Explanation:
Our solar system formed about 4.5 billion years ago from a dense cloud of interstellar gas and dust. The cloud collapsed, possibly due to the shockwave of a nearby exploding star, called a supernova. When this dust cloud collapsed, it formed a solar nebula—a spinning, swirling disk of material.
30 POINTS PLS HELP NO LINKS PLS :/
In a wave, each particle of the medium vibrates, or oscillates, around a _____________.
A. Corner
B. Noise
C. Variable position
D. Fixed position
Answer:
C
Explanation:
trust me
D. Fixed position ,mean position , Equilibrium position.
What is wave motion?Wave motion is the transfer of energy and momentum from one point of the medium to another point of the medium without actual transport of matter between two points.
The particles of the medium vibrate about their equilibrium position in a direction parallel to the direction of propagation of the wave is called a longitudinal waves.
Characteristics of Wave Motion
In wave motion, the disturbance travels through the medium due to repeated periodic oscillations of the particles of the medium about their mean position (or) Equilibrium position.
Energy and momentum are transferred from one point to another without any actual transfer of the particles of the medium.
There is a regular phase difference between the particles of the medium because each particle receives disturbance little later than its preceding particle.
Therefore,
In a wave, each particle of the medium vibrates, or oscillates, around a fixed position.
Learn more about wave motion here:
https://brainly.com/question/12512349
#SPJ2
A child makes a ramp to push his toy dump truck up to his sandbox. If he uses 5 newtons of force to push the 12-newton truck up the ramp, what is the mechanical advantage of his ramp?
Answer:
m = 2.4
Explanation:
Given that,
Input force, [tex]F_i=5\ N[/tex]
Output force, [tex]F_o=12\ N[/tex]
We need to find the mechanical advantage of the ramp. The ratio of output force to the input force is equal to mechanical advantage. So,
[tex]m=\dfrac{12}{5}\\\\m=2.4[/tex]
So, the mechanical advantage of his ramp is 2.4.
a cat is being chased by a dog both are running in a straight line at constant speed. The cat has a headstart
2. Bank robbers have pushed a 1000 kg safe to a second story floor-to-ceiling window. They plan to break the window, then lower the safe 3.0 m to their truck. They stack up 500 kg of furniture, tie a rope between the rope and the furniture, and then place the rope over a pulley. Then they push the safe out of the window. What is the safe speed when it hits the truck
Answer:
5.4 m/s
Explanation:
Given that
Mass of the safe, m1 = 1000 kg
Distance to lower the safe, d = 3 m
Mass of furniture, m2 = 500 kg.
Speed of the safe, v = ?
To get the final speed by the time that the safe hits the truck, we first find its acceleration.
The total mass of the system is M = 1000 + 500 kg = 1500 kg
One of the forces acting on the system is that of gravity, and it acts on the safe friction acting on the furniture. Using the formula, we have
= m1*g - mu*m2g
= 1000 * 9.81 - 0.5 * 500 * 9.81
= 7357.5 N
From this calculated weight, we find the acceleration.
Acceleration, a = F/m
Acceleration, a = 7357.5 / 1500
Acceleration, a = 4.905 m/s²
From the question, we know that the Initial speed = 0 m/s
So, employing the use of one of the equations of motion, we have
v² - u² = 2aS
v² - 0 = 2 * 4.905 * 3
v² = 29.43
v = √29.43
v = 5.4 m/s
Need help on question one ASAP pls help
Answer:
B
Explanation:
Because blocks 2 and 3 have sides with unequal forces while block 1 doesnt. Plz drop a follow if this helps! ❤
An ice cube in a glass of water is pushed to the bottom of the glass and held there with a straw. Consequently, the buoyant force on the ice cube is now a. the same as when the cube was floating at the top. b. exactly balanced by the weight of the ice cube. c. exactly balanced by the force exerted by the straw. d. greater than when the cube was floating at the top.
Answer:d
Explanation:
Given
Initially, the ice cube is floating over the water
When the cube is pressed to touch the bottom, it is submerged fully
Therefore more buoyant force is acting on it
At first, a part of the volume is submerged in the water, so the buoyant force is less, but as the entire cube is immersed in the water, the buoyant force increases.
A plano concave lens is one that has a surface that curves inward on one side and flat on the other, making the lens thinner at its center than at its edges. Its effect on light is :________
a. to diverge in incident eam of light
b. to make it appear as if incident parallel light is coming from a point close to the lens on the opposite side from the light source
c. to make it appear as if incident parallel light is coming from a point close to the lens on the same side as the light source
d. to converge light to a focus
Answer:
true statements are: A and C
Explanation:
In geometric optics, lenses are one of the most used elements, in general the curved surface, if they are convex, form real images, that is, the light rays have to converge at a point.
