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A solid, uniform disk of radius 0.250 m and mass 45.2 kg rolls down a ramp of length 5.40 m that makes an angle of 17.0° with th

serious [3.7K]

Explanation:

Given that,

Radius of the disk, r = 0.25 m

Mass, m = 45.2 kg

Length of the ramp, l = 5.4 m

Angle made by the ramp with horizontal, $\theta=17^{\circ}$

Solution,

As the disk starts from rest from the top of the ramp, the potential energy is equal to the sum of translational kinetic energy and the rotational kinetic energy or by using the law of conservation of energy as :

(a) $mgh=\dfrac{1}{2}mv^2+\dfrac{1}{2}I\omega^2$

h is the height of the ramp

$sin\theta=\dfrac{h}{5.4}$

$h=sin(17)\times 5.4=1.57\ m$

v is the speed of the disk's center

I is the moment of inertia of the disk,

$I=\dfrac{1}{2}mr^2$

$\omega=\dfrac{v}{r}$

$mgh=\dfrac{1}{2}mv^2+\dfrac{1}{2}\dfrac{1}{2}mr^2\times (\dfrac{v}{r})^2$

$gh=\dfrac{1}{2}v^2+\dfrac{1}{4}v^2$

$gh=\dfrac{3}{4}v^2$

$9.8\times 1.57=\dfrac{3}{4}v^2$

v = 4.52 m/s

(b) At the bottom of the ramp, the angular speed of the disk is given by :

$\omega=\dfrac{v}{r}$

$\omega=\dfrac{4.52}{0.25}$

$\omega=18.08\ rad/s$

Hence, this is the required solution.

4 0

2 years ago

Matthew drives 10 meters to go to the park at her the park he goes to the movie theatre which is 15 meters away from the park. H

Step2247 [10]

Answer: 0 m

Explanation:

Let's begin by stating clear that movement is the change of position of a body at a certain time. So, during this movement, the body will have a trajectory and a displacement, being both different:

The trajectory is the path followed by the body (is a scalar quantity).

The displacement is the distance in a straight line between the initial and final position (is a vector quantity).

According to this, in the description Matthew's home is placed at 0 on a number line, then he moves 10 m to the park (this is the distance between the park and Mattew's home), then 15 m to the movie theatre until he finally comes back to his home (position 0). So, in this case we are talking about the path followed by Matthew, hence his trajectory.

However, if we talk about Matthew's displacement, we have to draw a straight line between Matthew's initial position (point 0) to his final position (also point 0).

Now, being this an unidimensional problem, the displacement vector for Matthew is 0 meters.

4 0

2 years ago

A vehicle accelerates from 0 to 30 m/s in 10 seconds on a straight road

Solnce55 [7]

What's the question?

6 0

2 years ago

Read 2 more answers

Car A and Car B approach each other

vagabundo [1.1K]

The original frequency of horn of Car A is 1071 Hz.

Explanation:

Doppler effect describes the change in the frequency of sound waves with respect to the observer. As the sound waves emitted from a source need to travel the air medium to reach observer, it will undergo loss in energy. So there will be change in its frequency compared to original frequency. Depending upon the direction of travel of source and observer the shifting of frequency will vary.

$f'=\frac{v-v_{o} }{v-v_{s} } f$

Here vo is the observer velocity and vs is the velocity of the source. So Vo = 15 m/s as car B is the observer and Vs = 35 m/s as car A is the source. And f is the frequency of sound wave at source that is car A.

Similarly, the doppler shift in frequency is the frequency of sound heard by car B which is f' = 1140 Hz. And v is the speed of sound that is v = 343 m/s

1140 = $\frac{343-15}{343-35}*f= 1.0649 *f$

f = 1140/1.0649= 1071 Hz.

Thus, the original frequency of horn of Car A is 1071 Hz.

3 0

3 years ago

What is the average speed of the marble as it rolls across the floor?

dusya [7]

Answer:

1.5 m/s

Explanation:

5 0

2 years ago