The linear momentum is given by . Here
is mass
is velocity of the body. Given mass and velocities as
Initial momentum is and final momentum is
.
The correct answer is (A)
Red cabbage juice can be used as an acid-base indicator. When a solution is highly acidic, the juice turns red. As the acidity d
2 answers:
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d. Maintain constant velocity
Explanation:
A constant velocity leads to no acceleration.
Acceleration is defined as the change in velocity with time:
Acceleration =
If there is no change in velocity i.e constant velocity.
At constant velocity, the change in velocity is 0.
If we put zero in the equation above, we will obtain an acceleration value of 0.
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Answer:
The rule for kilometers is that every three seconds between a lightning flash and the following thunder gives the distance to the flash in kilometers.
Explanation:
In order to use the rule of thumb to find the speed of sound in meters per second, we need to use some conversion ratios. We know there is 1 mile per every 5 seconds after the lightning is seen. We also know that there are 5280ft in 1 mile and we also know that there are 0.3048m in 1ft. This is enough information to solve this problem. We set our conversion ratios like this:
notice how the ratios were written in such a way that the units got cancelled when calculating them. Notice that in one ratio the miles were on the numerator of the fraction while on the other they were on the denominator, which allows us to cancel them. The same happened with the feet.
The problem asks us to express the answer to one significant figure so the speed of sound rounds to 300m/s.
For the second part of the problem we need to use conversions again. This time we will write our ratios backwards and take into account that there are 1000m to 1 km, so we get:
This means that for every 3.11s there will be a distance of 1km from the place where the lightning stroke. Since this is a rule of thumb, we round to the nearest integer for the calculations to be made easily, so the rule goes like this:
The rule for kilometers is that every three seconds between a lightning flash and the following thunder gives the distance to the flash in kilometers.
A) Force of the wall on the ladder: 186.3 N
B) Normal force of the ground on the ladder: 725.2 N
C) Minimum value of the coefficient of friction: 0.257
D) Minimum absolute value of the coefficient of friction: 0.332
Explanation:
a)
The free-body diagram of the problem is in attachment (please rotate the picture 90 degrees clockwise). We have the following forces:
: weight of the ladder, with m = 20 kg (mass) and
(acceleration of gravity)
: weight of the person, with M = 54 kg (mass)
: normal reaction exerted by the wall on the ladder
: normal reaction exerted by the floor on the ladder
: force of friction between the floor and the ladder, with
(coefficient of friction)
Also we have:
L = 4.1 m (length of the ladder)
d = 3.0 m (distance of the man from point A)
Taking the equilibrium of moments about point A:
where
is the component of the weight of the ladder perpendicular to the ladder
is the component of the weight of the man perpendicular to the ladder
is the component of the normal force perpendicular to the ladder
And solving for , we find the force exerted by the wall on the ladder:
B)
Here we want to find the magnitude of the normal force of the ground on the ladder, therefore the magnitude of .
We can do it by writing the equation of equilibrium of the forces along the vertical direction: in fact, since the ladder is in equilibrium the sum of all the forces acting in the vertical direction must be zero.
Therefore, we have:
And substituting and solving for N2, we find:
C)
Here we have to find the minimum value of the coefficient of friction so that the ladder does not slip.
The ladder does not slip if there is equilibrium in the horizontal direction also: that means, if the sum of the forces acting in the horizontal direction is zero.
Therefore, we can write:
And re-writing the equation,
So, the minimum value of the coefficient of friction is 0.257.
D)
Here we want to find the minimum coefficient of friction so the ladder does not slip for any location of the person on the ladder.
From part C), we saw that the coefficient of friction can be written as
This ratio is maximum when N1 is maximum. From part A), we see that the expression for N1 was
We see that this quantity is maximum when d is maximum, so when
d = L
Which corresponds to the case in which the man stands at point B, causing the maximum torque about point A. In this case, the value of N1 is:
And substituting, we get
And therefore, the minimum coefficient of friction in order for the ladder not to slip is
Learn more about torques and equilibrium:
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