Final velocity of two blocks between a spring

In summary, two blocks of masses 1kg and 3kg are connected by a spring with a force constant of 720 N/m. The spring is initially compressed by 0.225m. After being released, the blocks experience an acceleration of 162m/s^2 and 54m/s^2 respectively. To find the final speed of the blocks after leaving the spring, you need to use conservation of energy, as the initial potential energy of the spring converts to kinetic energy for both masses. Using this conservation law, the final speeds are calculated to be 5.23m/s for the 1kg mass and 1.74m/s for the 3kg mass.
  • #1
PedroPicapiedra
3
0

Homework Statement


Two blocks have a spring compressed between them, Block A (mass 1kg) and block B (mass 3kg) . The spring has force constant 720 N>m and is
initially compressed 0.225 m from its original length. For each
block, what is (a) the acceleration just after the blocks are released;
(b) the final speed after the blocks leave the spring?

Homework Equations


Fspring = kx = ma
1/2kx^2 = 1/2 mv^2

The Attempt at a Solution


For a I got
Aa = 162m/s^2
Ab = 54m/s^2

However I cannot for the life of me figure out b. I have tried using kinematic equations and conservation of energy.
1/2(720N)(0.225)^2 = 1/2(1kg)(v)^2
Gives me 6.03m/s for the 1kg mass
and 3.4m/s for the 3kg mass.
I know these results are wrong. They are supposed to be 5.23m/s and 1.74m/s
Thanks
 
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  • #2
PedroPicapiedra said:

Homework Statement


Two blocks have a spring compressed between them, Block A (mass 1kg) and block B (mass 3kg) . The spring has force constant 720 N>m and is
initially compressed 0.225 m from its original length. For each
block, what is (a) the acceleration just after the blocks are released;
(b) the final speed after the blocks leave the spring?

Homework Equations


Fspring = kx = ma
1/2kx^2 = 1/2 mv^2

The Attempt at a Solution


For a I got
Aa = 162m/s^2
Ab = 54m/s^2

However I cannot for the life of me figure out b. I have tried using kinematic equations and conservation of energy.
1/2(720N)(0.225)^2 = 1/2(1kg)(v)^2
Gives me 6.03m/s for the 1kg mass
and 3.4m/s for the 3kg mass.
I know these results are wrong. They are supposed to be 5.23m/s and 1.74m/s
Thanks
The initial potential energy of the springs converts to the kinetic energy of both masses, 1/2mAvA2+1/2mBvB2.
 
  • #3
... and you will need to use another conservation law.
 

1. What is the final velocity of two blocks connected by a spring?

The final velocity of two blocks connected by a spring depends on several factors, including the masses of the blocks, the spring constant, and the initial conditions. It can be calculated using the equation vf = √(2k/m) * (x - xo), where vf is the final velocity, k is the spring constant, m is the total mass of the blocks, x is the distance the spring is compressed or stretched, and xo is the initial distance of the spring.

2. How does the spring constant affect the final velocity of two blocks connected by a spring?

The spring constant, represented by the variable k, is a measure of the stiffness of the spring. A higher spring constant means the spring is stiffer, and therefore the final velocity of the blocks will be greater. This is because a stiffer spring can exert a larger force on the blocks, resulting in a higher final velocity.

3. Can the final velocity of two blocks connected by a spring be negative?

Yes, the final velocity can be negative. This indicates that the blocks are moving in the opposite direction of the initial compression or stretch of the spring. This can occur if the spring is stretched initially and then compressed, or vice versa.

4. How does the mass of the blocks affect the final velocity?

The mass of the blocks, represented by the variable m, directly affects the final velocity. A heavier mass will result in a lower final velocity, while a lighter mass will result in a higher final velocity. This is because a heavier mass requires more force to be accelerated, while a lighter mass can be accelerated more easily.

5. What happens to the final velocity if the initial distance of the spring is increased?

If the initial distance of the spring, represented by the variable xo, is increased, the final velocity will also increase. This is because a larger initial distance means the spring has more potential energy, which will be converted into kinetic energy as the spring returns to its equilibrium position. This results in a higher final velocity for the blocks.

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