A body of mass 120 g is taken vertically upwards to reach the height of 5m,claculate work done

nikitadnepr [17]

Adjust the height of the wooden rod so that it just touches the surface of the water. Switch on the lamp and motor and adjust the speed of the motor until low frequency waves can be clearly observed... Count the number of waves passing a point in ten seconds then Divide by ten to record frequency.

6 0

2 years ago

An offshore oil well is 2 kilometers off the coast. The refinery is 4 kilometers down the coast. Laying pipe in the ocean is twi

shusha [124]

Answer:

Rectangular path

Solution:

As per the question:

Length, a = 4 km

Height, h = 2 km

In order to minimize the cost let us denote the side of the square bottom be 'a'

Thus the area of the bottom of the square, A = $a^{2}$

Let the height of the bin be 'h'

Therefore the total area, $A_{t} = 4ah$

The cost is:

C = 2sh

Volume of the box, V = $a^{2}h = 4^{2}\times 2 = 128$ (1)

Total cost, $C_{t} = 2a^{2} + 2ah$ (2)

From eqn (1):

$h = \frac{128}{a^{2}}$

Using the above value in eqn (1):

$C(a) = 2a^{2} + 2a\frac{128}{a^{2}} = 2a^{2} + \frac{256}{a}$

$C(a) = 2a^{2} + \frac{256}{a}$

Differentiating the above eqn w.r.t 'a':

$C'(a) = 4a - \frac{256}{a^{2}} = \frac{4a^{3} - 256}{a^{2}}$

For the required solution equating the above eqn to zero:

$\frac{4a^{3} - 256}{a^{2}} = 0$

a = 4

Also

$h = \frac{128}{4^{2}} = 8$

The path in order to minimize the cost must be a rectangle.

8 0

3 years ago

A baseball with a mass of 151 g is thrown horizontally with a speed of 39.5 m/s (88 mi/h) at a bat. The ball is in contact with

Oduvanchick [21]

Answer:

the average force exerted on the ball by the bat is 11,613.27 N

Explanation:

Given;

mass of the baseball, m = 151 g = 0.151 kg

initial velocity of the baseball, u = 39.5 m/s

final velocity of the baseball, v = 45.1 m/s

time of action, t = 1.10 ms = 1.10 x 10⁻³ s

The average force exerted on the ball by the bat is calculate as;

$F = ma = \frac{m(v-u)}{t} \\\\F = \frac{0.151(45.1-(-39.5))}{1.10\times 10^{-3}} \\\\F = \frac{0.151(45.1\ +\ 39.5)}{1.10\times 10^{-3}} \\\\F = 11,613.27 \ N$

Therefore, the average force exerted on the ball by the bat is 11,613.27 N

7 0

2 years ago

What is a difference between a law and a hypothesis?

AnnZ [28]

The correct answer is

C ). A hypothesis includes an explanation for why two variables affect each other, but a law only describes how they affect each other.

8 0

3 years ago

You set your stationary bike on a high 80-N friction-like resistive force and cycle for 30 min at a speed of 8.0 m/s . Your body

stellarik [79]

A) The change in internal chemical energy is $1.15\cdot 10^7 J$

B) The time needed is 1 minute

Explanation:

First of all, we start by calculating the power output of you and the bike, given by:

$P=Fv$

where

F = 80 N is the force that must be applied in order to overcome friction and travel at constant speed

v = 8.0 m/s is the velocity

Substituting,

$P=(80)(8.0)=640 W$

The energy output is related to the power by the equation

$P=\frac{E}{t}$

where:

P = 640 W is the power output

E is the energy output

$t = 30 min \cdot 60 = 1800 s$ is the time elapsed

Solving for E,

$E=Pt=(640)(1800)=1.15\cdot 10^6 J$

Since the body is 10% efficient at converting chemical energy into mechanical work (which is the output energy), this means that the change in internal chemical energy is given by

$\Delta E = \frac{E}{0.10}=\frac{1.15\cdot 10^6}{0.10}=1.15\cdot 10^7 J$