Chapter 6: Linear Momentum and Collisions
Problems & Exercises
6.1 Linear Momentum and Force
- (a) Calculate the momentum of a 2000-kg elephant charging a hunter at a speed of [latex]7\text{.}\text{50 m/s}[/latex].
(b) Compare the elephant’s momentum with the momentum of a 0.0400-kg tranquilizer dart fired at a speed of [latex]\text{600 m/s}[/latex].
(c) What is the momentum of the 90.0-kg hunter running at [latex]7\text{.}\text{40 m/s}[/latex] after missing the elephant?
Solution: (a) [latex]\text{1.50}×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{kg}\cdot \text{m/s}[/latex]; (b) 625 to 1; (c) [latex]6\text{.}\text{66}×{\text{10}}^{2}\phantom{\rule{0.25em}{0ex}}\text{kg}\cdot \text{m/s}[/latex] - (a) What is the mass of a large ship that has a momentum of [latex]1\text{.}\text{60}×{\text{10}}^{9}\phantom{\rule{0.25em}{0ex}}\text{kg}·\text{m/s}[/latex], when the ship is moving at a speed of [latex]\text{48.0 km/h?}[/latex]
(b) Compare the ship’s momentum to the momentum of a 1100-kg artillery shell fired at a speed of [latex]\text{1200 m/s}[/latex]. - (a) At what speed would a [latex]2\text{.}\text{00}×{\text{10}}^{4}\text{-kg}[/latex] airplane have to fly to have a momentum of [latex]1\text{.}\text{60}×{\text{10}}^{9}\phantom{\rule{0.25em}{0ex}}\text{kg}·\text{m/s}[/latex] (the same as the ship’s momentum in the problem above)?
(b) What is the plane’s momentum when it is taking off at a speed of [latex]\text{60.0 m/s}[/latex]?
(c) If the ship is an aircraft carrier that launches these airplanes with a catapult, discuss the implications of your answer to (b) as it relates to recoil effects of the catapult on the ship.
Solution: (a) [latex]8\text{.}\text{00}×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{m/s}[/latex]; (b) [latex]1\text{.}\text{20}×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{kg}·\text{m/s}[/latex]; (c) Because the momentum of the airplane is 3 orders of magnitude smaller than of the ship, the ship will not recoil very much. The recoil would be [latex]-0\text{.}\text{0100 m/s}[/latex], which is probably not noticeable. - (a) What is the momentum of a garbage truck that is [latex]1\text{.}\text{20}×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}\text{kg}[/latex] and is moving at [latex]10\text{.}\text{0 m/s}[/latex]? (b) At what speed would an 8.00-kg trash can have the same momentum as the truck?
- A runaway train car that has a mass of 15,000 kg travels at a speed of [latex]5\text{.4 m/s}[/latex] down a track. Compute the time required for a force of 1500 N to bring the car to rest.
Solution: 54 s - The mass of Earth is [latex]5\text{.}\text{972}×{10}^{\text{24}}\phantom{\rule{0.25em}{0ex}}\text{kg}[/latex] and its orbital radius is an average of [latex]1\text{.}\text{496}×{10}^{\text{11}}\phantom{\rule{0.25em}{0ex}}\text{m}[/latex]. Calculate its linear momentum.
- *An elephant and a hunter are having a confrontation.
(a) Calculate the momentum of the 2000.0-kg elephant charging the hunter at a speed of 7.50 m/s
(b) Calcula