Solve the problems and show your work please and the formulas are at the top to use each one
1 answer:
1) The momentum of the object is 1000 kg m/s
2) The force exerted on the wall is 20,000 N
Explanation:
1)
The momentum of an object is defined as
where
m is the mass of the object
v is its velocity
For the object in this problem, we have
m = 50 kg is its mass
v = 20 m/s is the velocity
Substutiting, we find the momentum
2)
For this part of the problem, we can use the impulse theorem, which states that the impulse exerted on an object (the product between force and time of collision) is equal to the change in momentum of the object:
where
F is the force on the object
t is the duration of the collision
m is the mass
is the change in velocity of the object
Here we have:
m = 5000 kg
(the car decelerates from 40 m/s to a stop)
t = 10 s
Solving, we find the force exerted on the car:
where the negative sign means the direction of the force is opposite to that of motion of the car. However, here we are asked to find the force exerted by the car on the wall: according to Newton's third law, that force will be equal and opposite to the force exerted by the wall on the car, so
F = 20,000 N
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Answer:
6) Wave 1 travels in the positive x-direction, while wave 2 travels in the negative x-direction.
Explanation:
What matters is the part , the other parts of the equation don't affect time and space variations. We know that when the sign is - the wave propagates to the positive direction while when the sign is + the wave propagates to the negative direction, but <em>here is an explanation</em> of this:
For both cases, + and -, after a certain time (
), the displacement <em>y</em> of the wave will be determined by the
term. For simplicity, if we imagine we are looking at the origin (x=0), this will be simply
.
To know which side, right or left of the origin, would go through the origin after a time (and thus know the direction of propagation) we have to see how we can achieve that same displacement <em>y</em> not by a time variation but by a space variation
(we would be looking where in space is what we would have in the future in time). The term would be then
, which at the origin is
. This would mean that, when the original equation has
, we must have that
for
to be equal to
, and when the original equation has
, we must have that
for
to be equal to
<em>Note that their values don't matter, although they are a very small variation (we have to be careful since all this is inside a sin function), what matters is if they are positive or negative and as such what is possible or not .</em>
<em />
In conclusion, when , the part of the wave on the positive side (
) is the one that will go through the origin, so the wave is going in the negative direction, and viceversa.