Question

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perform the following conversions. remember that 1 lb = 4.45 n.
a.) 77460 g = kg
b.) 39.7 kg = g
c.) 901 lb = n
d.) 743 n = lb
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1. - / 3 points details my notes ask your teacher

a.) a 300 kg stone has an acceleration of 62.4 m/s². determine the net force acting on the stone.
n
b.) a 95.2 n force is acting on a 880 kg slab. determine the acceleration of the slab.
m/s²
c.) a 27.3 n force acts on a block and causes an acceleration of 20.6 m/s². determine the mass of the block.
kg
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an object weighing 478 n on earth is taken to the moon. determine its mass on earth, its mass on the moon, and its weight on the
moon. the free fall acceleration on the moon is 1.6 m/s².
objects mass on earth = kg
objects mass on the moon = kg
objects weight on the moon = n
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calculate the gravitational force between the sun and neptune. the mass of the sun is 1.99×10³⁰ kg. the mass of neptune is
1020×10²³ kg. the distance between them is 450×10¹⁰ m.
n
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cloverleaf exits are approximately circular. a 1322 kg automobile is traveling 52 mph while taking a cloverleaf exit that has a radius of
41.6 m. calculate the centripetal acceleration of the car and the centripetal force on the car. remember that 1 mph = 0.447 m/s.
centripetal acceleration = m/s²
centripetal force = n
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Explanation:

1. a)

Step1: Convert grams to kilograms

Since \(1\ kg = 1000\ g\), to convert \(77460\ g\) to \(kg\), we use the formula \(m_{kg}=\frac{m_{g}}{1000}\).
\(m = \frac{77460}{1000}=77.46\ kg\)

1. b)

Step1: Convert kilograms to grams

Since \(1\ kg = 1000\ g\), to convert \(39.7\ kg\) to \(g\), we use the formula \(m_{g}=m_{kg}\times1000\).
\(m = 39.7\times1000 = 39700\ g\)

1. c)

Step1: Convert pounds to Newtons

Given \(1\ lb=4.45\ N\), to convert \(901\ lb\) to \(N\), we use the formula \(F = lb\times4.45\).
\(F=901\times4.45 = 4009.45\ N\)

1. d)

Step1: Convert Newtons to pounds

Given \(1\ lb = 4.45\ N\), to convert \(743\ N\) to \(lb\), we use the formula \(lb=\frac{N}{4.45}\).
\(lb=\frac{743}{4.45}\approx166.97\ lb\)

2. a)

Step1: Use Newton's second law \(F = ma\)

Given \(m = 300\ kg\) and \(a=62.4\ m/s^{2}\), then \(F=ma\).
\(F = 300\times62.4=18720\ N\)

2. b)

Step1: Use Newton's second law \(a=\frac{F}{m}\)

Given \(F = 95.2\ N\) and \(m = 880\ kg\), then \(a=\frac{F}{m}\).
\(a=\frac{95.2}{880}\approx0.108\ m/s^{2}\)

2. c)

Step1: Use Newton's second law \(m=\frac{F}{a}\)

Given \(F = 27.3\ N\) and \(a = 20.6\ m/s^{2}\), then \(m=\frac{F}{a}\).
\(m=\frac{27.3}{20.6}\approx1.33\ kg\)

3.

Step1: Find mass on Earth

On Earth, \(F = mg\) (where \(g = 9.8\ m/s^{2}\)). Given \(F = 478\ N\), then \(m=\frac{F}{g}\).
\(m=\frac{478}{9.8}\approx48.78\ kg\)

Step2: Mass on the Moon

Mass is a property of the object and does not change. So mass on the Moon \(m = 48.78\ kg\)

Step3: Weight on the Moon

On the Moon, \(F=mg_{moon}\) (where \(g_{moon}=1.6\ m/s^{2}\)).
\(F=48.78\times1.6 = 78.05\ N\)

4.

Step1: Use the gravitational force formula \(F=\frac{Gm_{1}m_{2}}{r^{2}}\)

where \(G = 6.67\times10^{- 11}\ Nm^{2}/kg^{2}\), \(m_{1}=1.99\times10^{30}\ kg\), \(m_{2}=1020\times10^{23}\ kg\), \(r = 450\times10^{10}\ m\)
\(F=\frac{6.67\times10^{-11}\times1.99\times10^{30}\times1020\times10^{23}}{(450\times10^{10})^{2}}\)
\(F=\frac{6.67\times1.99\times1020\times10^{-11 + 30+23}}{450^{2}\times10^{20}}\)
\(F=\frac{6.67\times1.99\times1020\times10^{42}}{202500\times10^{20}}\)
\(F=\frac{6.67\times1.99\times1020}{202500}\times10^{22}\)
\(F\approx6.6\times10^{21}\ N\)

5.

Step1: Convert speed to \(m/s\)

Given \(v = 52\ mph\), and \(1\ mph=0.447\ m/s\), then \(v = 52\times0.447 = 23.244\ m/s\)

Step2: Calculate centripetal acceleration \(a_{c}=\frac{v^{2}}{r}\)

Given \(r = 41.6\ m\) and \(v = 23.244\ m/s\), then \(a_{c}=\frac{(23.244)^{2}}{41.6}\)
\(a_{c}=\frac{540.28}{41.6}\approx13.0\ m/s^{2}\)

Step3: Calculate centripetal force \(F_{c}=ma_{c}\)

Given \(m = 1322\ kg\) and \(a_{c}\approx13.0\ m/s^{2}\), then \(F_{c}=1322\times13.0 = 17186\ N\)

Answer:

1. a) \(77.46\ kg\)

b) \(39700\ g\)
c) \(4009.45\ N\)
d) \(166.97\ lb\)

1. a) \(18720\ N\)

b) \(0.108\ m/s^{2}\)
c) \(1.33\ kg\)

1. Object's mass on Earth \(48.78\ kg\), Object's mass on the Moon \(48.78\ kg\), Object's weight on the Moon \(78.05\ N\)
2. \(6.6\times10^{21}\ N\)
3. Centripetal acceleration \(13.0\ m/s^{2}\), Centripetal force \(17186\ N\)