1. A thread with a weight suspended from it is deflected by an angle
Answer
2. 1. A body is thrown vertically upward with a velocity
- With what initial velocity must a ball be thrown from a height
so that it bounces to a height ? Assume the collision is elastic and air resistance is negligible.
Answer
1.
3. A stone is thrown horizontally from a tower of height
Answer
Hint
The initial values of kinetic and potential energy are respectively:
4. Determine the kinetic energy of a body with a mass of 1 kg, thrown horizontally with a velocity of
Answer
Solution
At the end of the fourth second, the velocity of the body, thrown horizontally with speed 
5. A flexible uniform rope of length
Answer
Solution
The entire rope is accelerated by the force of gravity acting on the hanging part
6. A rope of length
Answer
Hint
See the solution to problem 5. Initially, the center of mass of the rope was at a distance
7. A skater, having accelerated to a velocity
Answer
Solution
The decrease in the mechanical energy of the skater is equal to the work done against friction:
8. A body of mass
Answer
Hint
The work done by resistance forces is equal to the change in the mechanical energy of the body:
9. A stone with a mass of 50 g is thrown at an angle to the horizontal from a height of 20 m above the ground with a velocity of 18 m/s and lands with a velocity of 24 m/s. Find the work done to overcome air resistance.
Answer
Hint
See problem 8. The work done against resistance forces is positive.
10. An airplane with a mass
Answer
Hint
The work done by resistance forces
11. A body of mass
Answer
Hint
From the law of conservation of energy, it follows that
12. A weight attached to a vertical spring is slowly lowered to its equilibrium position, stretching the spring by a length
Answer
Solution
From the equilibrium condition of the load
13. A falling weight of mass
Answer
Solution
The work done against the resistance force of the soil is equal to the change in potential energy of the pile:
14. A sled slides down a hill of height
Answer
Solution
At the end of the path, the sled stops, and, consequently, all the initial potential energy is spent on work against friction forces on the inclined and horizontal sections of the path:
15. A steel ball of mass
Answer
a)
b)
Solution
The impulse of the force acting on the ball during the impact with the plate, in accordance with Newton's second law, is equal to:
16. A light ball begins to fall freely and, after traveling a distance
Answer
Solution
It is more convenient to solve the problem by considering the collision in a coordinate system associated with the moving plate. Since the speed of the plate changes negligibly due to the impact, this coordinate system can be considered inertial. In it, the ball before the impact with the plate has speed
17. A balloon held by a rope rises to a certain height. How does the potential energy of the balloon-air-Earth system change?
Answer
The potential energy of the ball-air-Earth system decreased, because as the ball rises, the volume occupied by the ball is replaced by air, which has a greater mass than the ball.
18. A hockey puck with an initial velocity
Answer
Hint
During the motion of the puck, its kinetic energy is spent on doing work against friction:
19. A body slides without friction off a wedge lying on a horizontal plane twice: first, the wedge is fixed; second, the wedge can slide without friction. Will the speed of the body at the end of the slide be the same in both cases if the body starts from the same height each time?
Answer
In the first case, the speed of the body is greater than in the second.
20. Why is it difficult to jump to shore from a light boat near the shore, but easy to do so from a steamship at the same distance?
Solution
Let
By jumping, the person performs work
This work is smaller, the smaller the ratio of the masses of the person and the boat (steamship). The mass of the steamship is many times greater than the mass of the person (
21. A skater of mass
Answer
Solution
Based on the laws of conservation of momentum and energy, we can write the equations:
Answer
Solution
The work that the person performs by throwing a stone from the cart is spent on imparting kinetic energy to the stone and the cart with the person:">
23. A rifle of mass !["Description"]("/book-images/Intro-Phys-Probl/P-5-23.png")
Answer
Solution
Based on the law of conservation of energy, we determine the recoil speed of the rifle after the shot
Solution
Based on the law of conservation of energy, we determine the recoil speed of the rifle after the shot
28. A pendulum consists of a thin rigid rod of length $l = 1.5 \, \text{m}$ with a steel ball of mass $M = 1 \, \text{kg}$ at its end. A steel ball of mass $m = 20 \, \text{g}$ flying horizontally with a velocity $v = 50 \, \text{m/s}$ strikes the pendulum ball. Determine the maximum deflection angle of the pendulum, assuming the collision is elastic and central. Neglect the mass of the rod.
