PHYS 1111L Chapter Force: Average Force & Angle Between Two Vectors

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2 Oct 2017

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The force applied by a body that"s traveling at a definite velocity (rate of speed) for a definite period of time is the average force. The word (cid:820)average(cid:821) is made use of to specify that this velocity is not an accurately measured or (cid:820)instantaneous(cid:821) velocity. Therefore, the mass of the body multiplied by the average velocity over the definite time is equivalent to average force. For a particular interval of time t, the force is described as the frequency of change of momentum. It is hard to compute the rate of change if the time interval is minor. There the term, average force makes an entrance. Over a period of intervals ( t) the rate of change of momentum is average force. Where, the mass of the body is m, the final momentum is v f, the initial momentum is v i, the change in time is t.

Related Questions

which of the vectors below best represents the direction of the impulse vector j⃗ ?

To learn about the impulse-momentum theorem and its applications in some common cases.

Using the concept of momentum, Newton's second law can be rewritten as

?F? =dp? dt, (1)

where ?F? is the net force F? net acting on the object, and dp? dt is the rate at which the object's momentum is changing.

If the object is observed during an interval of time between times t1 and t2, then integration of both sides of equation (1) gives

?t2t1?F? dt=?t2t1dp? dtdt. (2)

The right side of equation (2) is simply the change in the object's momentum p2??p1?. The left side is called the impulse of the net force and is denoted by J? . Then equation (2) can be rewritten as

J? =p2??p1?.

This equation is known as the impulse-momentum theorem. It states that the change in an object's momentum is equal to the impulse of the net force acting on the object. In the case of a constant net force F? net acting along the direction of motion, the impulse-momentum theorem can be written as

F(t2?t1)=mv2?mv1. (3)

Here F, v1, and v2 are the components of the corresponding vector quantities along the chosen coordinate axis. If the motion in question is two-dimensional, it is often useful to apply equation (3) to the x and y components of motion separately.

( The following questions will help you learn to apply the impulse-momentum theorem to the cases of constant and varying force acting along the direction of motion. First, let us consider a particle of mass m moving along the x-axis. The net force F is acting on the particle along the x-axis. F is a constant force.)

A) The particle starts from rest at t=0. What is the magnitude p of the momentum of the particle at time t? Assume that t>0.

B) The particle starts from rest at t=0. What is the magnitude v of the velocity of the particle at time t? Assume that t>0.

C) The particle has the momentum of magnitude p1 at a certain instant. What is p2, the magnitude of its momentum ?t seconds later?

D) The particle has the momentum of magnitude p1 at a certain instant. What is v2, the magnitude of its velocity ?t seconds later?

E) Find the magnitude of the impulse J delivered to the particle.

F) Which of the vectors below best represents the direction of the impulse vector J??
(Figure 1)

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puceworm982

The questions are below:

) Ion Rocket Engine. A special type of rocket engine useselectricity for propulsion: the ion engine. A soft metal, such ascesium, is vaporized and then electrified (ionized) with highvoltage. These cesium ions are the accelerated by strong electricfields to produce a current of atoms at high velocity. Outside theengine, the ions are then recombined with electrons to restoreelectrical neutrality.

A particular ion engine has an exhaust velocity of 20,000 m/sec.The mass flow (dm/dt) is just 1 milligram per second.

a) What is the thrust produced by this engine?

b) The engine propels a 200 kg spacecraft. What velocity change(delta-v) is achievable by running the engine continuously for onesolid year? (For simplicity, assume a constant mass for the system.One year = 31.56 million seconds.)
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) Potential Energy. How much work is required to lift one metricton (1000 kg) of water to an altitude of 1000 meters? (The Sun isdoing this all this time to the Earthâs weather.)
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q) Kinetic Energy 1. A car has a mass of 1200 kg. How much kineticenergy does it have when traveling at a speed of 30 m/sec?

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Kinetic Energy 2. The Space Shuttle orbits the Earth at a speed ofsome 7750 meters per second (which is about 260 times that of atypical highway driving speed). With a typical payload, the Shuttlehas a mass of 120,000 kg.

a) What is the kinetic energy of the Shuttle in orbit?
b) The Shuttle reaches orbit in some 500 seconds. At what rate ofwork (power) did the rocket engines perform on the Shuttle to placethe craft and its payload into orbit? Compare this to the maximumpower output of a typical nuclear electric generatingstation.
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Solar Power. In space, outside the atmosphere, some 1360 Watts ofradiant power pass through every square meter (at normalincidence).

a) What total amount of power does the Earth intercept from theSun? (The projected area of the Earth is ?RE2, where RE is theradius of the Earth, 6.38 million meters.)

b) Compare this figure to the total amount of power produced by allof human civilization, currently some 40 trillion (1012) Watts.What conclusions about solar power can you draw from thiscomparison?

q

-) Angular Momentum. Assuming a uniform distribution of mass insidethe Earth, calculate:

a) the Earthâs moment of inertia, I;
b) its angular momentum, L = omega(omega=2pi/T) the angularmomentum of the Moon in its orbit around the Earth (L = mvr).Compare these two values. (The sidereal period of the Moon is 27.3days; its mass is 1/81 of that of the Earth; its average orbitalradius is 383,000 km.)

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Q0 Water Pressure. Calculate the value of the water pressure at theChallenger Deep, the deepest known place on the surface of theEarth. The currently accepted depth of the water there is 10,911meters. (This is deep enough to cover Mount Everest, and still havemore than one mile of water above the peak. On January 23, 1960,Swiss explorer Jacques Piccard and US Navy Lieutenant Don Walshbecame the first, and so far, the only people ever to visit thisremote place, descending in the Italian-built bathyscaphTrieste.)

q-8
Mass of Earthâs Atmosphere. The pressure of the Earthâs atmosphereat sea level is 101,300 Pascals (Newtons per square meter.) Thismeans that every square meter of Earthâs surface supports a weightof 101,300 Newtons. From this, determine the mass of Earthâsatmosphere. What fraction of the Earthâs total mass is this?

PHYS 1111L Chapter Force: Average Force & Angle Between Two Vectors

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