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Check Your Understanding For [link] , find the acceleration when the farmer’s applied force is 230.0 N.
$a=2.78\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2}$
Can you avoid the boulder field and land safely just before your fuel runs out, as Neil Armstrong did in 1969? This version of the classic video game accurately simulates the real motion of the lunar lander, with the correct mass, thrust, fuel consumption rate, and lunar gravity. The real lunar lander is hard to control.
Use this interactive simulation to move the Sun, Earth, Moon, and space station to see the effects on their gravitational forces and orbital paths. Visualize the sizes and distances between different heavenly bodies, and turn off gravity to see what would happen without it.
What is the relationship between weight and mass? Which is an intrinsic, unchanging property of a body?
How much does a 70-kg astronaut weight in space, far from any celestial body? What is her mass at this location?
The astronaut is truly weightless in the location described, because there is no large body (planet or star) nearby to exert a gravitational force. Her mass is 70 kg regardless of where she is located.
Which of the following statements is accurate?
(a) Mass and weight are the same thing expressed in different units.
(b) If an object has no weight, it must have no mass.
(c) If the weight of an object varies, so must the mass.
(d) Mass and inertia are different concepts.
(e) Weight is always proportional to mass.
When you stand on Earth, your feet push against it with a force equal to your weight. Why doesn’t Earth accelerate away from you?
The force you exert (a contact force equal in magnitude to your weight) is small. Earth is extremely massive by comparison. Thus, the acceleration of Earth would be incredibly small. To see this, use Newton’s second law to calculate the acceleration you would cause if your weight is 600.0 N and the mass of Earth is $6.00\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{24}\phantom{\rule{0.2em}{0ex}}\text{kg}$ .
How would you give the value of $\overrightarrow{g}$ in vector form?
The weight of an astronaut plus his space suit on the Moon is only 250 N. (a) How much does the suited astronaut weigh on Earth? (b) What is the mass on the Moon? On Earth?
a. $\begin{array}{ccc}\hfill {w}_{\text{Moon}}& =\hfill & m{g}_{\text{Moon}}\hfill \\ \hfill m& =\hfill & 150\phantom{\rule{0.2em}{0ex}}\text{kg}\hfill \\ \hfill {w}_{\text{Earth}}& =\hfill & 1.5\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}\text{N}\hfill \end{array}$ ; b. Mass does not change, so the suited astronaut’s mass on both Earth and the Moon is $150\phantom{\rule{0.2em}{0ex}}\text{kg.}$
Suppose the mass of a fully loaded module in which astronauts take off from the Moon is $1.00\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{4}$ kg. The thrust of its engines is $3.00\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{4}$ N. (a) Calculate the module’s magnitude of acceleration in a vertical takeoff from the Moon. (b) Could it lift off from Earth? If not, why not? If it could, calculate the magnitude of its acceleration.
A rocket sled accelerates at a rate of ${49.0\phantom{\rule{0.2em}{0ex}}\text{m/s}}^{2}$ . Its passenger has a mass of 75.0 kg. (a) Calculate the horizontal component of the force the seat exerts against his body. Compare this with his weight using a ratio. (b) Calculate the direction and magnitude of the total force the seat exerts against his body.
a.
$\begin{array}{ccc}\hfill {F}_{\text{h}}& =\hfill & 3.68\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}\text{N and}\hfill \\ \hfill w& =\hfill & 7.35\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{2}\phantom{\rule{0.2em}{0ex}}\text{N}\hfill \\ \hfill \frac{{F}_{\text{h}}}{w}& =\hfill & 5.00\phantom{\rule{0.2em}{0ex}}\text{times greater than weight}\hfill \end{array}$ ;
b.
$\begin{array}{ccc}\hfill {F}_{\text{net}}& =\hfill & 3750\phantom{\rule{0.2em}{0ex}}\text{N}\hfill \\ \hfill \theta & =\hfill & 11.3\text{\xb0}\phantom{\rule{0.2em}{0ex}}\text{from horizontal}\hfill \end{array}$
Repeat the previous problem for a situation in which the rocket sled decelerates at a rate of ${201\phantom{\rule{0.2em}{0ex}}\text{m/s}}^{2}$ . In this problem, the forces are exerted by the seat and the seat belt.
A body of mass 2.00 kg is pushed straight upward by a 25.0 N vertical force. What is its acceleration?
$\begin{array}{ccc}\hfill w& =\hfill & 19.6\phantom{\rule{0.2em}{0ex}}\text{N}\hfill \\ \hfill {F}_{\text{net}}& =\hfill & 5.40\phantom{\rule{0.2em}{0ex}}\text{N}\hfill \\ \hfill {F}_{\text{net}}& =\hfill & ma\Rightarrow a=2.70\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2}\hfill \end{array}$
A car weighing 12,500 N starts from rest and accelerates to 83.0 km/h in 5.00 s. The friction force is 1350 N. Find the applied force produced by the engine.
A body with a mass of 10.0 kg is assumed to be in Earth’s gravitational field with $g=9.80\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2}$ . What is its acceleration?
$0.60\widehat{i}-8.4\widehat{j}\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2}$
A fireman has mass m ; he hears the fire alarm and slides down the pole with acceleration a (which is less than g in magnitude). (a) Write an equation giving the vertical force he must apply to the pole. (b) If his mass is 90.0 kg and he accelerates at $5.00\phantom{\rule{0.2em}{0ex}}{\text{m/s}}^{2},$ what is the magnitude of his applied force?
A baseball catcher is performing a stunt for a television commercial. He will catch a baseball (mass 145 g) dropped from a height of 60.0 m above his glove. His glove stops the ball in 0.0100 s. What is the force exerted by his glove on the ball?
497 N
When the Moon is directly overhead at sunset, the force by Earth on the Moon, ${F}_{\text{EM}}$ , is essentially at $90\text{\xb0}$ to the force by the Sun on the Moon, ${F}_{\text{SM}}$ , as shown below. Given that ${F}_{\text{EM}}=1.98\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{20}\phantom{\rule{0.2em}{0ex}}\text{N}$ and ${F}_{\text{SM}}=4.36\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{20}\phantom{\rule{0.2em}{0ex}}\text{N},$ all other forces on the Moon are negligible, and the mass of the Moon is $7.35\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{22}\phantom{\rule{0.2em}{0ex}}\text{kg},$ determine the magnitude of the Moon’s acceleration.
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