A 60.0 kg person bends his knees and then
jumps straight up. After his feet leave the floor, his motion is
unaffected by air resistance and his center of mass rises by a maximum
of 14.9 cm. Model the floor as completely solid and motionless.
(a) Does the floor impart impulse to the person?
Yes, am i correct to this part
(b) Does the floor do work on the person?
yes, since the floor exerts a force along the distance he jump, am i correct?
(c) With what momentum does the person leave the floor?
This part i'm stuck since p=mv, but i don't know how to find v in this case. Can you help me how to start it
(d) Does it make sense to say that this momentum came from the floor? Explain your answer.
Yes, since the guy exerts momentum on the floor, the floor also exerts same momentum in opposite direction
(e) With what kinetic energy does the person leave the floor?
do we use k=1/2mv^2, but again im stuck with finding velocity
(f) Does it make sense to say that this energy came from the floor? Explain your answer.
hm..how do you explain this part then
The assumption of the floor being motionless violates Newtons laws of motion.
The floor is connected to Earth. When one jumps, the Earth moves in the opposite direction. Mv=mV Assumptions cant change that. Nor can after leaving the floor, Gravitational force cannot be forgotten....Earth is attracted to you as you fall, Earth moves toward you, and has momentum toward you. If your center of mass rises, the Earth's center of mass declines, so that the cg of the system remains the same.
I don't know what to tell you. Your teacher has asked you to answer the questions with that fundamentally flawed assumption. If you answer those questions with my explanations from above, the questions have an entirely new light, and suddenly, Truth brings light on the answers.
If you view experimental situations with blinders on, such as the assumption the floor does not move, then one can make any conclusion, including erroneous conclusions to any work-energy situation, including the second law of thermodynamics.
Why don't you challenge the instructors assumptions, in view of well accepted laws of motion and work-energy?
(a) Yes, you are correct. When the person jumps, the floor imparts an impulse on the person, causing a change in momentum.
(b) Yes, you are correct again. Work is done when a force acts on an object to cause a displacement. In this case, the floor exerts a force on the person as they jump, causing them to move upward, so work is done.
(c) To find the momentum with which the person leaves the floor, you can use the principle of conservation of momentum. Since there are no external forces acting on the person-air system once the person leaves the floor, the momentum before the jump is equal to the momentum after the jump. The initial momentum can be calculated as:
Initial momentum = mass x initial velocity = 60.0 kg x 0 m/s (assuming the person is initially at rest)
Since the vertical motion is unaffected by air resistance, we know that the momentum after the jump is entirely in the vertical direction. Therefore, the magnitude of the final velocity can be calculated as follows:
Final momentum = mass x final velocity
Final momentum = 60.0 kg x final velocity
Since momentum is conserved, we can equate the initial and final momenta:
Initial momentum = Final momentum
0 = 60.0 kg x final velocity
From this equation, we find that the final velocity of the person is 0 m/s. This means that the person momentarily comes to a stop at the highest point of their jump.
(d) Yes, you are correct again. The momentum of the person leaving the floor is indeed equal and opposite to the momentum that the person imparted to the floor. This is due to Newton's third law of motion - for every action, there is an equal and opposite reaction.
(e) To calculate the kinetic energy with which the person leaves the floor, you can use the equation:
Kinetic energy = 1/2 x mass x velocity^2
Since we found that the final velocity is 0 m/s, the kinetic energy with which the person leaves the floor is also 0.
(f) No, in this case, it does not make sense to say that the energy came from the floor. The person's initial kinetic energy (0.5mv^2) came from the work done on them by their muscles and stored potential energy converted into kinetic energy during the jump. The floor only transfers the person's momentum but does not provide energy to the person.
(a) Yes, you are correct. The floor imparts impulse to the person. When the person jumps, the floor exerts an upward force on the person, causing a change in momentum.
(b) Yes, you are correct. The floor does work on the person. Work is done when a force is applied through a distance. In this case, the floor exerts a force on the person as they jump, causing them to move a certain distance.
(c) To find the momentum with which the person leaves the floor, we need to use the principle of conservation of momentum. Before the jump, the person is at rest, so their initial momentum is zero (p_initial = 0). When they jump, their final momentum (p_final) will be equal to their mass (m) multiplied by their final velocity (v). We can calculate the final velocity using the given information that the person's center of mass rises by a maximum of 14.9 cm (or 0.149 m). We know that the person starts and ends at rest vertically, so the change in velocity in the vertical direction is equal to the final velocity (v) itself. Therefore, v = √(2gh), where g is the acceleration due to gravity (9.8 m/s^2) and h is the height (0.149 m).
(d) No, it does not make sense to say that the momentum came from the floor. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. When the person jumps off the floor, they exert an equal and opposite force on the floor. The momentum of the person comes from the action of their legs pushing against the floor, not from the floor itself.
(e) To find the kinetic energy with which the person leaves the floor, we can use the formula K = 1/2mv^2, where K is the kinetic energy, m is the mass of the person (60.0 kg), and v is the final velocity. We can plug in the value of the final velocity calculated in part (c) into this equation.
(f) No, it does not make sense to say that the energy came from the floor. Energy is conserved. In this case, the kinetic energy of the person as they leave the floor comes from the potential energy stored in their muscles, which was released when they pushed off the floor. The floor does work on the person, but the energy transfer occurred from the person's own stored energy, not from the floor.