Kinetic Energy and Spring Experiment in Physics

QUESTION 1: If a car's velocity changes from 50 mi/h due east to 50 mi/h due west, what happens to the kinetic energy of the car? QUESTION 2: In a lab experiment using an air-track cart and a spring, what velocity should the instructor expect the cart to have after being launched by the spring? QUESTION 1: The kinetic energy of the car remains the same. QUESTION 2: The cart velocity she should expect after it is launched by the spring is √(2kx/m).

Kinetic Energy of a Car on a Straight Road

Kinetic energy is the energy of an object due to its motion. In physics, kinetic energy is calculated using the formula KE = (1/2)mv^2, where m is the mass of the object and v is its velocity.

Explanation: The kinetic energy of an object does not depend on the direction of its velocity but only on the magnitude of the velocity. Therefore, if a car's velocity changes from 50 mi/h due east to 50 mi/h due west, the kinetic energy of the car will remain the same. This is because the kinetic energy formula is based on the square of the velocity, which means as long as the magnitude of the velocity remains constant, the kinetic energy will not change.

Spring Experiment in Physics Lab

In a lab experiment using an air-track cart and a spring, the instructor compresses the spring by an amount x from its equilibrium length and then releases it to launch the cart.

Explanation: When the spring is compressed, it stores potential energy given by (1/2)kx^2, where k is the spring constant. When the spring is released, this potential energy is converted into kinetic energy of the cart which is given by (1/2)mv^2. By equating the potential energy of the spring to the kinetic energy of the cart, we find that the velocity v of the cart after being launched should be equal to √(2kx/m).

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