Maximum velocity in vertical circular motion derivation. Pendulum 1 has a bob with a mass of 10 kg.

Step 1: The object covers an arc length in a time interval , so . 0. Angular velocity is measured in rad/s. The two triangles in the figure are similar. 00 N/m is attached to the block, and the opposite end of the spring is attached to the wall. Hence, In the vertical direction (Y axis) `N cos ϴ = f sin ϴ + mg` ----- (i) Mar 8, 2024 · Determine the car’s velocity and acceleration at time t =3s. There are 2 π ‍ radians in a 360 ° ‍ circle or one revolution. Mar 28, 2024 · One way to have a force that is directed towards the center of the circle is to attach a string between the center of the circle and the object, as shown in Figure 6. Hence obtain the expression for acceleration, velocity and displacement of a particle performing linear simple harmonic motion. 0m/s. May 1, 2021 · 1) Uniform circular motion:-. If the string breaks when the tension in it exceeds 360N, calculate the maximum speed of rotation, and state where the object will be when the string breaks. 5 m is whirled in a vertical circle at constant angular speed if the maximum tension in the string is 5 kg wt. Unitless. At t = 0 , it is located on the x -axis. About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features NFL Sunday Ticket May 15, 2024 · If the wheel rotates at a uniform rate, the bug will travel in uniform circular motion. m (v 2 /r) = T + mg. Oct 7, 2014 · What is the maximum angle in a vertical circular motion? The maximum angle in a vertical circular motion is 90 degrees. Derive experssion for velocity of vehicle on level circular road. How is circular motion different from linear motion? Circular motion involves movement along a curved path Sep 12, 2022 · The plus sign is used for waves moving in the negative x -direction. F net = m a. Motion of a car on a banked road. 4. Hence, find the expression for the 20. 5 18A. image courtesy of MIT Technical Services. r r (t + ) r (t) r. 5 kg attached to a string of length 0. The projection of the position of P onto a fixed axis undergoes simple harmonic motion and is analogous to the Use Newton’s Second Law to derive the condition for motion in a vertical circle. The formula for the centripetal force is given by Fc = mv^2/r, where m is the mass of the body, v its velocity and r the radius of the circle. The projection of the position of P onto a fixed axis undergoes simple harmonic motion and is analogous to the Derivation of First Equation of Motion by Graphical Method. Acceleration Due to Gravity and Its Variation with Altitude and Depth. We call this projectile motion. OpenStax is part of Rice University, which is a 501 (c) (3) nonprofit. Considering vertical motion along the y-axis: Sep 12, 2022 · An engineer builds two simple pendulums. Jun 30, 2021 · This is an equation for a particle’s velocity at any point in a vertical circle while it is moving in a circular motion. v0 = (2πA)/T or T = (2πA)/v0 where T is the period and A is the amplitude and v0 is the maximum velocity. Its centre of mass rises to a maximum height of _____. Calculate the temperature of the surroundings. This force is called the centripetal force. 2 days ago · The motion in a vertical circle is considered nonuniform as the influence is observed the most at the lowest and the least at the highest point of the path. Feb 13, 2010 · Homework Statement An object of 6. Equations for VCM. We know that, v= R ω. 3. A body weighing 0. Q3. The rotation around a fixed axis of a three-dimensional body involves the circular motion It means all bodies (whether an iron ball or a piece of paper), when dropped (u = 0) from same height should fall with the same rapidity and should take the same time to reach the earth, i t is the minimum velocity given to the particle at the lowest point to complete the circle. 1) What is Vertical c Nov 10, 2005 · The maximum velocity in simple harmonic motion occurs at the equilibrium position, and its value is given by Vmax = ωA. Calculate the speed of the object and maximum number of revolutions it can complete in one minute. State the differential equation of linear simple harmonic motion. Suppose a body of mass ‘m’ performs vertical circular A particle of mass m, just completes the vertical circular motion. In case of vertical circular motion this is the minimum velocity that a body must be given at the lowest position to complete a vertical circle. It is an expression for the difference in tensions at the highest and lowest points for a particle performing the vertical circular motion. Click here:point_up_2:to get an answer to your question :writing_hand:derive an expression for maximum height and range of an object in projectile motion. Pendulum 1 has a bob with a mass of 10 kg. Let’s solve the example as below…. The equations of projectile motion are as follows: Horizontal velocity (Vx) = Vx0. 