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- Suppose you are navigating a spacecraft far from other objects. The mass of the spacecraft is 4.0 104 kg (about 40 tons). The rocket engines are shut off, and you're coasting along with a constant velocity of ‹ 0, 30, 0 › km/s. As you pass the location ‹ 6, 9, 0 › km you briefly fire side thruster rockets, so that your spacecraft experiences a net force of ‹ 5.0 105, 0, 0 › N for 20 s. The ejected gases have a mass that is small compared to the mass of the spacecraft. You then continue coasting with the rocket engines turned off. Where are you an hour later? (Think about what approximations or simplifying assumptions you made in your analysis. Also think about the choice of system: what are the surroundings that exert external forces on your system?)f = m(a) Find the speed at which Superman (mass=90.0 kg) must fly into a train (mass = 17485 kg) traveling at 65.0 km/hr to stop it. Running into the train at that speed would severely damage both train and passengers. (b) Calculate the minimum time Superman must take to stop the train if the passengers experience an average horizontal force of 0.410 their own weight. (c) How far does the train then travel while being slowed to a stop?Which one of the following forces is non-conservative? O The electric force The Elastic force O The gravitational force O Air resistance
- A boat with mass of 7.4 * 10° kg is traveling at 6.1 * 10' m/s. What is the magnitude of the force required to stop the boat if it undergoes a displacement of 1.2 * 10' m? Express your answer in Newtons.Two tug boats pull a barge directly against the current of the river. The tow ropes from the tugs are at an angle of 37° to each other; the forces exerted by the tugs along the ropes ate both 4200 N. If the current produces a force of 45 N, what is the force with which the barge is pulled forward?A 547g squirrel with a frontal surface area of 0.0145m2 falls to the ground from a 5.3m tree. Assume the density of air is 1.21kg/m3. Neglecting the drag force, what is the velocity, in meters per second, of a 56kg person after falling, from rest, by that same distance?
- A freight train consists of two 8.00×104 kg5.60×104 kg engines and 45 cars with average masses of 5.50×104 kg5.50×104 kg. (a) What force must each engine exert backward on the track to accelerate the train at a rate of 4.00×10−2 m/s if the force of friction is 6.20×105 N, assuming the engines exert identical forces? This is not a large frictional force for such a massive system. Rolling friction for trains is small, and consequently trains are very energy-efficient transportation systems. (b) What is the force in the coupling between the 37th and 38th cars (this is the force each exerts on the other), assuming all cars have the same mass and that friction is evenly distributed among all of the cars and engines?A truck is towing a 10,000-N car at a constant speed up a hill that makes an angle of a=5.0° above the horizontal. A rope is attached from the truck to the car at an angle ß=10.0° above the horizontal. (Friction is negligible.) (a) Draw a free-body diagram showing the forces acting on the car. Indicate the angle that each force makes either with either the vertical or horizontal direction. (b) What is the tension in the rope?