Physics, 07.03.2020 04:55 kordejah348

Suppose two masses labelled m1 and m2, are speeding toward each other at time t=0s. The first mass 1 has a mass and speed has values of m1=3 kg and v1,i= 2 m/s (to the right). Mass 2 has a mass and speed of m2 = 5kg with an initial speed of v2,I = 5 m/s (to the left). Then at some time t there is an elastic collision between the two masses. What is the final speed and direction of m1 and m2 after the collision.

Answers: 2

Show answers

Answers

Answer from: abby1919

The velocity of the first mass is 19.9 m/s to the left

The velocity of the second mass is 8.14 m/s to the left

Explanation:

In an elastic collision, both momentum and kinetic energy is conserved.

$\frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2 = \frac{1}{2}m_1v_{11}^2 + \frac{1}{2}m_2v_{22}^2\\m_1v_1 + m_2v_2 = m_1 v_{11} + m_2 v_{22}$

There is a lot of elaboration to solve these two equations, but substituting the values given in the question will ease the hard work.

$\frac{1}{2}(3)(2)^2 + \frac{1}{2}(5)(5)^2 = \frac{1}{2}(3)v_{11}^2 + \frac{1}{2}(5)v_{22}^2\\(3)(2) - (5)(5) = (3) v_{11} + (5) v_{22}\\6 + \frac{125}{2} = \frac{1}{2}(3)v_{11}^2 + \frac{1}{2}(5)v_{22}^2\\-19 = 3 v_{11} + 5 v_{22}\\v_{11}^2 = (\frac{-19 - 5v_{22}}{3})^2\\{\rm Plugging ~this ~into~the~kinetic~energy~equation~gives:}\\\frac{137}{2} = \frac{3}{2}(\frac{-19-5v_{22}}{3})^2 + \frac{5}{2}v_{22}\\137 = \frac{361 + 190v_{22} + 25v_{22}^2}{3} + \frac{5}{2}v_{22}$

Rearranging the equations gives

$137 = \frac{722 + 380v_{22} + 50v_{22}^2 + 15v_{22}}{6}\\822 = 722 + 395v_{22} + 50v_{22}^2\\50v_{22}^2 + 395v_{22} - 100 = 0\\10v_{22}^2 + 79v_{22} - 20 = 0$

Solving this equation quadratically gives the velocity of the second mass:

$v_{22} = -8.14~{\rm or}~0.24$

There are two roots to the quadratic equation, but we intuitively know that the bigger mass with the higher initial velocity will have the same direction after the collision.

Therefore, the final speed of the second mass is 8.14 m/s to the left.

Now, it is easy to calculate the velocity of the first mass.

$-19 = (3)v_{11} -(-8.14)5\\ v_{11} = -19.9$

Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

Answer from: Quest

Answer the above statement is ( false );

Other questions on the subject: Physics

Physics, 22.06.2019 01:10, caguil00

Asteam power plant operates on an ideal reheat rankine cycle between the pressure limits of 15 mpa and 10 kpa. the mass flow rate of steam through the cycle is 12 kg/s. steam enters both stages of the turbine at 500°c. if the moisture content of the steam at the exit of the low-pressure turbine is not to exceed 10 percent, determine (a) the pressure at which reheating takes place, (b) the total rate of heat input in the boiler, and (c) the thermal efficiency of the cycle. also, show the cycle on a t-s diagram with respect to the saturation lines. (2.15 mpa; 45.0 mw; 42.6%)

Answers: 3

continue

Physics, 22.06.2019 08:00, kaylaamberd

Aheat engine running backward is called a refrigerator if its purpose is to extract heat from a cold reservoir. the same engine running backward is called a heat pump if its purpose is to exhaust warm air into the hot reservoir. heat pumps are widely used for home heating. you can think of a heat pump as a refrigerator that is cooling the already cold outdoors and, with its exhaust heat qh, warming the indoors. perhaps this seems a little silly, but consider the following. electricity can be directly used to heat a home by passing an electric current through a heating coil. this is a direct, 100% conversion of work to heat. that is, 19.0 \rm kw of electric power (generated by doing work at the rate 19.0 kj/s at the power plant) produces heat energy inside the home at a rate of 19.0 kj/s. suppose that the neighbor's home has a heat pump with a coefficient of performance of 4.00, a realistic value. note: with a refrigerator, "what you get" is heat removed. but with a heat pump, "what you get" is heat delivered. so the coefficient of performance of a heat pump is k=qh/win. an average price for electricity is about 40 mj per dollar. a furnace or heat pump will run typically 200 hours per month during the winter. what does one month's heating cost in the home with a 16.0 kw electric heater? what does one month's heating cost in the home of a neighbor who uses a heat pump to provide the same amount of heating?

Answers: 2

continue

Physics, 22.06.2019 13:40, sbudlove2838

What is the thinnest soap film (excluding the case of zero thickness) that appears black when illuminated with light with a wavelength of 480 ? the index of refraction of the film is 1.34, and there is air on both sides of the film. express your answer in nanometers. hint 1. how to approach th

Answers: 1

continue

Physics, 22.06.2019 22:00, jayonelijah

Ultraviolet radiation is dangerous because it has a high enough energy to damage skin cells. what is the best explanation of the relationship between wavelength and wave energy? a) wave energy is related only to frequency, not wavelength. b) longer wavelengths have lower frequencies but higher energy. c) the shorter the wavelength, the lower the frequency and the higher the energy. d) the shorter the wavelength, the higher the frequency and the higher the energy.

Answers: 3

continue

You know the right answer?

Suppose two masses labelled m1 and m2, are speeding toward each other at time t=0s. The first mass 1...