0 m below its starting altitude will spend 3. ’S Having Same Period and Along Same Line. Consider a ball of mass Jan 23, 2021 · In this physics video, we discuss circular motion in a vertical circle. 2. The magnitude of this acceleration by comparing ratios of velocity and position around the circle. T = m (v 2 /r) - mg. Heyy Guyzz!!! This is Amol Balekar. Let the height at position D be 75 May 20, 2024 · The motion of the ball is constrained between \(-A\) and \(+A\) (the turning points), and the velocity of the ball, in the \(x\) direction, will be highest when \(x=0\). Composition of Two S. Go the other way you get: −m v2 r + m g + T = 0 − m v 2 r + m g + T = 0. Step 3: Equating the two expressions for gives , which simplifies to . Q) Difference between maximum and minimum tensions along the string is 60 N. Horizontal distance (x) = Vx0t. Find the value of θ. How is centripetal acceleration calculated? The formula for calculating centripetal acceleration is a = v^2/r, where v is the velocity of the object and r is the radius of the circular path. The frictional force supplies the centripetal force and is numerically equal to it. If the centripetal force is absent then the circular motion is not possible. Jan 16, 2020 · An object of mass 0. Kepler’s Laws. 8 \frac{m}{s^2} {/eq}), v is velocity in meters per second, h is the vertical height of the object in Consider an object moving in a circle with radius at a constant speed – i. Some of the examples are roller coasters, cars on hilly roads, etc. Pendulum 2 has a bob with a mass of 100 kg. Plot graph of displacement velocity and acceleration of particle performing SHM and starting A particle has velocity √ 3 r g at the highest point in a vertical circle. The point P is analogous to an object on the merry-go-round. 1 Geometric Derivation of the Velocity for Circular Motion . Then, the critical velocity is 2√gl. The work done in uniform circular motion is zero because the angle between force and displacement is 90ο. 1: Smoke rises smoothly for a while and then begins to form swirls and eddies. Vertical distance (y) = Vy0t – (1/2)gt^2. P) Maximum speed must be `5sqrt5` m/s. Centripetal force is not something new. Consider a particle undergoing circular motion. uniform circular motion. 2 Vertical projectile motion (ESCJW) In Grade 11, we studied the motion of objects in free fall and saw that such an object has a constant gravitational acceleration of \ (\vec {g}\). At time t , the position of the particle is \(\overrightarrow{\mathbf{r}}(t)\). Yes, if you are swinging a sling stone at the end of its strap in a vertical circle then the speed of the stone at the top 3. 4 L 3; L; 4 L 9; L 3 Feb 20, 2022 · Laminar flow is characterized by the smooth flow of the fluid in layers that do not mix. In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular arc. Question 3: Define circular motion and circular motion that is uniform. In this process the potential energy of the car. When the projectile reaches the maximum height then the velocity component along Y-axis i. Aug 13, 2020 · At the top of a circular trajectory the ball momentarily moves in the horizontal direction while it accelerates downwards in the vertical direction. 0 = m (v 2 /r) - mg. A car is accelerated on a leveled road and attains a velocity 4 times its initial velocity. A circular motion is said to be uniform if an object covers equal angular displacement in equal interval of time. Each pendulum hovers 2 cm above the floor. Sep 12, 2022 · An object undergoing circular motion, like one of the race cars shown at the beginning of this chapter, must be accelerating because it is changing the direction of its velocity. Vertical velocity (Vy) = Vy0 – gt. – Vy0 = vertical component of initial Welcome to an in-depth exploration of vertical circular motion in physics! In this video, we'll dive into the derivation of the principles governing objects A satellite is revolving in a circular orbit at a height ‘h’ from the earth’s surface (radius of earth R ; h < < R). 