An object accelerates at 20 m/s2. By how much does the speed change in one
1 answer:
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Answer:
B. w=12.68rad/s
C. α=3.52rad/s^2
Explanation:
B)
We can solve this problem by taking into account that (as in the uniformly accelerated motion)
( 1 )
where w0 is the initial angular speed, α is the angular acceleration, s is the arc length and r is the radius.
In this case s=3.7m, r=16.2cm=0.162m, t=3.6s and w0=0. Hence, by using the equations (1) we have
to calculate the angular speed w we can use
Thus, wf=12.68rad/s
C) We can use our result in B)
I hope this is useful for you
regards
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: