1. If a spring is stretched to 0.17 m away from the equilibrium point and the total potential energy of the spring is 65 J, what is the spring constant of the spring?
a. 7200 N/m^2
b. 3800 N/m^2
c. 4500 N/m^2**
d. 5100 N/m^2
2. A loaded cannon is stationary. If the cannon fires a cannonball giving it a positive velocity, the cannon will recoil and roll back. What would the cannon having a negative velocity indicate about the total kinetic energy of the system?
a. The total kinetic energy did not transfer entirely to the cannonball, so some had to go into the cannon**
b. The cannon produces its own kinetic energy to cause it to move
c. The Law of Conservation of Energy is not valid in this specific case
d. The explosion of the gunpowder is not an efficient method of energy transfer
3. If a spring compresses under a force a short distance, but stores a very large amount of potential energy in the spring, what can be said about the spring?
a. The spring is made of soft materials
b. The kinetic energy of the force is impossible to determine
c. The stiffness of the spring, represented by the spring constant value, must be very high
d. The amount of potential energy stored in the spring has to be half of what the original energy was**
Does anyone know any of the answers to these questions? I tried to guess but my answers are probably wrong.
All of them were right ^^ except for:
If a spring compresses under a force a short distance, but stores a very large amount of potential energy in the spring, what can be said about the spring?
Idk the right answer but mine was wrong.
yes you are correct
What about this one?
4. If a pendulum is swung in a situation with no friction, what can you say about the height the pendulum will reach?
a. The pendulum must be made of a copper alloy
b. The pendulum will reach a maximum height that will give it a a maximum potential energy equal to its maximum kinetic energy**
c. The energy of the pendulum will steadily decrease over time due to frictional forces
d. The amount of mechanical energy will slowly be lowered due to a conversion into non mechanical forms
Certainly! Let's go through each question and explain how to find the answers:
1. To find the spring constant, you can use the formula for potential energy stored in a spring: PE = (1/2)kx^2, where PE is the potential energy, k is the spring constant, and x is the displacement from the equilibrium position of the spring. Rearranging the formula, we have k = (2 * PE) / x^2. Plugging in the given values, k = (2 * 65 J) / (0.17 m)^2. Evaluating this expression, we find that k is approximately 7200 N/m^2. Therefore, the correct answer is option a. 7200 N/m^2.
2. When a loaded cannon fires a cannonball and moves in the opposite direction, it is due to the conservation of momentum. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. In this case, the forward motion of the cannonball results in a backward motion or recoil of the cannon. Since momentum is conserved, the total momentum before and after the firing of the cannonball is zero. This means that the total kinetic energy before and after firing should also be zero, as kinetic energy is proportional to the squared velocity. Therefore, if the cannon has a negative velocity after firing, it suggests that not all of the kinetic energy transferred to the cannonball. The correct answer is option a. The total kinetic energy did not transfer entirely to the cannonball, so some had to go into the cannon.
3. The potential energy stored in a spring is given by PE = (1/2)kx^2, where PE is the potential energy, k is the spring constant, and x is the displacement from the equilibrium position of the spring. Since the question states that the spring compresses under a force a short distance but stores a very large amount of potential energy, it implies that the displacement x is small, while the potential energy PE is large. According to the formula, if x is small, for PE to be large, the spring constant k must be high. Therefore, the correct answer is option c. The stiffness of the spring, represented by the spring constant value, must be very high.
I hope this helps! Let me know if you have any more questions.