3 is known as a simple harmonic wave function. The mass continues in SHM that has an amplitude A and a period T. The rotational analogue of linear velocity. It really doesn't matter whether you choose up or down as positive. The minimum speed of a particle is 5 m/s. Aug 29, 2022 · Understanding the Equations of Projectile Motion. ) The velocity corresponding to the circular orbit is sometimes called the first cosmic velocity, whereas in this context the escape velocity is referred to as the second cosmic velocity. " Centripetal Acceleration (α) = `v^2/r = rῶ^2`. Equation 16. Uniform circular motion: Motion in a circle at a constant speed: Radian: Ratio of an arc’s length to its radius. 2. Since there is no acceleration along the vertical direction, the net force along this direction must be zero. There are tons of videos online that show animations of this concept, just look up “SHM as a projection of circular motion” and you will get lots of different ways to Centripetal Acceleration. Step 2: The arc length can also be described in terms of the angle it subtends at the center of the circle: . (b) Velocity vectors forming a triangle. If As a result, non-uniform circular motion occurs as the body moves in a vertical circle. Crucial feature of uniform circular motion in the vertical plane: Constant downward force of gravity; Non-Constant upward normal force Step 5: Apply Newton's second law. Turbulent flow, or turbulence, is characterized by eddies and swirls that mix layers of fluid together. Jan 16, 2023 · If the speed of the particle is changing, the centripetal acceleration at any instant is (still) given by Equation 18A. 3. This relationship can be seen in the equation h = r (1-cosθ), where the period is represented by θ. Question 2: Is it possible to have a uniform circular motion in a vertical circle? Answer 2: No, the velocity will change due to gravity amid circular motion, so will not be uniform. The direction of friction force will be inwards. This can be caused by a centripetal force, which acts towards the center of the circle, or by a combination of velocity and inertia. that is, that we do not need to worry about any rotational energy of its wheels. We proved that this centrally directed acceleration, called centripetal acceleration, is given by the formula \[a_{c} = \frac{v^{2}}{r}\] where v is the velocity of Apr 19, 2015 · Equation of path of projectile (horizontal and angular projection) + derivation of corresponding formulas of maximum height , time and range centrifugral force derivation Chapter 5:- LAWS OF MOTION? 1st 2nd and 3rd law of motion the derivation of 1st and 3rd law of motion using 2nd law of motion recoil of a gun numericals on tension and free 6. The velocity of anybody undergoing motion in a vertical circle is given by v = u2 − 2gh− −−−−−−√. Feb 11, 2022 · Equation (4) gives the maximum safety speed of vehicle moving along the curved banked road. It is an example of non-uniform circular motion. ω. Illustration Nov 21, 2023 · As before, {eq}\theta {/eq} is the banking angle, g is the gravitational constant ({eq}9. What is the difference between simple harmonic motion and uniform circular motion? The maximum height of a object in a projectile trajectory occurs when the vertical component of velocity, vyvy, equals zero. Find the maximum height above horizontal level of point A if the string slacks at the point B as shown. 00-kg block is placed on a frictionless surface. , centripetal) acceleration is a = (v^2)/r, where v is the linear velocity, and r is the radius of the circle. View Solution. The height of a ball thrown upwards is given by h(t)=3. (e) The mass then continues to move in the positive direction until it stops at x = A x = A. State the factors on which the optimum speed depends. Find its 1. A particle of mass 1 kg, tied to a 1. At the bottom (y=up): ΣF r = N - mg = ma r = m v 2 /r N = m v 2 /r + mg. Railway track of curvature 2 km has inclination of θ 0 for a maximum velocity of 72 kmph. Let’s calculate maximum speed for the safe turn on horizontal circular rough surface whose coefficient friction is and radius is R. The formula for cos T is (u^2-2ga)/3ga. Therefore, f c = m R ω2. It can be uniform, with a constant rate of rotation and constant tangential speed, or non-uniform with a changing rate of rotation. The point P travels around the circle at constant angular velocity ω. As the projectile moves upwards it goes against gravity, and therefore the velocity begins to decelerate. Nov 29, 2005 · 1. ” i. The first equation of motion can be derived using a velocity-time graph for a moving object with an initial velocity of u, final velocity v, and acceleration a. Apr 22, 2010. Consider the centripetal force at point P. Variation of ‘G’ Due to Lattitude and Motion. The direction of a centripetal force is toward the center of curvature, the same as the direction of centripetal acceleration. t , the position of the particle is ! ! r (t) . The initial velocity for the motion along Y-axis (as said above) is V 0 sinθ. (Recall that density is mass per unit volume. Q2. Centripetal force is perpendicular to velocity and causes uniform circular motion. The angle the particle makes with the positive x -axis is given by \(\theta(t)=A t^{3}-B t\) where A and B are positive constants. Apr 22, 2010 · Circular Circular motion Maximum Motion Velocity. M. Consider the following statements. It is defined as the rate of change in angular displacement of a particle in a circular motion. Resolving vertically Its maximum angular velocity is 'ω'. According to Newton’s second law of motion, net force is mass times acceleration: F net = m a. Vertical Circular Motion Minimum velocity at the bottom of Circle in 4 minutes is done here in this video and this helps you to strengthen your JEE and NEET Oct 24, 2007 · It is always directed towards the center of the circle and is responsible for keeping the object in its circular motion. During the time interval Δ. 5 with the v v being the speed of the particle at that instant (and in addition to the centripetal acceleration, the particle also has some along-the-circular-path acceleration known as tangential acceleration). Consider the mass of a body m and the magnitude of the centripetal force f c, f c = mass × acceleration. We now study the motion of objects that are moving upwards or downwards while experiencing a force due to gravity. The minimum increase in its orbital velocity required, so that the satellite could escape from the earth’s gravitational field, is close to : (Neglect the effect of atmosphere. Weightlessness. So, In horizontal direction, There the maximum speed for safe turn on horizontal track is . Eventually the vertical velocity will reach zero, and the projectile is accelerated downward under gravity immediately. If the particle leaves the sphere at point A and meets it again at point B, where AM Periodic Time. 1) where A > 0 is the amplitude (maximum value). Both are suspended from small wires secured to the ceiling of a room. 2 m long string is whirled to perform the vertical circular motion, under gravity. Suppose a function of time has the form of a sine wave function, y(t) = Asin(2πt / T ) (23. It is projected from the lowest point of the sphere and at an angle T, the velocity is v and the normal reaction is R. Figure 12. Derive an expression for man height attained by an object projected vertically upwards with a velocity 'u'. Note: In case the particle is attached with a light rod of length l, at the highest point its minimum velocity may be zero. This is the maximum speed of a car in circular motion on a level road. The physics of objects in vertical circular motion. Q 5. A conical circular pendulum Consider a mass , m, attached to a string of length L moving around a horizontal circle of radius, R, at a constant speed, v, and the string make an angle θ with the vertical and have a tension, P. Derive the expression for the difference in tensions at the highest and the lowest points. The expressions for v and R are v= [u^2-2ga (1+cos T)]^1/2 and R=mu^2/a - mg (2+3cos T), respectively. The forces on the object are thus: →Fg. Also, find the maximum height reached by the ball. Acceleration in the horizontal projectile motion and vertical projectile motion of a particle: When a particle is projected in the air with some speed, the only force acting on it during its time in the air is the acceleration due to gravity Vertical circular motion derivation is used to find out the tension at the high and the low points as well as the velocity of the object in motion. 8 m, find the tension in the string when the body is at the top of the circle. The vector Δ→v points toward the center of the circle in the limit Δt → 0. [11] For a body in an elliptical orbit wishing to accelerate to an escape orbit the required speed will vary, and will be greatest at periapsis when the body is 3 days ago · Uniform circular motion occurs when an object moves with a constant speed and is always at a fixed distance from a point. Sep 12, 2022 · Figure 4. 5. View Solution Figure 1. 1. Vertical circular motion (VCM) is a special type of circular motion in which the body travels in a vertical plane. 21. Choose positive up and you get: m v2 r − m g − T = 0 m v 2 r − m g − T = 0. 1: (a) A particle is moving in a circle at a constant speed, with position and velocity vectors at times t and t + Δt. The larger the F c, the smaller the radius of curvature r and the sharper the curve. Minimum velocity at the top of a vertical circular Motion for JEE Nov 20, 2015 · How to find the critical velocity of an object in vertical circular motion. In JEE Advance Nov 30, 2017 · projectile motion: components of initial velocity V 0. 