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Chapter 6: Q15 P (page 276)

A baseball of mass $144 g$ has a velocity of $(22, 23, - 11)$ . What is the kinetic energy of the baseball?

Short Answer

Expert verified

The kinetic energy of the baseball is, $81.65 J$ .

Step by step solution

01

Identification of the given data

The given data can be listed below as,

- The mass of baseball is, $m = 144 g = 144 \times 10^{3} kg$

- The speed of baseball is, $v = (22, 23, - 11) m / s$

02

Significance of kinetic energy

The kinetic energy is a form of energy that an object or particle retains due to its motion.

03

Determination of the kinetic energy in +x direction

The relation of kinetic energy is expressed as,

$K - \frac{1}{2} m v^{2}$

(i)

Here $K$ is the kinetic energy, $m$ is the mass of the baseball and $V$ is the speed of the baseball.

The speed of the baseball is expressed as,

$V = (22 \hat{i} + 23 \hat{j} - 11 \hat{k}) m / s$

$\overset{L}{v} ∣ = \sqrt{22^{2} + 23^{2} + (- 11)^{2}} m / s$

$= 33.67 m / s$

Substitute $144 \times 10^{- 3} kg$ for $m$ and $33.67 m / s$ for $v$ in the equation (i).

$K = \frac{1}{2} \times 144 \times 10^{- 3} kg \times (33.67 m / s)^{2}$

$= 81.65 J$

Hence the kinetic energy of the baseball is, localid="1657723057055" $81.65 J$ .

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Most popular questions from this chapter

You throw a ball of mass 160gupward (Figure 6.79). When the ball is 2mabove the ground, headed upward (the initial state), its speed is 19m/s. Later, when the ball is again 2mabove the ground, this time headed downward (the final state), its speed is 19m/s. What is the change in the kinetic energy of the ball from initial to final state?

Figure 6.77 is a graph of the energy of a system of a planet interacting with a star. The gravitational potential energy $U g$ is shown as the thick curve, and plotted along the vertical axis are various values of $K + U g .$

Suppose that $K + U g$ of the system is A. Which of the following statements are true? (a) The potential energy of the system decreases as the planet moves from $r_{1}$ to $r_{2}$ . (b) When the separation between the two bodies is $r_{2}$ , the kinetic energy of the system is $(A - B)$ . (c) The system is a bound system; the planet can never escape. (d) The planet will escape. (e) When the separation between the two bodies is $r_{2}$ , the kinetic energy of the system is (B − C). (f) The kinetic energy of the system is greater when the distance between the star and planet is $r_{1}$ than when the distance between the two bodies is $r_{2}$ .

Suppose instead that $K + U g$ of the system is B. Which of the following statements are true? (a) When the separation between the planet and star is $r_{2}$ , the kinetic energy of the system is zero. (b) The planet and star cannot get farther apart than $r_{2}$ . (c) This is not a bound system; the planet can escape. (d) When the separation between the planet and star is $r_{2}$ , the potential energy of the system is zero.

Outside the space shuttle, you and a friend pull on two ropes to dock a satellite whose mass is $700 kg$ . The satellite is initially at position $(3 .5, - 1, 2 .4) m$ and has a speed of $4 m / s$ . You exert a force $(- 400, 310, - 250) N$ . When the satellite reaches the position $(7 .1, 3 .2, 1 .2) m$ its speed is $4 .01 m / s$ . How much work did your friend do?

A nucleus whose mass is $3 .917268 \times 10^{- 25} kg$ undergoes spontaneous alpha decay. The original nucleus disappears and there appear two new particles: a He-4 nucleus of mass $6 .640678 \times 10^{- 27} kg$ (an alpha particle consisting of two protons and two neutrons) and a new nucleus of mass $3 .850768 \times 10^{- 25} kg$ . (Note that the new nucleus has less mass than the original nucleus, and it has two fewer protons and two fewer neutrons.)

(a) What is the total kinetic energy of the alpha particle and the new nucleus?

(b) Use the conservation of momentum in order to determine the kinetic energy of the alpha particle and kinetic energy of the new nucleus.

In the preceding example, what fraction of the original neutron’s rest energy was converted into kinetic energy?

See all solutions

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