Concave lenses tend to create virtual images or I know that the extensions of the rays are what form the image.
The flat surface does not create changes in the image.
With these characteristics, let's examine the different true statements are: A and C
A) the rays diverge,
c) the rays parallel to the diverges their extensions are at a point on the same side of the lens this point is called focal length.
The plates of a vacuum-gap parallel plate capacitor have a 100.0 mm2 area, a vacuum gap of 5.00 mm and are connected to a 1.5-volt battery. After the capacitor is charged, the battery is disconnected from the capacitor. After the battery is disconnected, the plates are pulled apart until the vacuum gap is 7.50 mm. a. What are the initial and final energies stored in the capacitor
Answer:
E₀ = 2.0*10⁻¹¹ J = 0.2 pJ
Ef = 3.0*10⁻¹¹ J = 0.3 pJ
Explanation:
The energy stored between the plates of a parallel plate capacitor can be expressed in terms of the capacitance C and the potential difference between plates V as follows:[tex]E = \frac{1}{2} * C * V^{2} (1)[/tex]
When the capacitor is fully charged, the potential difference between plates must be equal to the voltage of the battery, 1.5 V.In a parallel plate capacitor, the value of the capacitance is independent of the applied voltage, and depends only on geometric constants and the dielectric constant of the medium between plates, as follows:[tex]C = \frac{\epsilon_{o}*A}{d} (2)[/tex]
We can find the initial value of C replacing in (2) by the givens below:A = 100.0 mm2d= 5.00 mmε₀ = 8.85*10⁻¹² F/m[tex]C_{o} = \frac{\epsilon_{o}*A}{d} = \frac{(8.85*(10)^{-12} F/m)*(10^{-4} m2)}{5.0*(10)^{-3}m} = 1.77*10^{-13} F (3)[/tex]With this value of C₀, and the value of the initial potential difference between plates (1.5 V), we can find the initial charge on the capacitor, starting from the definition of capacitance:[tex]C =\frac{Q}{V} (4)[/tex]Solving for Q in (4):[tex]Q = C_{o}* V = 1.77*10^{-13} F * 1.5 V = 2.65*10^{-13} C (5)[/tex]Finally, we can find the initial energy stored in the capacitor, replacing (3) and V in (1):[tex]E_{o} = \frac{1}{2} * C_{o} * V_{o} ^{2} = \frac{1}{2} * 1.77*10^{-13}F*(1.5V)^{2} = 0.2 pJ (6)[/tex]
If we pull apart the plates until the vacuum gap is 7.50 mm, we will change the expression of C in (2), decreasing its value due to the expanded gap.Replacing in (2) the new value of the gap (7.50 mm), we can find the new value of C, as follows:[tex]C = \frac{\epsilon_{o}*A}{d} = \frac{(8.85*10^{-12}F/m)*10^{-4} m2}{7.5*10^{-3}m} = 1.18*10^{-13} F (7)[/tex] In order to find the final energy stored in the capacitor, we need also the value of the final potential difference between plates.Once disconnected from the battery, the charge on any of the plates must remain the same, due to the principle of conservation of the charge.So, since we have the value of Q from (5) and the new value of C from (7), we can find the new potential difference between plates as follows:[tex]V_{f} = \frac{Q}{C_{f}} = \frac{2.7*10^{-13}C}{1.18*10^{-13}F} = 2.25 V (8)[/tex]With the values of Vf and Cf, we can find the value of the final energy stored in the capacitor, replacing these values in (1):[tex]E_{f} = \frac{1}{2} * C_{f} * V_{f} ^{2} = \frac{1}{2} * 1.18*10^{-13}F*(2.25V)^{2} = 0.3 pJ (9)[/tex]
A pendulum has a length of 2 m and a 30 kg mass hanging on the end. What is the period of the
pendulum?
Answer:
T = 2.83701481512 seconds
Explanation:
Hi!
The formula that you will want to use to solve this question is:
[tex]T = 2\pi *\sqrt{\frac{L}{g} }[/tex]
T--> period
L --> length of the pendulum
g --> acceleration due to gravity (9.8m/s^2)
since we know that the mass of the bob at the end of the pendulum does not affect the period of the pendulum, we can go ahead and ignore that bit of information (unless, of course, the weight causes the pendulum to stretch)
so now we can plug in our given info into the formula above and solve!
