A very heavy SUV collides head-on with a very light compact car. Which of these statements about the collision are correct? (a) The amount of kinetic energy lost by the SUV is equal to the amount of kinetic energy gained by the compact; (b) the amount of momentum lost by the SUV is equal to the amount of momentum gained by the compact; (c) the compact feels a considerably greater force during the collision than the SUV does; (d) both cars lose the same amount of kinetic energy.

Solution 26DQ Introduction The statements are related to kinetic energy change and momentum change. We have to figure out, using the conservation law of energy and momentum, which of the statements are true. Step 1 (a) According to the conservation of energy, the total energy of both SUV and small car remain same. Since, in the collision, the heavier object loses energy, the SUV will lose energy. Now, according to the law of conservation, the suv will gain same amount of energy. Hence the statement is true. (b) Again according to the conservation of momentum, the total momentum should remain unchanged. Hence the momentum lost by SUV should be equal to the momentum gain by small car. Hence the statement is true. (c) According to the newton’s third law of motion, the action and reaction are alway same and opposite. The force feel by compact car and SUV are action and reaction to each other. Hence the forces will be saem. Hence the force feel by SUV and compact car is same Hence the statement is not correct. (d) If both car loses kinetic energy then the conservation of energy will be violated. Hence both car can not lose energy together. So the statement is wrong.