Since astronauts in orbit are apparently weightless, a clever method of measuring their masses is needed to monitor their mass gains or losses to adjust diets. One way to do this is to exert a known force on an astronaut and measure the acceleration produced. Suppose a net external force of 50.0 N is exerted and the astronaut’s acceleration is measured to be 0.893 m/s2.
(a) Calculate her mass.
(b) By exerting a force on the astronaut, the vehicle in which they orbit experiences an equal and opposite force. Discuss how this would affect the measurement of the astronaut’s acceleration. Propose a method in which recoil of the vehicle is avoided.
(a) The mass of the astronaut is 56 kg.
(b) The vehicle will not recoil.
The Newton’s second law of motion states that the acceleration of a system is directly proportional to the net external force acting on the system and is inversely proportional to the mass of the system. It is mathematically represented as:
where Fnet is the net force, m is the mass, and a is the acceleration.
By putting values 50 N for Fnet and 0.893 m/s2 for a in equation (i) and we get,
Hence, the mass of the astronaut is 56 kg.
Write the expression for determining the acceleration due to another source.
Here, is the acceleration due to mass experienced by another source, . Is the acceleration of the astronaut, and is the acceleration of the vehicle.
When the force is exerted by another source, then the vehicle will not be able to recoil. Hence, the vehicle will not recoil.
Consider the tension in an elevator cable during the time the elevator starts from rest and accelerates its load upward to some cruising velocity. Taking the elevator and its load to be the system of interest, draw a free-body diagram. Then calculate the tension in the cable. Among the things to consider are the mass of the elevator and its load, the final velocity, and the time taken to reach that velocity.
Commercial airplanes are sometimes pushed out of the passenger loading area by a tractor.
(a) An 1800-kg tractor exerts a force of 1.75×104 N backward on the pavement, and the system experiences forces resisting motion that total 2400 N. If the acceleration is 0.150 m/s2, what is the mass of the airplane?
(b) Calculate the force exerted by the tractor on the airplane, assuming 2200 N of the friction is experienced by the airplane.
(c) Draw two sketches showing the systems of interest used to solve each part, including the free-body diagrams for each.
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