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Calculate the linear acceleration (in m/s2) of a car, the 0.310 m radius tires of which have an angular acceleration of 15.0 rad

love history [14]

Answer:

a) The linear acceleration of the car is $4.65\,\frac{m}{s^{2}}$ , b) The tires did 7.46 revolutions in 2.50 seconds from rest.

Explanation:

a) A tire experiments a general plane motion, which is the sum of rotation and translation. The linear acceleration experimented by the car corresponds to the linear acceleration at the center of the tire with respect to the point of contact between tire and ground, whose magnitude is described by the following formula measured in meters per square second:

$\| \vec a \| = \sqrt{a_{r}^{2} + a_{t}^{2}}$

Where:

$a_{r}$ - Magnitude of the radial acceleration, measured in meters per square second.

$a_{t}$ - Magnitude of the tangent acceleration, measured in meters per square second.

Let suppose that tire is moving on a horizontal ground, since radius of curvature is too big, then radial acceleration tends to be zero. So that:

$\| \vec a \| = a_{t}$

$\| \vec a \| = r \cdot \alpha$

Where:

$\alpha$ - Angular acceleration, measured in radians per square second.

$r$ - Radius of rotation (Radius of a tire), measured in meters.

Given that $\alpha = 15\,\frac{rad}{s^{2}}$ and $r = 0.31\,m$ . The linear acceleration experimented by the car is:

$\| \vec a \| = (0.31\,m)\cdot \left(15\,\frac{rad}{s^{2}} \right)$

$\| \vec a \| = 4.65\,\frac{m}{s^{2}}$

The linear acceleration of the car is $4.65\,\frac{m}{s^{2}}$ .

b) Assuming that angular acceleration is constant, the following kinematic equation is used:

$\theta = \theta_{o} + \omega_{o}\cdot t + \frac{1}{2}\cdot \alpha \cdot t^{2}$

Where:

$\theta$ - Final angular position, measured in radians.

$\theta_{o}$ - Initial angular position, measured in radians.

$\omega_{o}$ - Initial angular speed, measured in radians per second.

$\alpha$ - Angular acceleration, measured in radians per square second.

$t$ - Time, measured in seconds.

If $\theta_{o} = 0\,rad$ , $\omega_{o} = 0\,\frac{rad}{s}$ , $\alpha = 15\,\frac{rad}{s^{2}}$ , the final angular position is:

$\theta = 0\,rad + \left(0\,\frac{rad}{s}\right)\cdot (2.50\,s) + \frac{1}{2}\cdot \left(15\,\frac{rad}{s^{2}}\right)\cdot (2.50\,s)^{2}$

$\theta = 46.875\,rad$

Let convert this outcome into revolutions: (1 revolution is equal to 2π radians)

$\theta = 7.46\,rev$

The tires did 7.46 revolutions in 2.50 seconds from rest.

3 0

2 years ago

Gravity does not actually "pull" objects at

Radda [10]

I believe it’s (D. Any object)

5 0

2 years ago

A standing wave is created on a string of length 1.2 m. If the speed of the wave on the string is 60.0 m/s, what is the fundamen

coldgirl [10]

Answer:

Fundamental frequency in the string will be 25 Hz

Explanation:

We have given length of the string L = 1.2 m

Speed of the wave on the string v = 60 m/sec

We have to find the fundamental frequency

Fundamental frequency in the string is equal to $f=\frac{v}{2L}$ , here v is velocity on the string and L is the length of the string

So frequency will be equal to $f=\frac{v}{2L}=\frac{60}{2\times 1.2}=25Hz$

So fundamental frequency will be 25 Hz

6 0

2 years ago

Read 2 more answers

please tell th answer fast suppose A ball of mass M is thrown vertically upward with initial speed be its speed is continuously

Lisa [10]

Answer:.

the ball would go down and speed of it would not strike so that wouldnt be an example of the conversation momentum

Explanation:

The answer I think

3 0

2 years ago

A loop of wire lays flat on a horizontal surface in an area with uniform magnetic field directed vertically down. Magnetic field

zimovet [89]

Answer:

B. counterclockwise

Explanation:

We shall apply Lenz's law to find direction of induced current . According to it , direction of induced current is such that the magnetic field produced by it will try to nullify the change in magnetic field that produces it. Increase in magnetic field in down ward direction is producing it so to nullify it , magnetic field induced will be in upward direction. For it current induced will be anticlockwise.

4 0

2 years ago