A 2kg mass, initially at rest, is shot from a spring (k=550N/m) which is compressed by 1.3m. The 2kg
mass hits a stationary 6kg mass (the actual collision lasts 0.02seconds). After the collision the 2kg mass
is travelling 11m/s to the left. To the right of the 6kg mass is a rough patch that has a 0.4 coefficient of
friction. To the left of the 6kg mass there is no friction.
a. What is the distance that block two will move after the collision??
To find the distance that block two will move after the collision, we need to calculate the kinetic energy of block two before and after the collision.
1. Calculate the initial potential energy of the spring:
The potential energy stored in the spring can be calculated using the formula: PE = (0.5)kx^2, where k is the spring constant (550 N/m) and x is the compression distance (1.3 m).
PE = (0.5)(550 N/m)(1.3 m)^2
2. Calculate the initial kinetic energy of block one:
Since block one is initially at rest, the initial kinetic energy of block one is zero.
3. Calculate the total initial energy:
The total initial energy is the sum of the initial potential energy and kinetic energy for block one:
Total initial energy = PE + 0
4. Calculate the total final energy:
The final kinetic energy of block two can be calculated using the formula: KE = (0.5)mv^2, where m is the mass of block two (2 kg) and v is its final velocity (-11 m/s to the left).
KE = (0.5)(2 kg)(11 m/s)^2
5. Calculate the change in energy:
The change in energy is equal to the total initial energy minus the total final energy:
Change in energy = Total initial energy - Total final energy
6. Calculate the work done by friction:
The work done by friction can be calculated using the formula: Frictional force * distance, where the frictional force is equal to the coefficient of friction (0.4) multiplied by the normal force (which is equal to the weight of block two), and the distance is what we are trying to find.
7. Set the change in energy equal to the work done by friction:
Change in energy = Work done by friction
8. Rearrange the equation to solve for the distance:
Distance = (Change in energy) / (Frictional force)
Substitute the known values into the equation and solve for the distance to find the distance that block two will move after the collision.