A block attached to a spring with unknown spring constant oscillates with a period of 8.0 ss . Parts a to d are independent ques
1 answer:
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Answer:
Explanation:
given,
angle at which rock is thrown = 60°
rock lands at distance,d = 25 m
initial speed of rock, = ?
In horizontal direction
distance = speed x time
d = v₀ cos 60° t
25 = v₀ cos 60° t............(1)
now,
in vertical direction
displacement in vertical direction is zero
using equation of motion
putting the value of t in equation (1)
v
Hence, the initial speed of the rock is equal to 16.82 m/s
We need to write down momentum and energy conservation laws, this will give us a system of equation that we can solve to get our final answer. On the right-hand side, I will write term after the collision and on the left-hand side, I will write terms before the collision.
Let's start with energy conservation law:
This equation tells us that kinetic energy of two carts before the collision and 3 quarters of explosion energy is beign transfered to kinetic energy of the cart after the collision.
Let's write down momentum conservation law:
Because both carts have the same mass we can cancel those out:
Now we have our system of equation that we have to solve:
Part A
We need to solve our system for
. We will solve second equation for 
and then plug that in the first equation.
Now we have to plug this in the first equation:
We will multiply the first equation with 2 and divide by m:
Now we plug in the second equation into first one:
We end up with quadratic equation that we have to solve, I won't solve it by hand.
Coefficients are:
Solutions are:
Part B
We do the same thing here, but we must express from momentum equation:
Now we plug this into our energy conservation equation:
Again we end up with quadratic equation. Coefficients are:
Solutions are:
Let's start with energy conservation law:
This equation tells us that kinetic energy of two carts before the collision and 3 quarters of explosion energy is beign transfered to kinetic energy of the cart after the collision.
Let's write down momentum conservation law:
Because both carts have the same mass we can cancel those out:
Now we have our system of equation that we have to solve:
Part A
We need to solve our system for
Now we have to plug this in the first equation:
We will multiply the first equation with 2 and divide by m:
Now we plug in the second equation into first one:
We end up with quadratic equation that we have to solve, I won't solve it by hand.
Coefficients are:
Solutions are:
Part B
We do the same thing here, but we must express
Now we plug this into our energy conservation equation:
Again we end up with quadratic equation. Coefficients are:
Solutions are:
No. of ways in the elements of n be permuted is n!/4
Number of elements = n
Number of face in which the element of n be permuted if 1 must proceed 2 and 3 is to precede 4.
n = 4
The possible permutation will
(1,2,3,4), (1,3,2,4),(1,3,4,2),(3,4,1,2),(3,1,2,4),(3,1,4,2)
There are 6 possible outcomes
For n= 5
With 1,2,3,4 we add 5 in the arrangement with above terms
The possible number of permutation
5×6 = 30
When n = 6
30×6 = 180.
So for an element
If 1 precede 2 and 3 is yo precede 4 is
<h2>= n! ×6/4!
= n!/4
No. of ways in the elements of n be permuted is n!/4
To know more about permutation:
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