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BartSMP [9]
3 years ago
15

The drag on a pitched baseball can be surprisingly large. Suppose a 145 g baseball with a diameter of 7.4 cm has an initial spee

d of 40.2 m/s (90 mph). Drag coefficient for a pitched baseball equals 0.35.
Part A: What is the magnitude of the ball's acceleration due to the drag force?


Part B: If the ball had this same acceleration during its entire 18.4 m trajectory, what would its final speed be?
Physics
1 answer:
kupik [55]3 years ago
4 0

Answer:

<h2>Part A)</h2><h2>Acceleration of the ball is 10.1 m/s/s</h2><h2>Part B)</h2><h2>the final speed of the ball is given as</h2><h2>v_f = 35.3 m/s</h2>

Explanation:

Part a)

As we know that drag force is given as

F = \frac{C_d \rho A v^2}{2}

C_d = 0.35

A = \frac{\pi d^2}{4}

A = \frac{\pi(0.074)^2}{4}

A = 4.3 \times 10^{-3} m^2

v = 40.2 m/s

so we have

F = \frac{0.35\times 1.2 (4.3 \times 10^{-3})(40.2)^2}{2}

F = 1.46 N

So acceleration of the ball is

a = \frac{F}{m}

a = \frac{1.46}{0.145}

a = 10.1 m/s^2

Part B)

As per kinematics we know that

v_f^2 - v_i^2 = 2 a d

v_f^2 - 40.2^2 = 2(-10.1)(18.4)

v_f = 35.3 m/s

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2 years ago
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Example 4.6 provides a nice example of the overlap between kinematics and dynamics. It is known that the plane accelerates from
kodGreya [7K]

Answer:

ax = 2.60m/s^{2}, t = 26.92s

Explanation:

The acceleration of the plane can be determined by means of the kinematic equation that correspond to a Uniformly Accelerated Rectilinear Motion.

(vx)f^{2} = (vx)i^{2} + 2ax \Lambda x (1)

Where (vx)f^{2} is the final velocity, (vx)i^{2} is the initial velocity, ax is the acceleration and  \Lambda x is the distance traveled.

Equation (1) can be rewritten in terms of ax:

(vx)f^{2} - (vx)i^{2} = 2ax \Lambda x

2ax \Lambda x = (vx)f^{2} - (vx)i^{2}

ax = \frac{(vx)f^{2} - (vx)i^{2}}{2 \Lambda x}  (2)

Since the plane starts from rest, its initial velocity will be zero ((vx) = 0):

Replacing the values given in equation 2, it is gotten:

ax = \frac{(70m/s)^{2} - (0m/s)^{2}}{2(940m)}

ax = \frac{4900m/s}{2(940m)}

ax = \frac{4900m/s}{1880m}

ax = 2.60m/s^{2}

So, The acceleration of the plane is 2.60m/s^{2}    

Now that the acceleration is known, the next equation can be used to find out the time:

(vx)f = (vx)i + axt (3)

Rewritten equation (3) in terms of t:

t = \frac{(vx)f - (vx)i}{ax}

t = \frac{70m/s - 0m/s}{2.60m/s^{2}}

t = 26.92s

<u>Hence, the plane takes 26.92 seconds to reach its take-off speed.</u>

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3 years ago
convert watts to hpThe headlights of a moving car draw about 9 A from the 12 V alternator, which is driven by the engine. Assume
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Answer: 0.17hp

Explanation:

Power output = power input × 85%

Power output = power input × 0.85

Power input = IV/0.85

Power input = 9×12/0.85

Power input = 108/0.85

= 127.058 watts

Converting to horse power = 127.058W × 1horse power/745.7W

= 127.058 × 0.001341

= 0.17hp

4 0
3 years ago
Una cuerda de 20 pies se estira entre dos arboles. Un peso W cuelga del centro de la cuerda hace que el punto medio de la misma
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Answer:

La magnitud de la masa del peso es 78.447 libras-masa.

Explanation:

La tensión es una fuerza de reacción de la cuerda causada por la acción de una fuerza externa. En este caso, esa fuerza externa es el peso que cuelga en el centro de la cuerda. Abajo hemos adjuntado una representación simplificada del enunciado.

Por las leyes de Newton, tenemos la siguiente ecuación de equilibrio conformada por tres fuerzas:

\vec T_{1} + \vec T_{2} + \vec W = (0, 0)\, [N] (1)

Donde:

\vec T_{1}, \vec T_{2} - Tensiones a cada lado de la cuerda, en newtons.

\vec W- Peso, en newtons.

Si sabemos que \vec T_{1} = T\cdot (\cos \alpha, \sin \alpha), \vec T_{2} = T\cdot (-\cos \alpha, \sin \alpha) y \vec W = W\cdot (0, -1), entonces tenemos la siguiente ecuación vectorial:

T\cdot (\cos \alpha, \sin \alpha) + T\cdot (-\cos\alpha, \sin \alpha) + W\cdot (0, -1) = (0,0)

T\cdot (0, 2\cdot \sin \alpha) = W\cdot (0, 1)

Esto permite reducir la anterior expresión a una fórmula escalar:

2\cdot T\cdot \sin \alpha = W

Donde \alpha es el ángulo de inclinación de la cuerda, medido en grados sexagesimales.

El ángulo de inclinación de la cuerda se determina mediante la siguiente fórmula trigonométrica inversa es:

\alpha = \tan^{-1} \left(\frac{2\,ft}{10\,ft}\right)

\alpha \approx 11.310^{\circ}

Si conocemos que \alpha \approx 11.310^{\circ} y T = 200\,lbf, entonces la magnitud del peso es:

W = 2\cdot (200\,lb)\cdot \sin 11.310^{\circ}

W \approx 78.447\,lbf

En el Sistema Imperial, las fuerzas son medidas en forma gravitacional, entonces la magnitud de la fuerza gravitacional del peso equivale a la magnitud de su masa. En síntesis, la magnitud de la masa es 78.447\,lbm.

La magnitud de la masa del peso es 78.447 libras-masa.

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2 years ago
Are most main sequence stars larger or smaller than the sun?
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Answer: Main sequence stars fuse hydrogen atoms to form helium atoms in their cores. About 90 percent of the stars in the universe, including the sun, are main sequence stars. These stars can range from about a tenth of the mass of the sun to up to 200 times as massive.

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3 years ago
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