Answer
$\alpha = 2 \arcsin \dfrac{mv}{(m+M)\sqrt{gl}} \approx 30^{\circ}$.
29. Two masses $m_1$ and $m_2$ of unequal weights are suspended on a thread thrown over a pulley. Find the acceleration of the center of mass of this system. Solve the problem in two ways: 1) using the law of conservation of energy, and 2) using the law of motion of the center of mass. Neglect the masses of the pulley and the thread.
Answer
$a_{cm} = \left( \dfrac{m_1 - m_2}{m_1 + m_2} \right)^2 g$.
Solution
1st method. Write the law of conservation of energy for the center of mass of the system:" class="MathJax" jax="SVG" overflow="overflow" display="true">
28. A pendulum consists of a thin rigid rod of length">
39. To obtain slow neutrons, they are passed through hydrogen-containing substances (e.g., paraffin). Find the maximum fraction of kinetic energy a neutron (mass $m_0$) can transfer to: a) a proton (mass $m_0$); b) a lead nucleus (mass $207 m_0$). Maximum transfer corresponds to central elastic collision.
Answer
a) 100%. In an elastic collision of particles with equal mass, they exchange velocities;
b) 1.9%.
40. Two perfectly elastic balls of masses $m_1$ and $m_2$ move along the same line with velocities $v_1$ and $v_2$. During collision they deform, converting some kinetic energy to potential energy of deformation. Find the maximum potential energy of deformation during the collision.
Answer
$\Pi_{\text{max}} = \dfrac{1}{2} \dfrac{m_1m_2}{m_1+m_2} (v_1 - v_2)^2$.
Solution
At the moment of maximum deformation, the balls move together with the same velocity $u$. For this moment, the laws of conservation of mechanical energy and momentum take the following form:" class="MathJax" jax="SVG" overflow="overflow" display="true">E_0
39. To obtain slow neutrons, they are passed through hydrogen-containing substances (e.g., paraffin). Find the maximum fraction of kinetic energy a neutron (mass">
39. To obtain slow neutrons, they are passed through hydrogen-containing substances (e.g., paraffin). Find the maximum fraction of kinetic energy a neutron (mass">
39. To obtain slow neutrons, they are passed through hydrogen-containing substances (e.g., paraffin). Find the maximum fraction of kinetic energy a neutron (mass">
39. To obtain slow neutrons, they are passed through hydrogen-containing substances (e.g., paraffin). Find the maximum fraction of kinetic energy a neutron (mass">
39. To obtain slow neutrons, they are passed through hydrogen-containing substances (e.g., paraffin). Find the maximum fraction of kinetic energy a neutron (mass">
39. To obtain slow neutrons, they are passed through hydrogen-containing substances (e.g., paraffin). Find the maximum fraction of kinetic energy a neutron (mass">
39. To obtain slow neutrons, they are passed through hydrogen-containing substances (e.g., paraffin). Find the maximum fraction of kinetic energy a neutron (mass">
39. To obtain slow neutrons, they are passed through hydrogen-containing substances (e.g., paraffin). Find the maximum fraction of kinetic energy a neutron (mass">
39. To obtain slow neutrons, they are passed through hydrogen-containing substances (e.g., paraffin). Find the maximum fraction of kinetic energy a neutron (mass">
39. To obtain slow neutrons, they are passed through hydrogen-containing substances (e.g., paraffin). Find the maximum fraction of kinetic energy a neutron (mass">
39. To obtain slow neutrons, they are passed through hydrogen-containing substances (e.g., paraffin). Find the maximum fraction of kinetic energy a neutron (mass">
39. To obtain slow neutrons, they are passed through hydrogen-containing substances (e.g., paraffin). Find the maximum fraction of kinetic energy a neutron (mass">
39. To obtain slow neutrons, they are passed through hydrogen-containing substances (e.g., paraffin). Find the maximum fraction of kinetic energy a neutron (mass">
39. To obtain slow neutrons, they are passed through hydrogen-containing substances (e.g., paraffin). Find the maximum fraction of kinetic energy a neutron (mass">
3v_1^2 - 2\sqrt{3}vv_1 + v^2 = 0
v_1 = \frac{\sqrt{3}v}{3}
v_2 = \frac{2\sqrt{3}v}{3}
\beta = 30^\circ
$
