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Chapter 1: Q57P (page 42)

What is the velocity of aobject when its momentum is $<60, 150, - 30> k g . m / s$ ?

Short Answer

Expert verified

The velocity of the given object is $<20, 50, - 10> m / s .$

Step by step solution

01

Identification of the given information

The mass of the object is, m=3kg.
The momentum of the objectis, $\overset{鈬赌}{p} = <60, 150, - 30> k g . m / s .$

02

Definition of momentum

Momentum is the product of the mass (m) of a particle and its velocity(v).

The momentum can be expressed as,

p=mv.

Momentum is a type of vector quantity;it has both magnitude and direction.

The formula of momentumis given asfollows:

$\overset{鈬赌}{v} = \frac{\overset{鈬赌}{p}}{m}$

03

Step 3:Calculation of the velocity of an object

Substitute 3kg for mand $<60, 150, - 30> k g . m / s$ for $\overset{鈬赌}{p}$ into equation (i) to get the velocity vector.

$\overset{鈬赌}{v} = \frac{<60, 150, - 30> k g . m / s}{3 k g} = <20, 50, - 10> m / s$

Therefore, the velocity of the given object is $<20, 50, - 10> m / s .$ .

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Most popular questions from this chapter

Answer the following questions about the factor $纬$ (gamma) in the full relativistic equation for momentum:

(a) Is $纬$ a scalar or a vector quantity?

(b) What is the minimum possible value of $纬$ ?

(c) Does $纬$ reach its minimum value when an object鈥檚 speed is high or low?

(d) Is there a maximum possible value for $纬$ ?

(e) Does $纬$ become large when an object鈥檚 speed is high or low?

(f) Does the approximation $纬鈮� 1$ apply when an object鈥檚 speed is low or when it is high?

In the periodic table on the inside front cover of this book (or one you find on the internet), for each element there is given the "atomic number," the number of protons or electrons in an atom, and the "atomic mass," which is essentially the number of nucleons, protons plus neutrons, in the nucleus, averaged over the various isotopes of the element, which differ in the number of neutrons. Make a graph of the number of neutrons vs. the number of protons in the elements. You needn't graph every element, just enough to see the trend. What do you observe about the data? (This reflects the need for more neutrons in proton-rich nuclei in order to prevent the electric repulsion of the protons of each other from destroying the nucleus.)

At 10:00 AM you are at the location $<- 3, 2, 5>$ m. By 10:02 AM you have walked to location $<6, 4, 25>$ m. (a) What is $鈭� \overset{鈫�}{r}$ , the change in your position? (b) What is $鈭� t$ , the time interval during which your position changed?

A proton is located at $< 3 脳 10^{- 10}, - 3 脳 10^{- 10}, 8 脳 10^{- 10} > m$ .

(a)What is $\overset{鈫�}{r}$ , the vector from the origin to the location of the proton?

(b)What is $| \overset{鈫�}{r} |$ ?

(c)What is $\hat{r}$ , the unit vector in the direction of $\overset{鈫�}{r}$ ?

A space probe of mass 400 kg drifts past location $<0, 3 脳 10^{4}, - 6 脳 10^{4}> m$ with momentum $<6 脳 10^{3}, 0, - 3.6 脳 10^{3}> k g . m / s$ . Assuming the momentum of the probe does not change, what will be its position 2 minutes later?

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