Một vận động viên ném tạ quay một cái đĩa nặng 1kg với bán

Law of conservation of energy states that energy can neither be created nor be destroyed but it can only be transformed from one form to another form.

Here, the potential energy of the coffee filter is getting converted into kinetic energy of the coffee filter and some energy is lost by it which is gained by the air molecules in the form of kinetic energy.

So, calculating the potential energy of coffee filter, we use the equation:

P = mgh

where,

m = mass of coffee filter = 1.2 g = $1.2\times 10^{-3}kg$ (Conversion used: 1 kg = 1000 g)

g = acceleration due to gravity = $9.8m/s^2$

h = height of coffee filter = 1 m

Putting values in above equation, we get:

$P=1.2\times 10^{-3}kg\times 9.8m/s^2\times 1m\\\\P=1.176\times 10^{-2}J$

Calculating the kinetic energy of coffee filter, we use the equation:

$E=\frac{1}{2}mv^2$

where,

m = mass of coffee filter = 1.2 g = $1.2\times 10^{-3}kg$

v = speed of coffee filter = 0.8 m/s

Putting values in above equation, we get:

$E=\frac{1}{2}\times 1.2\times 10^{-3}kg\times (0.8m/s)^2\\\\E=3.84\times 10^{-4}J$

As, energy lost by coffee filter = energy gained by air molecules

So, energy lost by coffee filter = Potential energy - Kinetic energy

Energy lost by coffee filter = $(1.176\times 10^{-2})-(3.84\times 10^{-4})=0.011J$

Hence, the energy gained by the air molecules is 0.011 J.

5 0

3 years ago

The spring is compressed a total of 3.0 cm, and used to set a 500 gram cart into motion. Find the speed of the cart at the insta

BartSMP [9]

Answer:

1.15 m/s

Explanation:

Part of the question is missing. Found the missing part on google:

"1. A hanging mass of 1500 grams compresses a spring 2.0 cm. Find the spring constant in N/m."

Solution:

First of all, we need to find the spring constant. We can use Hooke's law:

$F=kx$

where

$F=mg=(1.5 kg)(9.8 m/s^2)=14.7 N$ is the force applied to the spring (the weight of the hanging mass)

x = 2.0 cm = 0.02 m is the compression of the spring

Solving for k, we find the spring constant:

$k=\frac{F}{x}=\frac{14.7}{0.02}=735 N/m$

In the second part of the problem, the spring is compressed by

x = 3.0 cm = 0.03 m

So the elastic potential energy of the spring is

$U=\frac{1}{2}kx^2=\frac{1}{2}(735)(0.03)^2=0.33 J$

This energy is entirely converted into kinetic energy of the cart, which is:

$U=K=\frac{1}{2}mv^2$

where

m = 500 g = 0.5 kg is the mass of the cart

v is its speed

Solving for v,

$v=\sqrt{\frac{2K}{m}}=\sqrt{\frac{2(0.33)}{0.5}}=1.15 m/s$

4 0

3 years ago

Use appropriate units and significant figures. USE THE LAW OF COSINES AND LAW OF SINES.

N76 [4]

Answer:

The resultant velocity is 86.1 mi/h.

Explanation:

The law of cosines is given by:

$c^{2} = a^{2} + b^{2} - 2abcos(\theta)$

Where:

c: is the resultant velocity =?

a: is the velocity of the plane = 75.0 mi/h

b: is the velocity of the wind = 15.0 mi/h

θ: is the angle between "a" and "b"

The angle between "a" and "b" can be found as follows:

$\theta = 180.0 - 46.0 = 134.0 ^{\circ}$

Now, by using the law of cosines we have:

$c^{2} = (75.0)^{2} + (15.0)^{2} - 2*75.0*15.0*cos(134.0) = 7413.0$

$c = 86.1 mi/h$

Therefore, the resultant velocity is 86.1 mi/h.

The law of sines is:

$\frac{a}{sin(\gamma)} = \frac{b}{sin(\alpha)} = \frac{c}{sin(\theta)}$

Where:

γ: is the angle between "b" and "c"

α: is the angle between "a" and "c"

So, if we want to find "c" by using the law of sines, we need to know another angle besides θ (γ or α), and the statement does not give us.

I hope it helps you!

3 0

2 years ago