Question

Nate the Skate was an avid physics student whose main non-physics interest in life was high-speed skateboarding. In particular, Nate would often don a protective suit of Bounce-Tex, which he invented, and after working up a high speed on his skateboard, would collide with some object. In this way, he got a gut feel for the physical properties of collisions and succeeded in combining his two passions.* On one occasion, the Skate, with a mass of 117 kg, including his armor, hurled himself against a 801-kg stationary statue of Isaac Newton in a perfectly elastic linear collision. As a result, Isaac started moving at 1.89 m/s and Nate bounced backward. What were Nate\'s speeds immediately before and after the collision? (Enter positive numbers.) Ignore friction with the ground.

 

Answer 1

Concepts and reason

The concepts used to solve this question are kinetic energy, conservation of momentum, linear momentum, and conservation of energy.

First, derive the relation between initial and final speeds of the skate and statue of Isaac by using the concept of conservation of momentum and conservation of energy.

Later determine the initial and final speed of the skate by using the equation of conservation of kinetic energy and momentum.

Fundamentals

Kinetic energy:

Kinetic energy is defined as the work required for accelerating a mass of a body from rest to a specific velocity.

The kinetic energy of an object is because of its motion.

Mathematically, the kinetic energy can be written as,

Here, is the kinetic energy of the object, is mass of the object and is the speed of the object.

Conservation of energy:

The conservation of energy is defined as energy cannot be created nor destroyed only it can convert one form to another form of energy.

Linear momentum:

The linear momentum of an object is the product of its mass and speed. It is generally denoted by letter p. The unit of momentum is.

The expression of momentum is:

Here, is the mass of an object andis the speed of the object.

Conservation of momentum:

The conservation of momentum is defined as the total momentum of an isolated system always remains is conserved.

The conservation of momentum for an isolated system can be mathematically expressed as,

Here, and are the initial and final momentum of the isolated system.

Write the expression for the momentum of skate and statue of Isaac by using the concept of the conservation of momentum as

Here, are the masses of the skate and statue of Isaac, are the initial speed of the skate and statue of Isaac,are the final speed of the skate and statue of Isaac.

Simplify the above expression.

……. (1)

Write the expression for the kinetic energy of skate and statue of Isaac by using the concept of the conservation of energy as

Simplify the above expression.

…… (2)

Divide equation (2) by equation (1).

Simplify the above expression.

…… (3)

Substitute the value of from equation (3) in equation (1).

Substitute for in above-obtained expression.

Substitute for, for and for in above-obtained expression.

Substitute the value of from equation (3) in equation (1).

Substitute for in above-obtained expression.

Substitute for, for and for in above-obtained expression.

Here, the negative sign indicates the opposite direction of motion of the skate as its initial direction.

Ans:

The speed of the skate before and after the collision is and.