9. Newton’s first law
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Newton's First Law | Newton's First Law | ||
If the resultant force on a particle is zero, then it will move with constant velocity or remain at rest. | If the resultant force on a particle is zero, then it will move with constant velocity or remain at rest. | ||
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A helicopter of mass 880 kg is rising vertically at a constant rate. Find the magnitude of the lift force acting on the helicopter. How would your answer change if the helicopter was descending at a constant rate? | A helicopter of mass 880 kg is rising vertically at a constant rate. Find the magnitude of the lift force acting on the helicopter. How would your answer change if the helicopter was descending at a constant rate? | ||
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'''Solution''' | '''Solution''' | ||
As the helicopter is rising at a constant rate the forces on it must be in equilibrium. | As the helicopter is rising at a constant rate the forces on it must be in equilibrium. | ||
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[[Image:TF9.1.GIF]] | [[Image:TF9.1.GIF]] | ||
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The lift force is 8624 N. | The lift force is 8624 N. | ||
If the helicopter is descending at a constant rate the lift force will be 8624 N. | If the helicopter is descending at a constant rate the lift force will be 8624 N. | ||
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'''[[Example 9.2]]''' | '''[[Example 9.2]]''' | ||
A cyclist, of mass 75 kg, freewheels down a slope inclined at to the horizontal at a constant speed. Find the magnitude of the resistance force acting on the cyclist. | A cyclist, of mass 75 kg, freewheels down a slope inclined at to the horizontal at a constant speed. Find the magnitude of the resistance force acting on the cyclist. | ||
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'''Solution''' | '''Solution''' | ||
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Resolving parallel to the slope gives: | Resolving parallel to the slope gives: | ||
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<math>P=735\sin 6{}^\circ =76.8\text{ N}</math> | <math>P=735\sin 6{}^\circ =76.8\text{ N}</math> | ||
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A skier, of mass 60 kg, skis down a slope inclined at to the horizontal at a constant speed. If the coefficient of friction between her skis and the slope is 0.1, find the magnitude of the air resistance force acting on her. | A skier, of mass 60 kg, skis down a slope inclined at to the horizontal at a constant speed. If the coefficient of friction between her skis and the slope is 0.1, find the magnitude of the air resistance force acting on her. | ||
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'''Solution''' | '''Solution''' | ||
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forces acting, where the resistance | forces acting, where the resistance | ||
force has magnitude . | force has magnitude . | ||
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Resolving perpendicular to the slope gives: | Resolving perpendicular to the slope gives: | ||
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<math>R=588\cos 30{}^\circ </math> | <math>R=588\cos 30{}^\circ </math> | ||
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Then using | Then using | ||
<math>F=\mu R</math> | <math>F=\mu R</math> | ||
, because the skier is sliding gives: | , because the skier is sliding gives: | ||
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<math></math> | <math></math> | ||
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Resolving parallel to the slope gives: | Resolving parallel to the slope gives: | ||
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<math>\begin{align} | <math>\begin{align} | ||
Revision as of 16:32, 15 February 2010
| Theory | Exercises |
Key Points
Newton's First Law
If the resultant force on a particle is zero, then it will move with constant velocity or remain at rest.
A helicopter of mass 880 kg is rising vertically at a constant rate. Find the magnitude of the lift force acting on the helicopter. How would your answer change if the helicopter was descending at a constant rate?
Solution
As the helicopter is rising at a constant rate the forces on it must be in equilibrium.
The lift force is 8624 N.
If the helicopter is descending at a constant rate the lift force will be 8624 N.
A cyclist, of mass 75 kg, freewheels down a slope inclined at to the horizontal at a constant speed. Find the magnitude of the resistance force acting on the cyclist.
Solution
The cyclist and cycle is modelled as a particle.
The diagram shows the forces acting, where the resistance force has magnitude P.
Resolving parallel to the slope gives:
\displaystyle P=735\sin 6{}^\circ =76.8\text{ N}
A skier, of mass 60 kg, skis down a slope inclined at to the horizontal at a constant speed. If the coefficient of friction between her skis and the slope is 0.1, find the magnitude of the air resistance force acting on her.
Solution
The skier is modelled as a particle.
The diagram shows the forces acting, where the resistance force has magnitude .
Resolving perpendicular to the slope gives:
\displaystyle R=588\cos 30{}^\circ
Then using \displaystyle F=\mu R , because the skier is sliding gives:
\displaystyle
Resolving parallel to the slope gives:
\displaystyle \begin{align} & F+P=588\sin 30{}^\circ \\ & P=588\sin 30{}^\circ -F \\ & =588\sin 30{}^\circ -58.8\cos 30{}^\circ \\ & =243\text{ N} \end{align}
