A 0.3 g mosquito is flying toward a girl with a speed of 4.5 mph. Just before landing on the girl, the fly is swatted straight b
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Answer:
The sled needed a distance of 92.22 m and a time of 1.40 s to stop.
Explanation:
The relationship between velocities and time is described by this equation: , where
is the final velocity,
is the initial velocity,
the acceleration, and
is the time during such acceleration is applied.
Solving the equation for the time, and applying to the case: , where
because the sled is totally stopped,
is the velocity of the sled before braking and,
is negative because the deceleration applied by the brakes.
In the other hand, the equation that describes the distance in term of velocities and acceleration:, where
is the distance traveled,
is the initial velocity,
the time of the process and,
is the acceleration of the process.
Then for this case the relationship becomes: .
<u>Note that the acceleration is negative because is a braking process.</u>
Answer:
Train accaleration = 0.70 m/s^2
Explanation:
We have a pendulum (presumably simple in nature) in an accelerating train. As the train accelerates, the pendulum is going move in the opposite direction due to inertia. The force which causes this movement has the same accaleration as that of the train. This is the basis for the problem.
Start by setting up a free body diagram of all the forces in play: The gravitational force on the pendulum (mg), the force caused by the pendulum's inertial resistance to the train(F_i), and the resulting force of tension caused by the other two forces (F_r).
Next, set up your sum of forces equations/relationships. Note that the sum of vertical forces (y-direction) balance out and equal 0. While the horizontal forces add up to the total mass of the pendulum times it's accaleration; which, again, equals the train's accaleration.
After doing this, I would isolate the resulting force in the sum of vertical forces, substitute it into the horizontal force equation, and solve for the acceleration. The problem should reduce to show that the acceleration is proportional to the gravity times the tangent of the angle it makes.
I've attached my work, comment with any questions.
Side note: If you take this end result and solve for the angle, you'll see that no matter how fast the train accelerates, the pendulum will never reach a full 90°!
