Question: 40
Graph shapes and math: five small step-function style graphs are shown across the upper part of the page, each with a horizontal axis and a piecewise constant/step-like line; position_hint=top-left.
19) 36 g of a star at its velocity v.
The velocity-time graph below shows the
velocity of a car before, during, and after
the reaction time and braking of the
driver. The driver’s reaction time is 0.50 s
and then the car decelerates uniformly
to rest. The graph has labeled intervals
and a sloping downward segment.
20) Two blocks A and B of masses 4 kg and 2 kg respectively, are simultaneously projected on a
horizontal surface towards each other with velocities 4 m/s and 2 m/s respectively. They collide and
stick together. The coefficient of friction of each block with the horizontal plane is BC = 0.2.
The motion of A and B after collision is represented by a common horizontal line in the figure.
(i) Determine the
respective velocity of A and B after the collision.
(ii) The velocity of A after collision can be found by considering the
system of the two blocks. Use the figure.
21) Two blocks P and Q of masses 3 kg and 4 kg respectively are simultaneously projected in a
horizontal plane with velocities 3 m/s and 5 m/s respectively. The coefficient of friction between
the blocks and the plane is 0.2. They collide head-on and stick together. After the collision,
determine the velocity of the combined body and how much time after the collision does Q take to reach the ground?Conservation de Momentum
top-right: a hand holding the page; a simple line graph/angle sketch with two marked points and a slanted line rising to the right, near the upper-right area.
top-left: handwritten annotations and circled numbers near the page edge.11. (i) Calculate the maximum force that the tractor can exert on the log when the truck is stationary, and when it is moving up the incline with a speed of 0.5 m s 61.
(ii) In the second case, if the tractor starts to move faster, the frictional force becomes more difficult to calculate. Why?
(iii) Draw the forces acting on the log.
12. There are a few major aircraft laws. The aircraft plate is capable of a class of the following tasks, and its location is on the face and other different positions in the aircraft, as shown in figure.
(i) State the principle of the two pictures in the above figure.
(ii) Find values of the moment of force.
(iii) What are the assumptions to be satisfied in order to find the moment of force from the above information?
(iv) Are the measurements measured from the centre of the wheel?
(v) An object has a moment of force of 3N m.
(vi) A stick with a force and the object is kept on a smooth horizontal surface, with a weight of 1 N. It has a moment of force of 1 N m.
13. An arrow is shown in the following figure, corresponding to the principle of moments. The diagram shows the axis of rotation of a ruler with a body weighing 1 N and 2 N respectively, as shown in the diagram. The ruler is in equilibrium, as shown.
graph shape: a horizontal rectangle/beam near the middle-left with three small circles underneath it and labels A, B, C above the circles; another shorter rectangle/beam near the upper-right with two circles underneath; position_hint = center48)
17)
18)
19)
20)
21)
Graph shapes: top-left shows several small step-like line graphs with piecewise constant/linear motion curves and arrows; position_hint in {top-left}.
Graph shapes: center shows a horizontal track with two small blocks/cartons on it, one labeled A and one labeled B, with a rightward arrow near the left block; position_hint in {center}.conversation in two dimensions
x = 0
y = 0
graph shape: a line segment rises diagonally upward from a left point to a top point, then another line segment goes straight downward to a right lower point; position_hint = top-rightMath text visible (approximate transcription; image is rotated/blurry):
Learning
A box moves 10m east to the right... (text unclear)
Three trolley A, B and C are motionless between 1.30 m a zero line...
A
B
C
(i) Find the magnitude and direction of the resultant force?
(ii) What are the equilibrium conditions?
(iii) What is the direction of the right? (unclear)
(iv) ... a distance ... (unclear)
Graph/shape description:
position_hint = center 64 A horizontal line diagram with three carts labeled A, B, and C on a track, with boxes above them; one box shows 13c, another 11c, and another appears blank/unclear.top-right: graph with five small step-like line plots arranged horizontally; each plot shows a vertical axis on the left and a piecewise-constant function that drops or steps at one or more points, with arrows indicating the time axis direction.
20. It is a hard fact of common experience that A, who has never seen a cannonball before, watches B, who is experienced and knows the cannonball has approached by a spine (p). A, by who is already in, will be in motion for a time after it leaves the cannonball. A then realizes that the cannonball is moving with respect to the block.
21. A block of mass 4 kg is held from a gun of mass 4 kg with a velocity of 11 m/s as shown in figure. The gun is fired and the bullet of mass 2 kg moves with the bullet after the bullet is gone. The bullet leaves the gun and the block is moving with a velocity of 11 m/s. The block and the gun are in the same direction.
22. The mass is 50 kg in hand from a gun of mass 4 kg, with a velocity of 15 m/s. If a bullet is fired from the gun and the bullet has velocity 12 m/s after it leaves the gun, find the velocity of the block after the bullet is gone.
23. Two blocks A and B of masses 2 kg and 4 kg respectively are simultaneously projected with a velocity 5 m/s as shown in figure. A collides with B and sticks to it. Find the final velocity of the combination after the collision.
24. A block and a gun are together with linear momentum. If the bullet is returned to the gun, find the ground. Then they move together.User: answer
1. **Problem Statement:**
Two blocks A and B with masses $m_A = 4\,\text{kg}$ and $m_B = 2\,\text{kg}$ are projected towards each other with velocities $v_A = 4\,\text{m/s}$ and $v_B = 2\,\text{m/s}$ respectively. They collide and stick together. The coefficient of friction with the surface is $\mu = 0.2$. We need to find the velocity of the combined block after collision.
2. **Relevant Formula:**
Since the blocks stick together after collision, this is a perfectly inelastic collision. We use conservation of linear momentum:
$$m_A v_A + m_B (-v_B) = (m_A + m_B) v_f$$
Note: $v_B$ is negative because blocks move towards each other.
3. **Calculate final velocity $v_f$ after collision:**
$$4 \times 4 + 2 \times (-2) = (4 + 2) v_f$$
$$16 - 4 = 6 v_f$$
$$12 = 6 v_f$$
$$v_f = \frac{12}{6} = 2\,\text{m/s}$$
The combined block moves at $2\,\text{m/s}$ in the direction of block A's initial velocity.
4. **Explanation:**
The momentum before collision is the sum of momenta of both blocks, taking direction into account. After collision, the blocks stick and move together with velocity $v_f$.
5. **Friction after collision:**
The friction force $f = \mu (m_A + m_B) g$ will decelerate the combined block. This affects motion after collision but not the velocity immediately after collision.
---
**Final answer:**
The velocity of the combined blocks after collision is $\boxed{2\,\text{m/s}}$ in the direction of block A's initial velocity.