T = 2*pi * sqrt(2/9.8)
T = 2.83701481512 seconds
*Note*
- I used 3.14 to pi, if you need to use a different value for pi (a longer version, etc) your answer will be slightly different
I hope this helped!
What is energy transfer in a car crash
Force energy- kinetic energy
Answer:
Kinetic and thermal
Explanation:
Kinetic because a moving car is transferring movement energy into the other one. Thermal because, in a car crash, the touching surfaces of both cars friction and that produces heat.
4. When scientists calculate the trajectory a satellite takes on its way to
study a planet, what do you think they use?
5 points
A Speed and velocity
B. Velocity and acceleration
O C. Speed, velocity, and acceleration
O D. Speed only
When scientists calculate the trajectory a satellite takes on its way to
study a planet, they use C. Speed, Velocity, and acceleration.
A trajectory, often known as a flight path, is the route taken by an object moving under the influence of gravity. Typically, the phrase is applied when referring to projectiles or satellites. A parabola curve is usually a decent approximation of the trajectory form when an object is propelled for in a short distance.
When scientists calculate the trajectory a satellite takes on its way to
study a planet they take the speed, velocity, and acceleration into consideration.
The formula for calculating the trajectory can be expressed as:
[tex]\mathbf{y = h + xtan (\alpha) - \dfrac{gx^2 }{2V_o^2cos^2 (\alpha)}}[/tex]
where;
h = height show the distanceV = velocityg = acceleration due to gravityLearn more about trajectory here:
https://brainly.com/question/88554?referrer=searchResults
What are some possible injuries that can occur as a result of anabolic steroid use?
How does increasing the number of resistors in a parallel branch change the total resistance of the system?
Increasing the number of resistors in a parallel branch, decreases the total resistance of the system.
What is parallel branch?Parallel resistive circuit is one where the resistors are connected to the same two points (or nodes) and is identified by the fact that it has more than one current path connected to a common voltage source.
As more and more resistors are added in parallel to a circuit, the equivalent resistance of the circuit decreases and the total current of the circuit increases.
To learn more about Parallel circuit here
https://brainly.com/question/11409042
#SPJ2
Surface tension is often calculated using a machine that lifts a wire ring from the surface of a liquid. In this case the ring and liquid have some cohesive forces and attract rather than repel. In order to lift a ring of radius 2.75 cm off of the surface of a pool of blood plasma, a vertical force of 2.00*10-2 N greater than the weight of the ring is required. Consider the situation just before the ring breaks contact with the blood plasma where the blood plasma makes a contact angle of approximately zero degrees along the circumference of the ring and is stretched down vertically on both sides of the ring.
Required:
Calculate the surface tension of blood plasma from this information.
Answer:
0.116 N/m
Explanation:
Since the net force acting on the ring must be greater than 2.00 × 10⁻² N, and the surface tension T = F/L where F = net force = 2.00 × 10⁻² N and L = circumference of ring = 2πr where r = radius of ring = 2.75 cm = 2.75 × 10⁻² m.
So, T = F/L
= F/2πr
= 2.00 × 10⁻² N ÷ 2π(2.75 × 10⁻² m)
= 1/2.75π N/m
= 1/8.64 N/m
= 0.116 N/m
A solid sphere of radius R, a solid cylinder of radius R, and a rod of length R all have the same mass, and all three are rotating with the same angular velocity The sphere is rotating around an axis through its center. The cylinder is rotating around its long axis, and the rod is rotating around an axis through its center but perpendicular to the rod. Which one has the greatest rotational kinetic energy? a. the sphere b. the cylinder c. the rod d. the rod and the cylinder have the same rotational kinetic energy e. they all have the same kinetic energy
Answer:
b. the cylinder
Explanation:
From the information given:
We understood that the mass of the sphere, cylinder, and rod length is the same with the same angular speed.
Taking their moments:
For the solid sphere; [tex]\text{The moment of inertia :}[/tex] [tex]I_s[/tex] = [tex]\dfrac{2}{5} \times m \times r^2[/tex]
The moment of inertia of the cylinder, [tex]I_c = 0.5\times m \times r^2[/tex]
The moment of inertia of rod, [tex]I_r =\dfrac{ m * r^2 }{12}[/tex]
The rotational kinetic energy is directly corresponding to the moment of inertia.
Thus, the cylinder has the greatest rotational kinetic energy.
