses of vehicles A and B are 2300 kg and 1500 kg, respectively, specify which of the cars was speeding at the moment of impact and by how much it exceeded the speed limit. Express your result in km / h for the purposes of the expertise.
- You wake up one morning to find yourself in a strange room with opaque walls, and no visible doors or windows. You decide to do some experiments to find out more about your strange situation. Your own body mass is 56.0 kg. You pick up an object and drop it from rest, starting at a height of 2.35 meters above the floor, and it hits the floor 0.346 seconds later. You can ignore air resistance. Based on the outcome of this experiment, when you step on the scale provided for you, what weight will it register for your body? 549.4 N 1,100 N 1,466 N 2,199 NA person is standing still on a horizontal surface. They are holding a dumbbell weighing 10 kg in their right hand, with their arm extended horizontally. The person's mass is 70 kg. Assume that the force due to gravity acts at the center of mass of the person, which is located 1 meter above the ground and directly above the midpoint of their feet. The center of mass of the dumbbell is 0.5 meters from the shoulder joint (the point where the arm is attached to the body). Draw a free body diagram for the person and the dumbbell. Identify all the forces acting on the person. Calculate the torque about the feet caused by the weight of the person and the dumbbell.A wagon is rolling forward on level ground. Friction is negligible. The person sitting in the wagon is holding a rock. The total mass of the wagon, rider, and rock is 99.5 kg. The mass of the rock is 0.277 kg. Initially the wagon is rolling forward at a speed of 0.488 m/s. Then the person throws the rock with a speed of 16.6 m/s. Both speeds are relative to the ground. Find the speed of the wagon after the rock is thrown (a) directly forward in one case and (b) directly backward in another. (a) vi (b) v-
- In a research facility, a person lies on a horizontal platform which floats on a film of air. When the person's heart beats, it pushes a mass m of blood into the aorta with speed v, and the body and platform move in the opposite direction with speed V. Assume that the blood's speed is 56.5 cm/s. The mass of the person + platform is 54.0 kg. The platform moves 5.95 ✕ 10−5 m in 0.160 s after one heartbeat. Calculate the mass (in g) of blood that leaves the heart. Assume that the mass of blood is negligible compared with the total mass of the person, and the person + platform is initially at rest. (Also assume that the changes in velocity are instantaneous.)Three ice skaters meet at the center of a rink and each stands at rest facing the center, within arm's reach of the other two. On a signal, each skater pushes himself away from the other two across the frictionless ice. After the push, skater A with mass mA = 85.0 kg moves in the negative y-direction at 3.00 m/s and skater B with mass mB = 95.0 kg moves in the negative x-direction at 4.00 m/s. Find the x- and y-components of the 90.0 kg skater C's velocity (in m/s) after the push. vCx = vCy =A person is crossing a bridge. The bridge is 3.2 meters long and is 25 kg. One side of the bridge rests on the ground while the other side of the bridge is elevated 25 degrees above the ground. The end of the bridge that is elevated is connected to a rope, which is attached to a overhanging section of a cliff. The person walking across is 62 kg, and walks three quarters of the way to the rope end of the bridge then stops. Please determine the magnitude of the force that the ground exerts on the bridge. (use image for reference)
- To keep the calculations fairly simple, but still reasonable, we shall model a human leg that is 92.0 cm long (measured from the hip joint) by assuming that the upper leg and the lower leg (which includes the foot) have equal lengths and that each of them is uniform. For a 70.0 kg person, the mass of the upper leg is 8.60 kg, while that of the lower leg (including the foot) is 5.25 kg. Find the location of the center of mass of this leg, relative to the hip joint, if it is (a) fully extended, and (b) bent at the knee to form a right angle with the upper leg.A rod of length 30.50 cm has linear density (mass per length) given by A = 50.0 + 25.0x where x is the distance from one end, and A is measured in grams/meter. (a) What is its mass? (b) How far from the x = 0 end is its center of mass? mA rocket motor is undergoing a "bench test." It is attached to a fixed support by four large springs of constant 10^6 N/m. The motor burns fuel at a rate of 50 kg/s. When the motor is running the springs are observed to stretch 1.5 cm. Determine the exhaust speed of the burned fuel.