A mother and her small child are standing in an inflatable bouncy house on opposite sides. The mother jumps up and comes back down again, transferring her kinetic energy to the child through the floor. How will the motion of the small child change?
1 The child will move up at a faster speed because the child has less mass.
2 The child will move up at the same speed at which the mother came down.
3 The child will move up at a slower speed because the child has less mass.
4 The child will move down at the same speed at which the mother came down.
3 The child will move up at a slower speed because the child has less mass.
This is because kinetic energy is transferred from the mother to the child through the floor, but the child has less mass than the mother. Therefore, the child will not be able to absorb all the energy of the mother's jump and move up at the same speed. The transfer of energy will cause the child to move up, but at a slower speed compared to the mother.
To understand how the motion of the small child will change when the mother jumps up and comes back down in the inflatable bouncy house, we need to consider the conservation of energy and Newton's third law of motion.
When the mother jumps up, she gains potential energy due to her increased height from the ground. As she comes back down, this potential energy is converted into kinetic energy, which she transfers to the child through the floor.
According to Newton's third law of motion, for every action, there is an equal and opposite reaction. When the mother transfers her kinetic energy to the child, the child will experience an upward force from the floor of the bouncy house.
Now, let's analyze the given options:
1. The child will move up at a faster speed because the child has less mass:
This statement is incorrect. The speed at which the child moves up depends on the amount of kinetic energy transferred by the mother. The mass of the child doesn't directly affect the speed in this scenario, only the force experienced.
2. The child will move up at the same speed at which the mother came down:
This statement is not entirely accurate. The child will move up but not necessarily at the exact same speed as the mother came down. The speed at which the child moves up will depend on various factors, including the amount of kinetic energy transferred and the child's mass.
3. The child will move up at a slower speed because the child has less mass:
This statement is more accurate. Since the child has less mass, they will experience a smaller upward force from the floor of the bouncy house. This reduced force will result in a slower upward motion for the child compared to the mother's downward motion.
4. The child will move down at the same speed at which the mother came down:
This statement is incorrect. The child will not move down, as the kinetic energy transferred by the mother will be transformed into the child's upward motion.
Therefore, the correct answer is option 3: The child will move up at a slower speed because the child has less mass.
The correct answer is 2: The child will move up at the same speed at which the mother came down.
When the mother jumps and comes back down, her kinetic energy is transferred to the child through the floor. According to the law of conservation of energy, the total energy of the system (mother, child, bouncy house) remains constant. This means that the total kinetic energy of the system is conserved.
Since the mother and child are initially at rest, the mother's kinetic energy after jumping is equal to the child's kinetic energy after transferring the energy. Therefore, the child will move up at the same speed that the mother came down, resulting in equal and opposite motions.