How Good Are the Bumpers? In a particular crash test, a car of mass 1,600 kg collides with a wall as shown in the figure. The initial and final velocities of the car are v, - -15.0i m/s and v, = 2.60i m/s, respectively. If the collision lasts 0.180 s, find the impulse caused by the collision and the average net force exerted on the car. In a crash test, much of the car's initial kinetic The car's momentum changes as a energy is transformed into energy associated with result of its collision with the wall. the damage to the car. Before -15.0 m/s After +2.60 m/s SOLUTION Conceptualize The collision time is short, so we can imagine the car being brought to rest very rapidly and then moving back in the opposite direction with --Select--- v speed. Categorize Let us assume that the force exerted on the car by the wall and friction from the ground is large compared with other forces on the car (such as air resistance). Furthermore, the gravitational force and the normal force exerted by the road on the car are ---Select--- v to the motion and therefore do not affect the horizontal momentum. Therefore, we categorize the problem as one in which we can apply the impulse approximation in the horizontal direction. We also see that the car's momentum changes due to an impulse from the environment. Therefore, we can apply the nonisolated system (momentum) model. Analyze Use the impulse-momentum theorem to find the impulse (in kg - m/s) on the car (Indicate the direction with the sign of your answer.): i - 45 - B, - B, - mv, - mv, = m(v, - v,) li kg - m/s Evaluate the average net force (in N) exerted on the car (Indicate the direction with the sign of your answer.): IN At p/www.webassign.aet'web/Stadent/Assigument-Responsesisubmirpos-2adep-26947395ugs-tosavelquestion0ssos 2 S/13 5/21,451 PM 95ICH9- Active Tutorial EC3 - PHY208 12-WEEKS, section 20-S ONLINE, Fall 2021 I WebAssiga Finalize The net force found above is a combination of the normal force on the car from the wall and any friction force between the tires and the ground as the front of the car crumples. If the brakes are not operating while the crash occurs and the crumpling metal does not interfere with the free rotation of the tires, this friction force could be relatively small due to the freely rotating wheels. Notice that the signs of the velocities in this example indicate the reversal of directions. What would the mathematics be describing if both the initial and final velocities had the same sign? EXERCISE Now in "real life," this automobile is cruising at 16.5 m/s (equal to 59.4 km/hr) when it is about to hit a pedestrian stuck in the middle of the road. The super hero Mr. Incredible comes to the rescue. He does not want to get sued, however. Therefore, he will not push the car with a force greater than 2.0 x 104 N; otherwise, the bumper will get damaged. How much time (in s) does he need to stop this car? Hint Need Help? Read It

How Good Are the Bumpers? In a particular crash test, a car of mass 1,600 kg collides with a wall as shown in the figure. The initial and final velocities of the car are v, - -15.0i m/s and v, = 2.60i m/s, respectively. If the collision lasts 0.180 s, find the impulse caused by the collision and the average net force exerted on the car. In a crash test, much of the car's initial kinetic The car's momentum changes as a energy is transformed into energy associated with result of its collision with the wall. the damage to the car. Before -15.0 m/s After +2.60 m/s SOLUTION Conceptualize The collision time is short, so we can imagine the car being brought to rest very rapidly and then moving back in the opposite direction with --Select--- v speed. Categorize Let us assume that the force exerted on the car by the wall and friction from the ground is large compared with other forces on the car (such as air resistance). Furthermore, the gravitational force and the normal force exerted by the road on the car are ---Select--- v to the motion and therefore do not affect the horizontal momentum. Therefore, we categorize the problem as one in which we can apply the impulse approximation in the horizontal direction. We also see that the car's momentum changes due to an impulse from the environment. Therefore, we can apply the nonisolated system (momentum) model. Analyze Use the impulse-momentum theorem to find the impulse (in kg - m/s) on the car (Indicate the direction with the sign of your answer.): i - 45 - B, - B, - mv, - mv, = m(v, - v,) li kg - m/s Evaluate the average net force (in N) exerted on the car (Indicate the direction with the sign of your answer.): IN At p/www.webassign.aet'web/Stadent/Assigument-Responsesisubmirpos-2adep-26947395ugs-tosavelquestion0ssos 2 S/13 5/21,451 PM 95ICH9- Active Tutorial EC3 - PHY208 12-WEEKS, section 20-S ONLINE, Fall 2021 I WebAssiga Finalize The net force found above is a combination of the normal force on the car from the wall and any friction force between the tires and the ground as the front of the car crumples. If the brakes are not operating while the crash occurs and the crumpling metal does not interfere with the free rotation of the tires, this friction force could be relatively small due to the freely rotating wheels. Notice that the signs of the velocities in this example indicate the reversal of directions. What would the mathematics be describing if both the initial and final velocities had the same sign? EXERCISE Now in "real life," this automobile is cruising at 16.5 m/s (equal to 59.4 km/hr) when it is about to hit a pedestrian stuck in the middle of the road. The super hero Mr. Incredible comes to the rescue. He does not want to get sued, however. Therefore, he will not push the car with a force greater than 2.0 x 104 N; otherwise, the bumper will get damaged. How much time (in s) does he need to stop this car? Hint Need Help? Read It