A 10 kg box initially at rest is pulled with a 50 N horizontal force for 4 m across a level surface. The force of friction acting on the box is a constant 20 N. How much work is done by the normal force pushing up on the box from the ground?
A. 10 J
B. 0 J
C. 100 J
D. 50 J
Answer: 0 j
Explanation:
It is given that,
Mass of the box, m = 10 kg
Force with which the box is pulled, F = 50 N
It is moved a distance of 4 m
Force of friction acting on the box, f = 20 N
We need to find the initial kinetic energy the box have. It is clear that the box is at rest initially. As there is no motion in the box at that time. The formula for the kinetic energy of the box is given by :
As v = 0
So, the initial kinetic energy of the box is 0. Hence, this is the required solution.
Why is the answer (A)?
In details please
Explanation:
resistance of wire can be determined by this equation
R = Rho . L / A
L = the length of wire
A = the Area, A = πr²
Rho = density of resictance
we can do some rational
R1/R2 = ( Rho L1/A1) / (Rho L2/A2)
L2 is the condition when the length is doubled and
L2 = 2 x L
A2 is the condition when the diameter is doubled
A2 = 4A1
R/R2 = (L1/A1)/(L2/A2)
R/R2 = (L/A) / (2L/4A)
R/R2 = 1 / ½
R2 = ½ R.
then we use formula of Voltage
V = I R
1st condition
V = 0.3 R
2nd condition ( V is constant)
V = I2 R2
0.3 R = I2 x ½R
i2 = 0.3/ ½
i2 = 0.6 Ampere
If an object is placed between the focal point and twice the focal length of a convex lens, which type of image will be produced?
A.
real, upright, and magnified
B.
virtual, inverted, and smaller
C.
virtual, upright, and magnified
D.
real, inverted, and magnified
E.
real, upright, and smaller
Answer: I think its D
Explanation: Hope this was helpful...
I need help with science o.o:
Question 1:
An egg yolk is unicellular.
True
False
___________________________
Question 2:
Your body has more than a billion cells.
True
False
_____________________
Question 3:
Almost all cells are not microscopic.
True
False
please dont steal my points :>
Answer:
TrueTrueFalseExplanation:
this is the answer
Answer:
1.true
2true
3.false
Explanation:
espero que te ayude
A vessel having a capacity of 0.05 m³ contains a mixture of saturated water an saturated steam at a temperature 245°C the mass of the liquid present is 10 kg. find the following: i- The pressure. ii- The mass. iii- The specific volume. iv- The specific enthalpy. v- The specific internal energy.
A car's bumper is designed to withstand a 7.20 km/h (2.0 m/s) collision with an immovable object without damage to the body of the car. The bumper cushions the shock by absorbing the force over a distance. Calculate the magnitude of the average force (in N) on a bumper that collapses 0.195 m while bringing a 830 kg car to rest from an initial speed of 2.0 m/s.
Answer:
8512 N
Explanation:
From the work energy theorem we know that: The net work done on a particle equals the change in the particles kinetic energy:
[tex]W=\Delta K=K_{f}-K_{i} \\ \\qquad \begin{array}{r} W=F \cdot d, \Delta K=\frac{1}{2} m v_{f}^{2}-\frac{1}{2} m v_{i}^{2} \\ F \cdot d=\frac{1}{2} m v_{f}^{2}-\frac{1}{2} m v_{i}^{2}[/tex]
Where:
-W is the work done by the force.
- F is the force actin on the.
- d is the distance travelled.
- m is the mass of the car.
- [tex]v_{f}, v_{i}[/tex] are the final and the initial velocity of the car
[tex]K_{f}, K_{i}[/tex] are the final and the kinetic energy of the car.
Givens: [tex]m=830 \mathrm{~kg}, v_{i}=2 \mathrm{~m} / \mathrm{s}, v_{f}=0 \mathrm{~km} / \mathrm{h}, d=0.195 \mathrm{~m}[/tex]
Plugging known information to get:
[tex]F \cdot d &=\frac{1}{2} m v_{f}^{2}-\frac{1}{2} m v_{i}^{2} \\ F &=\frac{\frac{1}{2} m v_{f}^{2}-\frac{1}{2} m v_{i}^{2}}{d} \\ &=\frac{0-\frac{1}{2} \times 830 \times 2^{2}}{0.195} \\ &=8.512 \times 10^{3} \\ F &=8.512 \times 10^{3} \mathrm{~N}[/tex]
Which of the following is an
example of thermal energy?
