While the cart is moving along an aisle, it comes in contact with a smear of margarine that had recently been dropped on the flo
1 answer:
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Answer:
a) the mug hits the floor 0.7425m away from the end of the bar. b) |V|=5.08m/s θ= -72.82°
Explanation:
In order to solve this problem, we must first start by doing a drawing of the situation. (see attached picture).
a)
From the drawing we can see that we are dealing with a two dimensions movement problem. So in order to find out how far away from the bar the mug will fall, we need to start by finding how long it will take the mug to be in the air, so we analyze the vertical movement of the mug.
In order to find the time we need to use the following formula, which contains the data we know:
we know that and that
as well, so the formula is simplified to:
we can now solve this for t, so we get:
we know that and that
the acceleration of gravity is negative because the mug is moving downwards. So we substitute them into the given formula:
which yields:
t=0.495s
we can now use this to find the horizontal distance the mug travels. We know that:
so we can solve this for x, so we get:
and we can now substitute the values we know:
x=(1.5m/s)(0.495s)
which yields:
x=0.7425m
b) Now that we know the time it takes the mug to hit the floor, we can use it to find the final velocity in the y-direction by using the following formula:
we know the initial velocity in the vertical direction is zero, so we can simplify the formula:
so we can solve this for the final velocity:
in this case the acceleration is the same as the acceleration of gravity (which is negative) so we can substitute that and the time we found on the previous part to get:
which yields:
so now we know the components of the final velocity, which are:
and
so now we can find the speed by determining the magnitude of the vector, like this:
so we get:
which yields:
|V|=5.08m/s
now, to find the direction of the impact, we can use the following equation:
so we get:
which yields:
If no frictional work is considered, then the energy of the system (the driver at all positions is conserved.
Let
position 1 = initial height of the diver (h₁), together with the initial velocity (v₁).
position 2 = final height of the diver (h₂) and the final velocity (v₂).
The initial PE = mgh₁ and the initial KE = (1/2)mv₁²
where g = acceleration due to gravity,
m = mass of the diver.
Similarly, the final PE and KE are respectively mgh₂ and (1/2)mv₂².
PE in position 1 is converted into KE due to the loss in height from position 1 to position 2.
Therefore
(KE + PE) ₁ = (KE + PE)₂
Evaluate the given answers.
A) The total mechanical energy of the system increases.
FALSE
B) Potential energy can be converted into kinetic energy but not vice versa.
TRUE
C) (KE + PE)beginning = (KE + PE) end.
TRUE
D) All of the above.
FALSE
Let
position 1 = initial height of the diver (h₁), together with the initial velocity (v₁).
position 2 = final height of the diver (h₂) and the final velocity (v₂).
The initial PE = mgh₁ and the initial KE = (1/2)mv₁²
where g = acceleration due to gravity,
m = mass of the diver.
Similarly, the final PE and KE are respectively mgh₂ and (1/2)mv₂².
PE in position 1 is converted into KE due to the loss in height from position 1 to position 2.
Therefore
(KE + PE) ₁ = (KE + PE)₂
Evaluate the given answers.
A) The total mechanical energy of the system increases.
FALSE
B) Potential energy can be converted into kinetic energy but not vice versa.
TRUE
C) (KE + PE)beginning = (KE + PE) end.
TRUE
D) All of the above.
FALSE