Conservation of kinetic energy/linear momentum problem

In summary, the problem involves a sphere and a block with given masses and initial velocities, with the block being on a 45° inclined surface and the sphere striking it 1 meter above the ground. The impact is perfectly elastic and the goal is to determine the final velocities of both objects using two equations. The 45° incline can be resolved into its horizontal component to use in the equations.
  • #1
jhahler
15
0

Homework Statement


An 8-kg sphere A is moving to the left with a velocity of 15 m/s when it strikes the 45° inclined surface of a 10-kg block B which is moving to the right a 5 m/s. The ball strikes the block 1 meter above the ground. The block is supported by rollers and impact is perfectly elastic. Determine the speeds of A and B after the impact.


Homework Equations


1/2mb(vb)^2 + 1/2ma(va)^2 = 1/2mb(vb)^2 + 1/2ma(va)^2 (initial kin. energy = final kin. energy)
mbvb + mava = mbvb + mava (initial linear mom. = final linear mom.)

The Attempt at a Solution


I know to use those 2 equations to solve for the 2 unknowns Vb final and Va final, but the only thing that's messing me up is what to do with the 45° incline on the block, and I think that the ball striking the block 1 foot about the ground is irrelevant, but I'm not positive. Any help is much appreciated.
 
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  • #2
Try and resolve the 'v' of the inclined block into its horizontal component. And then put the derived 'v' into the equation.
 

What is the conservation of kinetic energy/linear momentum problem?

The conservation of kinetic energy/linear momentum problem is a principle in physics which states that the total amount of kinetic energy and linear momentum in a closed system will remain constant over time, regardless of any internal changes or external forces acting on the system.

Why is the conservation of kinetic energy/linear momentum important?

The conservation of kinetic energy/linear momentum is important because it allows us to understand and predict the behavior of objects in motion. It is a fundamental principle in classical mechanics and is used in many real-world applications, such as analyzing collisions and designing efficient energy systems.

How is the conservation of kinetic energy/linear momentum calculated?

The conservation of kinetic energy/linear momentum is calculated using the equations Ek=1/2mv2 and p=mv, where Ek is the kinetic energy, m is the mass, v is the velocity, and p is the linear momentum. By plugging in the values before and after a collision or interaction, we can determine if the total kinetic energy and linear momentum have been conserved.

What are some real-world examples of the conservation of kinetic energy/linear momentum?

Some real-world examples of the conservation of kinetic energy/linear momentum include billiard balls colliding on a pool table, a car crashing into a wall, and a pendulum swinging back and forth. In each of these scenarios, the total kinetic energy and linear momentum of the system remain constant.

Are there any exceptions to the conservation of kinetic energy/linear momentum?

In classical mechanics, the conservation of kinetic energy/linear momentum is considered to be a universal law and has been successfully applied in many scenarios. However, in extreme cases such as at the quantum level or in situations involving extremely high speeds or strong gravitational forces, the principle may not hold true and may need to be modified by incorporating other factors such as relativistic effects.

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