Momentum, Collisions and Explosions Legacy Problem #12 Guided Solution
Problem*
Mr. H ignites the enthusiasm of the class with a home-made cannon demonstration. The 1.27-kg cannon is loaded with a 54-gram tennis ball and placed on the floor. Mr. H adds the fuel, waits for its vapors to fill the reaction chamber and then brings a match nearby. The explosion stuns the crowd and propels the ball forward. A photogate measurement determines that the cannon recoiled backwards with a speed of 7.8 m/s. Determine the speed of the ball.
Audio Guided Solution
An effective problem solver has the habit of reading the problem carefully, identifying the known and the unknown quantities, and using their conceptual reasoning skills and understanding of mathematical equations in order to go from the known to the unknown quantities. Here we read of a homemade cannon and a tennis ball at rest on the floor. Fuel is added to the cannon and an explosion takes place, sending the ball screaming forward and the cannon backwards. We're given the mass of both ball and cannon. These masses are given in different units, one being in kilograms and the other being in grams. We're also given the post-explosion speed of the cannon. We can use the principle that the momentum change in the cannon equals the momentum change in the ball in order to solve this problem. In using the principle, we'll begin by calculating the momentum change in the cannon. After all, we have the cannon's pre-collision speed, zero, and post-collision speed, 7.8, and mass, and this is sufficient information to calculate the momentum change of the cannon. In doing so, we multiply the 1.27 kilograms, the mass of the cannon, times the velocity change of the cannon, which is a 7.8 meters per second. That gives us a 9.906 kilogram meter per second momentum change for the cannon. We know the ball encounters the same magnitude of momentum change, only in the opposite direction. So to determine the velocity change of the ball, we go m times delta v for the ball equal this 9.906 kilogram meter per second. Thus, we have to take the mass of the ball and divide it into the momentum change of the ball. So we go 9.906 divided by 0.054. That's where I'm doing my conversion of the grams to kilograms. When I calculate the result, I get about 183 meters per second, and we can round this to two significant digits, such that it becomes 180 meters per second.
Solution
180 m/s
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities in an organized manner. Equate given values to the symbols used to represent the corresponding quantity - e.g., \(m = 1.50 \unit{kg}\), \(v_i = 2.68 \unit{\meter\per\second}\), \(F = 4.98 \unit{\newton}\), \(t = 0.133 \unit{\second}\), \(v_f = \colorbox{gray}{Unknown}\).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
Read About It!
Get more information on the topic of Momentum, Collisions and Explosions at The Physics Classroom Tutorial.