Which of the following expressions for power or dimensionally correct?

A lion has a mass of 45 kg. Answer the following questions about it, using correct units. a. The lion runs at a speed of 14.2 m/

Eva8 [605]

A) The kinetic energy of an object is given by:
$K= \frac{1}{2}mv^2$
where m is the mass of the object, and v its speed. For the lion in our problem, m=45 kg and v=14.2 m/s, so its kinetic energy is
$K= \frac{1}{2}mv^2= \frac{1}{2}(45 kg)(14.2 m/s)^2=4537 J$

b) the increase in gravitational potential energy of the lion is given by:
$\Delta U = mg \Delta h$
where g is the gravitational acceleration, and $\Delta h$ is the increase in altitude of the lion. In this problem, $\Delta h=28 m$ , so the increase in gravitational potential energy is
$\Delta U=mg \Delta h=(45 kg)(9.81 m/s^2)(28 m)=12361 J$

c) When the fox reaches the top of the tree, its gravitational potential energy is
$U=mgh=(1.8 kg)(9.81 m/s^2)(3.8 m)=67 J$
As it jumps, its kinetic energy is
$K= \frac{1}{2}mv^2= \frac{1}{2}(1.8 kg)(8.1 m/s)^2=59 J$
So the total mechanical energy of the fox as it jumps is
$E=U+K=67 J + 59 J =126 J$

6 0

3 years ago

A 20 liter cylinder of helium at a pressure of 150 atm and a temperature of 27ÁC is used to fill a balloon at 1.00 atm and 37ÁC.

djyliett [7]

<u>Answer</u>

D) 3100 Liters

<u>Explanation</u>

To get the volume if the balloon you need to use the combined equation of the low of gases.

P₁V₁/T₁ = P₂V₂/T₂

(20×150)/(27+273) = (1×V₂)/(37+273)

3000/300 = V₂/310

10 = V₂/310

V₂ = 10 × 310

= 3100 Liters

7 0

3 years ago

Read 2 more answers

A ferry coming into port is sailing at 12 m/s. It takes 2.5km to come to rest in the port. Calculate the deceleration of the fer

pogonyaev

Answer: -0.0288 m/s^2

Explanation:

Let's suppose that the ferry decelerates at a constant rate A (deceleration is an acceleration in the opposite direction to the original motion of an object)

Then the acceleration equation of the ferry will be:

a(t) = -A

(the negative sign is because this acceleration is in the opposite direction with respect to the movement of the ferry)

To get the velocity equation of the ferry, we need to integrate with respect to the time, t, we will get:

v(t) = -A*t + v0

where v0 is the initial velocity of the ferry, v0 = 12m/s.

v(t) = -A*t + 12m/s

For the position equation of the ferry we need to integrate again over time:

p(t) = (-A/2)*t^2 + (12m/s)*t + p0

Where p0 is the initial position of the ferry, in this case, it can be zero, because it will depend on where we put the origin on our coordinate axis.

then p0 = 0m

P(t) = (-A/2)*t^2 + (12m/s)*t

The ferry will come to rest at the moment when it's velocity is equal to zero, this will happen when:

v(t) = 0m/s = -A*t + 12m/s

We need to find the value of t.

A*t = 12m/s

t = (12m/s)/A

Now we can replace this in the position equation because we know that the ferry needs 2.5 km or 2500 meters to come to rest.

p( (12m/s)/A) = 2500m = (-A/2)*( (12m/s)/A)^2 + (12m/s)*((12m/s)/A)

2500m = (-72 m^2/s^2)/A + (144m^2/s^2)/A

2500m = (72 m^2/s^2)/A

2500m*A = (72 m^2/s^2)

A = (72 m^2/s^2)/2500m = 0.0288 m/s^2

and the acceleration of the ferry was -A, then the acceleration of the ferry is:

-0.0288 m/s^2

4 0

2 years ago

What would you have loved to press the pause button on so you could go deeper

kiruha [24]

Answer:

~Banana Fish~

3 0

3 years ago

A 62 kg bungee jumper jumps from a bridge. She is tied to a bungee cord whose unstretched length is 12 m. She falls a total of 3

Andrew [12]

Answer:

k = 104.46 N/m

Explanation:

Here we can use energy conservation

so we will have

initial gravitational potential energy = final total spring potential energy

as we know that she falls a total distance of 31 m

while the unstretched length of the string is 12 m

so the extension in the string is given as

$x = L - L_o$

$x = 31 - 12 = 19 m$

so we have

$mgH = \frac{1}{2}kx^2$

$62(9.81)(31) = \frac{1}{2}k (19^2)$

$k = 104.46 N/m$

5 0

3 years ago