a beach ball is left in the bed of a pickup truck. Describe what happens to the ball when the truck accelerates forward

A small metal ball is suspended from the ceiling by a thread of negligible mass. The ball is then set in motion in a horizontal

Gemiola [76]

Answer:

Time taken, $T=2\pi \sqrt{\dfrac{l\ cos\theta}{g}}$

Explanation:

It is given that, a small metal ball is suspended from the ceiling by a thread of negligible mass. The ball is then set in motion in a horizontal circle so that the thread’s trajectory describes a cone as shown in attached figure.

From the figure,

The sum of forces in y direction is :

$T\ cos\theta-mg=0$

$T=\dfrac{mg}{cos\theta}$

Sum of forces in x direction,

$T\ sin\theta=\dfrac{mv^2}{r}$

$mg\ tan\theta=\dfrac{mv^2}{r}$ .............(1)

Also, $r=l\ sin\theta$

Equation (1) becomes :

$mg\ tan\theta=\dfrac{mv^2}{l\ sin\theta}$

$v=\sqrt{gl\ tan\theta.sin\theta}$ ...............(2)

Let t is the time taken for the ball to rotate once around the axis. It is given by :

$T=\dfrac{2\pi r}{v}$

Put the value of T from equation (2) to the above expression:

$T=\dfrac{2\pi r}{\sqrt{gl\ tan\theta.sin\theta}}$

$T=\dfrac{2\pi l\ sin\theta}{\sqrt{gl\ tan\theta.sin\theta}}$

On solving above equation :

$T=2\pi \sqrt{\dfrac{l\ cos\theta}{g}}$

Hence, this is the required solution.

4 0

3 years ago

2. A person began running due east and covered 15 kilometers in 2.0 hours. What is the average velocity of the person?

Angelina_Jolie [31]

Answer:

7.5 km/h (2.1 m/s) due east

Explanation:

The average velocity of the person is given by:

$v=\frac{d}{t}$

where

d is the displacement

t is the time taken

In this problem,

d = 15 km is the displacement

t = 2.0 h is the time elapsed

so the average velocity is

$v=\frac{15 km}{2.0 h}=7.5 km/h$

and the direction is the same as the displacement (east).

We can also convert the velocity into SI units (m/s). We have:

d = 15 km = 15,000 m

t = 2.0 h * 3600 s/h = 7200 s

$v=\frac{15,000 m}{7200 s}=2.1 m/s$

4 0

3 years ago

Read 2 more answers

A space vehicle of mass m has a speed v. At some instant, it separates into two pieces, each of mass 0.5m. One of the pieces is

Damm [24]

Answer:

W = ½ m v²

Explanation:

In this exercise we must solve it in parts, in a first part we use the conservation of the moment to find the speed after the separation

We define the system formed by the two parts of the rocket, therefore the forces during internal separation and the moment are conserved

initial instant. before separation

p₀ = m v

final attempt. after separation

$p_{f}$ = m /2 0 + m /2 v_{f}

p₀ = p_{f}

m v = m /2 $v_{f}$

v_{f}= 2 v

this is the speed of the second part of the ship

now we can use the relation of work and energy, which establishes that the work is initial to the variation of the kinetic energy of the body

initial energy

K₀ = ½ m v²

final energy

$K_{f}$ = ½ m/2 0 + ½ m/2 v_{f}²

K_{f} = ¼ m (2v)²

K_{f} = m v²

the expression for work is

W = ΔK = K_{f} - K₀

W = m v² - ½ m v²

W = ½ m v²

5 0

3 years ago

The Eco-Marathon is an annual competition sponsored by Shell Oil, in which participants build special vehicles to achieve the

OverLord2011 [107]

Answer:

(1) V=0.03348 gallons

(2) L= 576.813 km .

Explanation:

Write the relation between the density and volume for ethanol.

density ( ρ )= m/V

Volume ( V )= m/ρ .......... (1)

Here, V is the volume of ethanol, m is the mass of ethanol, and is the density of ethanol.

Write the relation between the specific gravity of ethanol and density of water

ρ=γ*ρ(water) ............. (2)

Here, is specific gravity of ethanol and is the density of water.

Determine the volume of ethanol by substituting equation (2) in equation (1)

V=m/γ*ρ(water)

Substitute 100 gm , for m, for , and 1000 kg/m for.

V= $\frac{100*10^{-3} }{0.789*1000}$

V=0.000112674 $m^{3$

Convert m³ to gallons

V= (0.000112674*264.172 )

V=0.03348 gallons

Step 2:

Determine the distance travelled by the special vehicle named “Micro joule” runs with ethanol.

L=C*V .......... (3)

Here, is the rate of consumption of ethanol by Micro joule.

Substitute 10,705 mi/gallons for C and 0.03348 gallons for .

By using eq. 3.

L= 10750*0.03348

L=358.416 mi.

Convert the distance travelled by Micro joule from miles to kilometres

L= (358.416* 1.60934)

L = 576.813 km

Thus, the distance travelled by Micro joule is 576.813 km .

4 0

3 years ago

Please answer this fast <br>I 'll marks them brainliest answer <br>

Reptile [31]

answer

64 is C (c) 1-Bromo-3-methylbutane

63 is D

i is secondary ii is primary

8 0

2 years ago