Question

Consists of a cart of known mass connected to one end of a string that is looped over a pulley of negligible friction, with its other end connected to a hanging mass. the cart is initially at rest on a horizontal surface and rolls without slipping when released. the inertia of the cart's wheels is negligible. students have access to common laboratory equipment to make measurements of components of the system. question students take measurements of the force f 0 , directed to the left, needed to hold the cart in place as well as the tension f t in the horizontal section of string. the students take three measurements for each force. which of the following sets of measurements would provide the most precise determination of the correct relationship between the net force and the vector sum of the individual forces exerted on the cart?

Answer 1

To find the mass of Cart B after a one-dimensional inelastic collision with Cart A, apply the conservation of momentum by equating the total momentum before and after the collision. Measure the velocities before and after the collision to solve for Cart B's mass. Newton's second law can be applied to analyze tension and acceleration in similar systems without friction.

Step-by-step explanation:

To determine the mass of cart B using a one-dimensional collision where Cart A, with a known mass (mA), collides with Cart B, which is initially at rest, the law of conservation of momentum is applied. This law states that the total momentum before the collision is equal to the total momentum after the collision, provided no external forces are acting on the system.

In this case, when Cart A sticks to Cart B after the collision, we can set up the equation for conservation of momentum as mA * velocity of Cart A before collision = (mA + mass of Cart B) * velocity of both carts after collision.

Rearranging this equation allows us to solve for the mass of Cart B. By measuring the velocity of Cart A before the collision and the combined velocity after, the mass of Cart B can be calculated.

Assuming negligible friction and wheel inertia, Newton's second law can also be used to analyze other aspects of the system, such as the tension in the string connecting two carts going over a pulley.

If one cart is hanging and the other is on a track, and the system is released from rest, the tension in the string and the acceleration of the carts can be found by applying Newton's second law and considering the forces acting on the system such as the weights of the masses and the tension in the string.