0m with a speed of 8. 2) Non uniform circular motion:-. Derive the expression for the maximum speed of a vehicle on the banked road. 2 . V y becomes 0. Homework Equations Our mission is to improve educational access and learning for everyone. Find the ratio of tension at the highest and lowest point. where C is the drag coefficient, A is the area of the object facing the fluid, and ρ ρ is the density of the fluid. Angular velocity (ω ‍ ) Measure of how an angle changes over time. Oct 6, 2020 · In mechanics for jee main as well as in NEET every year questions are asked on different cases of Vertical Circular Motion of simple pendulum. a = a c. A particle is moving in a circle of radius R. The body starts whirling in a vertical circle. Simply plug in the values and solve for v. A particle is moving along the y-axis, and its velocity is given by v(t)= 2t 2-3t+5 m/s. Mar 29, 2017 · The Point of Maximal Tension for Vertical Circular Motion can be calculated using the equation T = mg + (mv^2)/r, where T is the tension force, m is the mass of the object, g is the acceleration due to gravity, v is the speed of the object, and r is the radius of the circular path. 1 Circular Motion Kinematics. The fact that it has to remain at the same distance while maintaining a constant speed implies that it&#x27;s velocity keeps changing. 2 m/s and lands 10. If the radius of the circle is 0. . What is the role of centripetal force in uniform circular motion? Centripetal force is the force that keeps an object moving in a circular path. 5 kg tied to a string is projected with a velocity of 10 m/s. 5 C ρ A. Derive an expression for the velocity of a particle performing linear SHM using differential equation. A spring with a force constant of k = 32. e. Step 6: Solve. Here's the video on BANKING OF ROADS which contains Derivation & Numericals on BANKING OF ROADS which is a part Circular Figure 3 shows the basic relationship between uniform circular motion and simple harmonic motion. Describe how the motion of the pendulums will differ if the bobs are both displaced by 12°. It is denoted by. The maximum linear speed is the velocity, and the rotational speed is 6. Expression for Tension in String in Motion of Body in Vertical Circle. Binding Energy and Escape Velocity of a Satellite. (g =acceleration due to gravity) When the bob performs a vertical circular motion and the string rotates in a vertical plane, the difference in the tension in the string at horizontal position and uppermost position is _____. Jul 12, 2008 · The "Max Height of Swing in Circular Motion" is directly proportional to the period of the swing. In summary, the mass is attached to a string that is whirled around a horizontal circle. For instance, the speed of the ball going around the circle is given by distance divided by time. In uniform circular motion, this force is The time for projectile motion is determined completely by the vertical motion. Definition of Vertical Circular Motion. For uniform circular motion, the acceleration is the centripetal acceleration:. Sep 14, 2023 · Vertical Circular Motion | Minimum Velocity To Complete a Circle | Complete Circular Motion JEE |Vertical Circular Motion | Minimum Velocity To Complete a Ci Jul 12, 2024 · Hint:In a vertical circular motion, the motion is considered to be non-uniform because of gravitation force, the velocity and tension of the object will differ in magnitude at different directions. Examples of circular motion 1. H. A 2. v = d s /dt. Communication satellite and its uses. r !. 1 12. 2: Determining the Equations of Motion for a Block and a Spring. Jul 20, 2022 · Example 6. A body cools from 80 o C to 70 o C in 5 minutes and to 62 o C in the next 5 minutes. From figure, cosθ = (r – h) ⁄ r 3 days ago · Banking circular motion Centripetal Force. (b) We can find the final horizontal and vertical velocities v x v x and v y v y with the use of the result from (a). 