A. turning on a lamp so you can read
B. rubbing your hands together to get warm
C. kicking a ball
A capacitor with an initial potential difference of 100 V is discharged through a resistor when a switch between them is closed at t 0.At t 10.0 s, the potential difference across the capacitor is 1.00 V. (a) What is the time constant of the circuit
Answer:
τ = RC = 2.17 s
Explanation:
The voltage through a capacitor can't change instantaneously, so immediately after the switch is closed, the potential difference will keep at 100 V.This voltage will produce a flow of charge (a current) from the capacitor to the resistor, which will be diminishing continuously, till the capacitor be totally discharged, and the current becomes zero.The voltage through the capacitor will follow an exponential function of time, as follows:[tex]V_{C} =V_{o} * e^{-t/RC} (1)[/tex]
Replacing by the givens in (1):[tex]V_{C} = 1.00 V\\V_{o} = 100V\\t = 10.0 s[/tex]
[tex]\frac{1.00V}{100 V} = e^{-10s/RC} (2)[/tex]
Taking ln on both sides in (2), and solving for RC, we have:[tex]R*C= \frac{-10s}{ln 0.01} = 2.17s (3)[/tex]
So, the time constant of the circuit (the product of R times C) is equal to 2.17s.An electron is accelerated through a potential difference of 3.5 kV and directed into a region between two parallel plates separated by 29 mm with a potential difference of 100 V between them. The electron is moving perpendicular to the electric field when it enters the region between the plates. What magnetic field is necessary perpendicular to both the electron path and the electric field so that the electron travels in a straight line
Answer: [tex]0.985\times 10^{-4}\ T[/tex]
Explanation:
Given
Electron is accelerated 3.5 kV potential difference
Distance between plates d=29 mm
The potential difference between plates is V=100 V
here, the kinetic energy of an electron is acquired through a potential difference of 3.5 kV
[tex]\Rightarrow \dfrac{1}{2}m_ev^2=e\times 3.5\times 10^3\\\\\Rightarrow v=\sqrt{\dfrac{2\times 3.5\times 10^3e}{m_e}}=\sqrt{\dfrac{7\times 10^3\times 1.6\times 10^{-19}}{9.1\times 10^{-31}}}\\\\\Rightarrow v=\sqrt{1.23\times 10^{15}}=3.5\times 10^7\ m/s[/tex]
To move in a straight line Force due to magnetic field must be balanced by force due to charge
[tex]\Rightarrow F_B=F_q\\\\\Rightarrow evB=eE\\\\\Rightarrow B=\dfrac{E}{v}\\\\\Rightarrow B=\dfrac{\frac{V}{d}}{3.5\times 10^7}=\dfrac{\frac{100}{0.029}}{3.5\times 10^7}\\\\\Rightarrow B=\dfrac{3.448\times 10^3}{3.5\times 10^7}=0.985\times 10^{-4}\ T[/tex]
Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. If the coffee has a temperature of 185 degrees Fahrenheit when freshly poured, and 3 minutes later has cooled to 172 degrees in a room at 78 degrees, determine when the coffee reaches a temperature of 147 degrees.
Answer:
6.77 minutes
Explanation:
172 degree - 78 degree = (185 degree - 78 degree)e−2 k
=> 94 = 107
e−2 k => 94 ÷ 107
k => ln (94÷107) / 2
147 - 78 = (185 - 78)e ^[ln (94÷107) / 2]
=> 69 = 107 e^ [ln (94÷107) / 2]
e^[ln (94÷107) / 2] =69 ÷ 107
=> t = [ln (69 ÷ 107)] ÷ [ln (94÷107) / 2]
t=> -0.4387 ÷ -0.0648
t => 6.77 minutes.
Therefore, the final answer to the question is 6.77 minutes.
A man whose mass is 69 kg and a woman whose mass is 52 kg sit at opposite ends of a canoe 5 m long, whose mass is 20 kg. Suppose that the man moves quickly to the center of the canoe and sits down there. How far does the canoe move in the water
Answer:
the canoe moved 1.2234 m in the water
Explanation:
Given that;
A man whose mass = 69 kg
A woman whose mass = 52 kg
at opposite ends of a canoe 5 m long, whose mass is 20 kg
now let;
x1 = position of the man
x2 = position of canoe
x3 = position of the woman
Now,
Centre of mass = [m1x1 + m2x2 + m3x3] / m1 + m2 + m3
= ( 69×0 ) + ( 52×5) + ( 20× 5/2) / 69 + 52 + 20
= (0 + 260 + 50 ) / ( 141 )
= 310 / 141
= 2.19858 m
Centre of mass is 2.19858 m
Now, New center of mass will be;
52 × 2.5 / ( 69 + 52 + 20 )
= 130 / 141
= 0.9219858 m { away from the man }
To get how far, the canoe moved;
⇒ 2.5 + 0.9219858 - 2.19858
= 1.2234 m
Therefore, the canoe moved 1.2234 m in the water
The canoe move in the water will be 1.2234 m. The canoe move depending on the center of mass of the bodies.
