(a) Given that an object of mass m moves from x 1 to x 2 in the time interval [ t 1 , t 2 ] due to the force F ( x ) acting on the object in the direction of the motion. Using the change of variables show that the work performed is equal to W = ∫ x 1 x 2 F ( x ) d x = ∫ t 1 t 2 F ( x ( t ) ) v ( t ) d t .

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Answer 1

Question

Chapter 6.5, Problem 39E

To determine

(a)

Given that an object of mass $m$ moves from $x_{1}$ to $x_{2}$ in the time interval $[t_{1}, t_{2}]$ due to the force $F (x)$ acting on the object in the direction of the motion. Using the change of variables show that the work performed is equal to $W = \int_{x_{1}}^{x_{2}} F (x) d x = \int_{t_{1}}^{t_{2}} F (x (t)) v (t) d t$ .

To determine

(b)

Use Newton’s Second Law, $F (x (t) = m a (t)$ to show that $\frac{d}{d t} (\frac{1}{2} m v {(t)}^{2}) = F (x (t)) v (t)$

To determine

(c)

Prove the Work Energy Theorem, using the fundamental of theory of calculus. Given that $\frac{d}{d t} (\frac{1}{2} m v {(t)}^{2}) = F (x (t)) v (t)$

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Answer 2

Question

Chapter 6.5, Problem 39E

To determine

(a)

Given that an object of mass $m$ moves from $x_{1}$ to $x_{2}$ in the time interval $[t_{1}, t_{2}]$ due to the force $F (x)$ acting on the object in the direction of the motion. Using the change of variables show that the work performed is equal to $W = \int_{x_{1}}^{x_{2}} F (x) d x = \int_{t_{1}}^{t_{2}} F (x (t)) v (t) d t$ .

To determine

(b)

Use Newton’s Second Law, $F (x (t) = m a (t)$ to show that $\frac{d}{d t} (\frac{1}{2} m v {(t)}^{2}) = F (x (t)) v (t)$

To determine

(c)

Prove the Work Energy Theorem, using the fundamental of theory of calculus. Given that $\frac{d}{d t} (\frac{1}{2} m v {(t)}^{2}) = F (x (t)) v (t)$

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 6.5, Problem 39E

To determine

(a)

Given that an object of mass $m$ moves from $x_{1}$ to $x_{2}$ in the time interval $[t_{1}, t_{2}]$ due to the force $F (x)$ acting on the object in the direction of the motion. Using the change of variables show that the work performed is equal to $W = \int_{x_{1}}^{x_{2}} F (x) d x = \int_{t_{1}}^{t_{2}} F (x (t)) v (t) d t$ .

To determine

(b)

Use Newton’s Second Law, $F (x (t) = m a (t)$ to show that $\frac{d}{d t} (\frac{1}{2} m v {(t)}^{2}) = F (x (t)) v (t)$

To determine

(c)

Prove the Work Energy Theorem, using the fundamental of theory of calculus. Given that $\frac{d}{d t} (\frac{1}{2} m v {(t)}^{2}) = F (x (t)) v (t)$

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 6.5, Problem 39E

To determine

(a)

Given that an object of mass $m$ moves from $x_{1}$ to $x_{2}$ in the time interval $[t_{1}, t_{2}]$ due to the force $F (x)$ acting on the object in the direction of the motion. Using the change of variables show that the work performed is equal to $W = \int_{x_{1}}^{x_{2}} F (x) d x = \int_{t_{1}}^{t_{2}} F (x (t)) v (t) d t$ .

To determine

(b)

Use Newton’s Second Law, $F (x (t) = m a (t)$ to show that $\frac{d}{d t} (\frac{1}{2} m v {(t)}^{2}) = F (x (t)) v (t)$

To determine

(c)

Prove the Work Energy Theorem, using the fundamental of theory of calculus. Given that $\frac{d}{d t} (\frac{1}{2} m v {(t)}^{2}) = F (x (t)) v (t)$

Expert Solution & Answer

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Answer 5

Chapter 6.5, Problem 39E

To determine

(a)

Given that an object of mass $m$ moves from $x_{1}$ to $x_{2}$ in the time interval $[t_{1}, t_{2}]$ due to the force $F (x)$ acting on the object in the direction of the motion. Using the change of variables show that the work performed is equal to $W = \int_{x_{1}}^{x_{2}} F (x) d x = \int_{t_{1}}^{t_{2}} F (x (t)) v (t) d t$ .

To determine

(b)

Use Newton’s Second Law, $F (x (t) = m a (t)$ to show that $\frac{d}{d t} (\frac{1}{2} m v {(t)}^{2}) = F (x (t)) v (t)$

To determine

(c)

Prove the Work Energy Theorem, using the fundamental of theory of calculus. Given that $\frac{d}{d t} (\frac{1}{2} m v {(t)}^{2}) = F (x (t)) v (t)$

Answer 6

Chapter 6.5, Problem 39E

To determine

(a)

Given that an object of mass $m$ moves from $x_{1}$ to $x_{2}$ in the time interval $[t_{1}, t_{2}]$ due to the force $F (x)$ acting on the object in the direction of the motion. Using the change of variables show that the work performed is equal to $W = \int_{x_{1}}^{x_{2}} F (x) d x = \int_{t_{1}}^{t_{2}} F (x (t)) v (t) d t$ .

Answer 7

Chapter 6.5, Problem 39E

To determine

(a)

Given that an object of mass $m$ moves from $x_{1}$ to $x_{2}$ in the time interval $[t_{1}, t_{2}]$ due to the force $F (x)$ acting on the object in the direction of the motion. Using the change of variables show that the work performed is equal to $W = \int_{x_{1}}^{x_{2}} F (x) d x = \int_{t_{1}}^{t_{2}} F (x (t)) v (t) d t$ .

Answer 8

To determine

(b)

Use Newton’s Second Law, $F (x (t) = m a (t)$ to show that $\frac{d}{d t} (\frac{1}{2} m v {(t)}^{2}) = F (x (t)) v (t)$

Answer 9

To determine

(b)

Use Newton’s Second Law, $F (x (t) = m a (t)$ to show that $\frac{d}{d t} (\frac{1}{2} m v {(t)}^{2}) = F (x (t)) v (t)$

Answer 10

To determine

(c)

Prove the Work Energy Theorem, using the fundamental of theory of calculus. Given that $\frac{d}{d t} (\frac{1}{2} m v {(t)}^{2}) = F (x (t)) v (t)$

Answer 11

To determine

(c)

Prove the Work Energy Theorem, using the fundamental of theory of calculus. Given that $\frac{d}{d t} (\frac{1}{2} m v {(t)}^{2}) = F (x (t)) v (t)$

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E