A constant force F is exerted on a dart of mass m in the horizontal direction as it moves through a tube of length L. After exiting the tube, the dart collides with a box of mass M that sits at rest on a table with coefficient of friction μk. The dart/block system then slides across the table and comes to rest after traveling a distance D. Required:
a. Students experiment with a variety of tubes. Assuming that air resistance is negligible, and that all other parts of the experiment remain the same, should the students use a long tube, or a short tube make the stopping distance D the longest?
b. Students then change the force so that it can be described as a function of position F(x)=12x. Explain how the students could use the equation given above to find the launch speed of the dart, if the length of the tube is 2 meters.
c. Predict what will happen to the launch velocity of the dart if the length of the tube was doubled. Justify your answer.

    m₁v₁ + m₂v₂ = (m₁ + m₂)vmomentum is conserved.the left-hand side of the equation represents the momentum in the system before the collision.the right-hand side represents the momentum in the system after the collisionm₁ and v₁ represents the mass and the velocity of the physics blockm₂ and v₂ represents the mass and velocity of the ball of puttyv represents the final velocity of the combined mass.the question states the two masses stick together. they combined mass has its own velocity with the body mass the sum of the two objects' massestheir combined momentum is (m₁ + m₂)vto find the magitude of (m₁ + m₂)v, we need to add the vectors on the left-hand side of the equation: m₁v₁ + m₂v₂.note the diagram. i have positioned the vectors in accordance with their directions.the magnitude of the resultant can be calculated using the pythagorean theorem since this is a right triangle situation (north and west are perpendicular)|(m₁ + m₂)v| =  √[ (m₁v₁)² + (m₂v₂)² ]|(m₁ + m₂)v| =  √[ (1.5kg·8.0m/s)² + (0.40kg·20m/s)² ]|(m₁ + m₂)v| =  14.4 kg m/sfor two significant figures (assuming that 20m/s is two), this rounds to 14 kg m/s

Isso9