What is the center of mass?The center of mass of an item or set of objects is a place specified relative to it. It's the average location of all the system's components, weighted by their mass.
The centroid is the location of the center of mass for simple rigid objects with homogeneous density. The center of mass of a uniform disc shape, for example, would be at its center.
The given data in the problem is;
m₁ is the mass of man = 69 kg
m₂ is the mass of woman whose= 52 kg
m₃ is the mass of canoe = 20 kg
L is the length of canoe = 5 m
x₁ is the position of the man
x₂ is the position of the canoe
x₃ is the position of the woman
The center of mass will be;
[tex]\rm COM= \frac{[m_1x_1 + m_2x_2 + m_3x_3]}{ m1 + m2 + m3} \\\\ \rm COM= \frac{[69 \times 0 +52 \times 5 + 20 \times 2.5]}{ 69+ 52 + 20} \\\\ \rm COM= (0 + 260 + 50 ) / ( 141 )\\\\ \rm COM = 310 / 141 \\\\ \rm COM = 2.19858 m[/tex]
The new center of mass is;
[tex]\rm COM= \frac{52 \times 2.5 }{69+52+20} \\\\ \rm COM=\frac{130}{141} \\\\ \rm COM= 0.9219 m[/tex]
The distance to find how the canoe moved will be found by;
[tex]\rm x= 2.5+0.9219-2.1985 = 1.2234[/tex]
Hence the canoe move in the water will be 1.2234 m.
To learn more about the center of mass refer to the link;
https://brainly.com/question/8662931
Brainliest!!! Write: Forces are all around us. Imagine that your teacher has asked you to teach a lesson to your peers about forces. Explain, in detail, how you experience forces in your everyday life. Give 3 examples
If you drag a bag across floor, you are experiencing a friction force
if you throw a paper or feather up, it floats side ways slowly. It is called air Resistance.
if you push or pull a Door, it is Normal force.
I hope this helped!
have an amazing Day!!
Based on the image which parachuter will fall fastest
A
B
Or C
Explanation:
c willl fall fast then a and b
The modern model of the atom describes electrons in a little less specific detail than earlier models did. Why is it that being less sure about the placement of electrons in an atom is actually an improvement over earlier models?
The plum pudding model of the atom states that
Answer:
It is because one cannot know exactly the position of the electron within the atom.
One formulation of Heisenberg's Uncertainty Principle tells us that one cannot know simultaneously the position and momentum of the electron, so one cannot specify exactly either coordinate because the other would be infinite.
Bohr specified the most probable position of the electron at its lowest energy level in hydrogen and the product of the two would be about the Heisenberg value.
A 3.0-kg and a 1.0-kg box rest side-by-side on a smooth, level floor. A horizontal force of 32 N is applied to the 1.0-kg box pushing it against the 3.0-kg box, and, as a result, both boxes slide along the floor. How hard do the two boxes push against each other
Considering both boxes as one body, it would have a total mass of 4.0 kg. By Newton's second law, the 32 N force applies an acceleration a such that
∑ F = 32 N = (4.0 kg) a → a = 8.0 m/s²
and both boxes share this acceleration. (There is no friction, so the given force is the only one involved in the direction of the boxes' motion.)
Now consider just the smaller box. It is feeling the effect of the 32 N push in one direction and, as it comes into contact with the larger box, a normal force that points in the opposite direction. Let n be the magnitude of this normal force; this is what you want to find. By Newton's second law,
∑ F = 32 N - n = (1.0 kg) (8.0 m/s²)
n = 32 N - 8.0 N
n = 24 N
Just to make sure that this is consistent: by Newton's third law, the larger box feels the same force but pointing in the opposite direction. On the smaller box, n opposes the pushing force, so points backward. So from the larger box's perspective, n acts on it in the forward direction. This is the only force acting on the larger box, so Newton's second law gives
∑ F = 24 N = (3.0 kg) (8.0 m/s²)