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Svetlanka [38]
3 years ago
7

Students were asked to place a mint in their mouths and determine how long it took for the mint to dissolve. The condition of th

e mint varied in each student group. One group of students were asked to leave a whole mint in their mouth, not moving it around, and let it dissolve. Another group swirled a mint, while the other groups used mints broken into smaller pieces. See the chart for all of the manipulated variable. After reviewing that data table, what kind of result would you predict for the swirled, whole mint?
Physics
2 answers:
Llana [10]3 years ago
7 0

Students were asked to place a mint in their mouths and determine how long it took for the mint to dissolve. The condition of the mint varied in each student group. One group of students were asked to leave a whole mint in their mouth, not moving it around, and let it dissolve. Another group swirled a mint, while the other groups used mints broken into smaller pieces. See the chart for all of the manipulated variable. After reviewing that data table, what kind of result would you predict for the swirled, whole mint?


A) The time is likely between 10-30 seconds.  

B) The time is likely between 40-80 seconds.  

C) The time is likely between 90-160 seconds.  

D)    The time is likely between 100-200 seconds.

 

            ANSWER: B) The time is likely between 40-80 seconds.


  EXPLANATION:The time is likely between 40-80 seconds.

By swirling the mint, this is agitating and creating a higher frequency of collisions between the saliva particles and mint particles, increasing the rate of dissolution. Therefore, the time is likely to be less than the mint cut in half but probably more than the mint when it is in small pieces.

AnnZ [28]3 years ago
7 0

Answer: B

Explanation: The answer is B.

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exis [7]

a) The speed of the block at a height of 0.25 m is 2.38 m/s

b) The compression of the spring is 0.25 m

c) The final height of the block is 0.54 m

Explanation:

a)

We can solve the problem by using the law of conservation of energy. In fact, the total mechanical energy (sum of kinetic+gravitational potential energy) must be conserved in absence of friction. So we can write:

U_i +K_i = U_f + K_f

where

U_i is the initial potential energy, at the top

K_i is the initial kinetic energy, at the top

U_f is the final potential energy, at halfway

K_f is the final kinetic energy, at halfway

The equation can be rewritten as

mgh_i + \frac{1}{2}mu^2 = mgh_f + \frac{1}{2}mv^2

where:

m = 2.7 kg is the mass of the block

g=9.8 m/s^2 is the acceleration of gravity

h_i = 0.54 is the initial height

u = 0 is the initial speed

h_f = 0.25 m is the final height of the block

v is the final speed when the block is at a height of 0.25 m

Solving for v,

v=\sqrt{u^2+2g(h_i-h_f)}=\sqrt{0+2(9.8)(0.54-0.25)}=2.38 m/s

b)

The total mechanical energy of the block can be calculated from the initial conditions, and it is

E=K_i + U_i = 0 + mgh_i = (2.7)(9.8)(0.54)=14.3 J

At the bottom of the ramp, the gravitational potential energy has become zero (because the final heigth is zero), and all the energy has been converted into kinetic energy. However, then the block compresses the spring, and the maximum compression of the spring occurs when the block stops: at that moment, all the energy of the block has been converted into elastic potential energy of the spring. So we can write

E=E_e = \frac{1}{2}kx^2

where

k = 453 N/m is the spring constant

x is the compression of the spring

And solving for x, we find

x=\sqrt{\frac{2E}{k}}=\sqrt{\frac{2(14.3)}{453}}=0.25 m

c)

If there is no friction acting on the block, we can apply again the law of conservation of energy. This time, the initial energy is the elastic potential energy stored in the spring:

E=E_e = 14.3 J

while the final energy is the energy at the point of maximum height, where all the energy has been converted into gravitational potetial energy:

E=U_f = mg h_f

where h_f is the maximum height reached. Solving for this quantity, we find

h_f = \frac{E}{mg}=\frac{14.3}{(2.7)(9.8)}=0.54 m

which is the initial height: this is correct, because the total mechanical energy is conserved, so the block must return to its initial position.

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