Note! You must include correct and consistent signs in your answers, or you will lose points. Assume that all motions and forces in the following problem set lie along the same straight line.
Newton’s Laws and Automobile Safety
Newton’s three laws of motion govern the behavior of all ordinary objects in nature, including automobiles. You will be much better equipped to understand vehicular safety if you have truly mastered Newton’s Laws. To demonstrate this, consider the following situation:
You are a passenger in an automobile. At a speed of 30 mi/hr, your crash head on into a brick wall. You are not wearing seat belts.
1.) Despite the fact that the car has crunched to a total stop, one of Newton’s Laws predicts that you will continue to fly forward at 30 mi/hr until you collide with the windshield or dash. Which law? Explain! (Do not simply quote the law! Show how it applies to this particular situation.)
2.) Show that your initial velocity of 30 mi/hr can be converted to 13.4 m/s.
3.) Your collision with the windshield/dash is called the “second collision” (the first collision occurred when the car collided with the brick wall). It is quite possible that in this second collision you (the passenger) may go right through the windshield, but instead let us assume that you are brought to a dead stop (zero velocity) in 0.10 seconds. Write down the appropriate formula for calculating acceleration in terms of velocity (we used this in the section on Motion). What is your acceleration in m/s2 ?
4.) According to Newton’s 2nd Law your sudden deceleration in the “second collision” ( the person’s collision with the windshield/dash, not the car’s collision with the wall) implies that there is a force acting on you (the person) at this moment. Which object is the direct source of this force (i.e., which object does this force come directly from), and which one of Newton’s Laws explains its origin?
5.) Assuming that your mass is 70 kg, and using the acceleration obtained in problem #3, calculate the force on you in Newtons. (The directions of all vector quantities, and the plus and minus signs that describe them for straight line motion, should be consistent with the ones you used in problem # 3.)
6.) Change your answer to pounds, using 1 N = 0.225 lb. (Include the correct sign in your answer.)
HOMEWORK # 3,
Useful Information: G = 6.67 x 10-11 Nm
WEIGHT :
1. What is the weight of a 70 kg astronaut
a) on the Earth
b) on the moon, where g = 1.7 m/s2
c) on Venus, where g = 8.7 m/s2
d) in outer space ?
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CIRCULAR MOTION :
2. A stone is spun with a speed of 2.5 m/s in a circle of radius 0.5m .
a) What is the stone’s centripetal acceleration?
b) If the stone has a mass of 2 kg , what is the force on the stone?
c) Relative to the circle, in what direction is the force on the stone?
3. A jet plane, traveling at a speed of 300 m/s, pulls out of a dive in a circular arc of radius 2500 m.
a) What is the plane’s acceleration?
b) Acceleration can also be measured in units of “g’s”, where one g of acceleration is defined as
g = 9.8m/s2 . Given your calculation of the plane’s acceleration, how many “g’s” of acceleration is the pilot of the plane experiencing? (Hint: Construct a conversion factor using the equation
1g = 9.8m/s2 and convert your acceleration from units of m/s2 to an acceleration in units of “g’s”.)
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GRAVITY :
4. Calculate the force of gravity between two 200 kg refrigerators that are 1.0 m apart (center to center).
5. If the mass of the earth was suddenly tripled, by what factor would your weight be changed? (That is, your new weight would be what factor times your old weight)?
6. If the moon changed its orbit so that it was only half as distant as it is now, by what factor would the gravitational force on the moon due to the earth be changed? ( That is, by
what factor must one multiply the old force to get the new force?)
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