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adelina 88 [10]
3 years ago
14

Each tire on a car has a radius of 0.330 m and is rotating with an angular speed of 11.7 revolutions/s. Find the linear speed v

of the car, assuming that the tires are not slipping against the ground. v
Physics
1 answer:
Eduardwww [97]3 years ago
7 0

Answer:

The linear speed of the car, v, is 24.26 m/s

Explanation:

Given;

radius of the car's tire, r = 0.330 m

angular speed of the car, ω = 11.7 revolutions/s

The angular speed of the car in radian per second:

\omega = 11.7 \ \frac{rev}{s} \times \frac{2\pi \ rad}{1 \ rev} \\\\\omega = 73.523 \ rad/s

The linear speed of the car, v, is calculated as;

v = ωr

v = 73.523 rad/s  x  0.33 m

v = 24.26 m/s

Therefore, the linear speed of the car, v, is 24.26 m/s

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In a flying ski jump, the skier acquires a speed of 110 km/h by racing down a steep hill and then lifts off into the air from a
matrenka [14]

Answer:

Approximately \displaystyle\rm \left[ \begin{array}{c}\rm191\; m\\\rm-191\; m\end{array}\right].

Explanation:

Consider this 45^{\circ} slope and the trajectory of the skier in a cartesian plane. Since the problem is asking for the displacement vector relative to the point of "lift off", let that particular point be the origin (0, 0).

Assume that the skier is running in the positive x-direction. The line that represents the slope shall point downwards at 45^{\circ} to the x-axis. Since this slope is connected to the ramp, it should also go through the origin. Based on these conditions, this line should be represented as y = -x.

Convert the initial speed of this diver to SI units:

\displaystyle v = \rm 110\; km\cdot h^{-1} = 110 \times \frac{1}{3.6} = 30.556\; m\cdot s^{-1}.

The question assumes that the skier is in a free-fall motion. In other words, the skier travels with a constant horizontal velocity and accelerates downwards at g (g \approx \rm -9.81\; m\cdot s^{-2} near the surface of the earth.) At t seconds after the skier goes beyond the edge of the ramp, the position of the skier will be:

  • x-coordinate: 30.556t meters (constant velocity;)
  • y-coordinate: \displaystyle -\frac{1}{2}g\cdot t^{2} = -\frac{9.81}{2}\cdot t^{2} meters (constant acceleration with an initial vertical velocity of zero.)

To eliminate t from this expression, solve the equation between t and x for t. That is: express t as a function of x.

x = 30.556\;t\implies \displaystyle t = \frac{x}{30.556}.

Replace the t in the equation of y with this expression:

\begin{aligned} y = &-\frac{9.81}{2}\cdot t^{2}\\ &= -\frac{9.81}{2} \cdot \left(\frac{x}{30.556}\right)^{2}\\&= -0.0052535\;x^{2}\end{aligned}.

Plot the two functions:

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  • \displaystyle y= -0.0052535\;x^{2},

and look for their intersection. Refer to the diagram attached.

Alternatively, equate the two expressions of y (right-hand side of the equation, the part where y is expressed as a function of x.)

-0.0052535\;x^{2} = -x,

\implies x = 190.35.

The value of y can be found by evaluating either equation at this particular x-value: x = 190.35.

y = -190.35.

The position vector of a point (x, y) on a cartesian plane is \displaystyle \left[\begin{array}{l}x \\ y\end{array}\right]. The coordinates of this skier is approximately (190.35, -190.35). The position vector of this skier will be \displaystyle\rm \left[ \begin{array}{c}\rm191\\\rm-191\end{array}\right]. Keep in mind that both numbers in this vectors are in meters.

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3 years ago
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malfutka [58]

If one of two interacting charges is doubled, the force between the charges will double.

Explanation:

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q2= charge on second particle

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Now if the first charge is doubled,

we get F'=\frac{k (2q1) q2}{r^{2}}

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Thus the force gets doubled.

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