Ask question

Ask question

All categories

2 years ago

12

You are at the park with your little brother, when you notice a small merry-go-round with a radius that looks to be about 1.5 m.

Your brother climbs on, and you give him a spin. From rest, you speed up smoothly, completing one full lap in 3.0 seconds. You wonder what sort of acceleration (magnitude and direction) your brother experiences at the very start of the motion, and at the very end of the first lap. He is quite young and hasn't studied any physics, so he does not know how to answer your question. You decide to give him your smartphone (which has a built-in accelerometer), and repeat the experiment. What will the smartphone record

1 answer:

Elodia [21]2 years ago

7 0

Answer:

Explanation:

angle covered in one rotation = 2π radian

θ = ωt + 1/2 αt²

θ is angle rotated in time t with initial angular velocity of ω and angular acceleration α .

Putting the values

2π = 0 + 1/2 x α x 3²

α = 1. 4 radian / s²

linear acceleration = α x r = 1.4 x 1.5 = 2.1 m / s².

Initial acceleration = 2.1 m /s²

final angular velocity = α t = 1.4 x 3 = 4.2 radian / s

linear velocity = 4.2 x 1.5 = 6.3 m /s

centripetal acceleration = v² / R = 6.3² / 1.5 = 26.46 m /s²

radian acceleration = 26.46 m /s

tangential acceleration = 2.1 m /s²

Total final acceleration = √ ( 26.46² + 2.1² )

= √ ( 700.13 + 4.41)

Final acceleration = 26.53 m / s²

You might be interested in

A short current element dl⃗ = (0.500 mm)j^ carries a current of 5.40 A in the same direction as dl⃗ . Point P is located at r⃗ =

SashulF [63]

Answer:

The magnetic field along x axis is

$B_{x}=1.670\times10^{-10}\ T$

The magnetic field along y axis is zero.

The magnetic field along z axis is

$B_{z}=3.484\times10^{-10}\ T$

Explanation:

Given that,

Length of the current element $dl=(0.5\times10^{-3})j$

Current in y direction = 5.40 A

Point P located at $\vec{r}=(-0.730)i+(0.390)k$

The distance is

$|\vec{r}|=\sqrt{(0.730)^2+(0.390)^2}$

$|\vec{r}|=0.827\ m$

We need to calculate the magnetic field

Using Biot-savart law

$B=\dfrac{\mu_{0}}{4\pi}\timesI\times\dfrac{\vec{dl}\times\vec{r}}{|\vec{r}|^3}$

Put the value into the formula

$B=10^{-7}\times5.40\times\dfrac{(0.5\times10^{-3})\times(-0.730)i+(0.390)k}{(0.827)^3}$

We need to calculate the value of $\vec{dl}\times\vec{r}$

$\vec{dl}\times\vec{r}=(0.5\times10^{-3})\times(-0.730)i+(0.390)k$

$\vec{dl}\times\vec{r}=i(0.350\times0.5\times10^{-3}-0)+k(0+0.730\times0.5\times10^{-3})$

$\vec{dl}\times\vec{r}=0.000175i+0.000365k$

Put the value into the formula of magnetic field

$B=10^{-7}\times5.40\times\dfrac{(0.000175i+0.000365k)}{(0.827)^3}$

$B=1.670\times10^{-10}i+3.484\times10^{-10}k$

Hence, The magnetic field along x axis is

$B_{x}=1.670\times10^{-10}\ T$

The magnetic field along y axis is zero.

The magnetic field along z axis is

$B_{z}=3.484\times10^{-10}\ T$

7 0

2 years ago

An iguana runs back and forth along the ground. The horizontal position of the iguana in meters over time is shown

mafiozo [28]

Answer:

Displacement between 0s and 6s = 2

Distance between 0s and 6s = 14

Explanation:

Displacement: 0+2 = 2

Distance: |-2|+6+6

5 0

2 years ago

In the introduction of this activity, we mentioned the temperature of your home on hot and cold days. Your body is kept warm in

Alecsey [184]

Answer:

a - The walls of the house are warmer during the summer. Therefore, they radiate more infrared light that can serve to warm our body.

Explanation:

The answer is Option(a). According to studies, the reason to feel warmer inside the house is the absorption of infrared radiations emitted by the walls. Also more the temperature of the body, the more the heat radiated by it. During summer the walls of the house are at higher temperature for which they emit more infrared radiations which our body absorbs and make us feel more warmer.

3 0

2 years ago

Read 2 more answers

A football player kicks a football downfield. The height of the football increases until it reaches a maximum height of 15 yards

Trava [24]

Answer:

kick 1 has travelled 15 + 15 = 30 yards before hitting the ground

so kick 2 travels 25 + 25 = 50 yards before hitting the ground

first kick reached 8 yards and 2nd kick reached 20 yards

Explanation:

1st kick travelled 15 yards to reach maximum height of 8 yards

so, it has travelled 15 + 15 = 30 yards before hitting the ground

2nd kick is given by the equation

y (x) = -0.032x(x - 50)

$Y = 1.6 X - 0.032x^2$

we know that maximum height occurs is given as

$x = -\frac{b}{2a}$

$y =- \frac{1.6}{2(-0.032)} = 25$

and maximum height is

$y = 1.6\times 25 - 0.032\times 25^2$

y = 20

so kick 2 travels 25 + 25 = 50 yards before hitting the ground

first kick reached 8 yards and 2nd kick reached 20 yards

8 0

2 years ago

Read 2 more answers

A passenger compartment of a rotating amusement park ride contains a bench on which a book of mass

Basile [38]

a) 120 s

b) v = 0.052R [m/s]

Explanation:

a)

The period of a revolution in a simple harmonic motion is the time taken for the object in motion to complete one cycle (in this case, the time taken to complete one revolution).

The graph of the problem is missing, find it in attachment.

To find the period of revolution of the book, we have to find the time between two consecutive points of the graph that have exactly the same shape, which correspond to two points in which the book is located at the same position.

The first point we take is t = 0, when the position of the book is x = 0.

Then, the next point with same shape is at t = 120 s, where the book returns at x = 0 m.

Therefore, the period is

T = 120 s - 0 s = 120 s

b)

The tangential speed of the book is given by the ratio between the distance covered during one revolution, which is the perimeter of the wheel, and the time taken, which is the period.

The perimeter of the wheel is:

$L=2\pi R$

where R is the radius of the wheel.

The period of revolution is:

$T=120 s$

Therefore, the tangential speed of the book is:

$v=\frac{L}{T}=\frac{2\pi R}{120}=0.052R$

8 0

2 years ago