96 s in the air. Find the speed of the object at various positions around the circle by using conservation of energy principles. Thus, any projectile that has an initial vertical velocity of 21. ! Ex. 79 s in the air. ω = lim ∆t→0 (∆θ/∆t) = dθ/dt. At the top (y=down) ΣF r = N + mg = ma r = m v 2 /r N = m v 2 /r - mg. We are going to assume that the car "slides" along the track …. Apart from angular velocity and angular speed, a particle in circular motion also possesses linear velocity and corresponding linear speed. If a body of mass m is moving with speed v along a circle of radius r, the magnitude of centripetal force is, \[Fc = \frac{mv^{2}}{r}\] A particle is projected with velocity √ 3 g L at point A (lowest point of the circle) in the vertical plane. Q 3. Give today and help us reach more students. At time . One of the most important examples of periodic motion is simple harmonic motion (SHM), in which some physical quantity varies sinusoidally. The second curve has the same v, but a larger F c produces a smaller r′. Equation (5) give s optimum speed of vehicle moving along curved banked road. This is the force acting on a body moving in a circular path. 9t 2, find its velocity and acceleration as a function of time. t) with a displacement Δ. This force is known as centripetal force. Jun 8, 2012 · In non-uniform circular motion, the object's velocity is not constant, meaning it is either accelerating or decelerating as it moves around the circle. The maximum acceleration occurs at the extreme positions, and its value is given by amax = ω²A. 5t-4. 0kg is whirled round in a vertical circle of radius 2. Jul 20, 2022 · Geometric Derivation of the Velocity for Circular Motion. 3 m/s and lands 20. Nov 22, 2015 · Minimum velocity at the top of a vertical circular Motion for JEE and NEET Physics in 4 Minutes is done here in this video. If we wanted to calculate the minimum or critical velocity needed for the block to just be able to pass through the top of the circle without the rope sagging then we would start by letting the tension in the rope approaches zero. In vertical direction, Normal force is balanced with weight. Determine (a) the velocity vector, and (b) the acceleration vector. The object’s maximum speed occurs as it passes through equilibrium. r (t + Δ. The spring can be compressed or extended. Formulas used: (d) The mass now begins to accelerate in the positive x-direction, reaching a positive maximum velocity at x = 0 x = 0. The tension in the string causes a centripetal force that balances the weight of the mass. The formula for tangential acceleration is a = Ar, where See full list on ocw. . Derive an expression for the kinetic energy of a rotating body with uniform angular velocity. A rotating body feels an attraction towards the centre of rotation along the radius of the circular path. 45m/s. This free textbook is an OpenStax resource written to increase student access to high-quality, peer-reviewed learning materials. We also discuss how to find the min speed/critical speed for an object moving in a ci Jan 22, 2019 · For driven motion, there is no velocity too small ( or too large) for the motion to be circular. Oct 12, 2008 · To calculate the velocity in circular motion, you can use the formula v = √(T/mr) where T is the tension, m is the mass, and r is the radius. This means that as the period increases, the max height also increases. m (v 2 /r) = mg. Solution for (b) NEET. Select the correct option. Figure 6. This is because the object's velocity at the top of the circle is zero, and any further increase in the angle would result in the object moving in a downward direction. Q 4. Figure 3 shows the basic relationship between uniform circular motion and simple harmonic motion. In summary, y(x, t) = Asin(kx − ωt + ϕ) models a wave moving in the positive x -direction and y(x, t) = Asin(kx + ωt + ϕ) models a wave moving in the negative x -direction. "It refers to an acceleration that acts on the body in circular motion, whose direction is always towards the centre of the path. This downwards acceleration is provided by the combination of gravity and whatever force the string or the rod provides. Say the time required to reach this maximum height is t max. Where: – Vx0 = horizontal component of initial velocity. If you complain that the wheel is slightly unbalanced due to the presence of the bug, add a second bug positioned opposite the first. t , the particle moves to the position . 5. Displacement vector for May 27, 2020 · In this video we discuss full concept of Vertical circular motion Which Contain Definition Concept,Derivation For Tension and Velocity. edu The time for projectile motion is completely determined by the vertical motion. mit. ) This equation can also be written in a more generalized fashion as F D = b v n, F D = b v n, where b is a constant equivalent to 0. What is the relation between velocity and radius in circular motion? The velocity in circular motion is directly proportional to the radius. Velocity is defined by speed and direction, so although an object&#x27;s speed is constant, its direction changes constantly as it moves The red-triangular marker, along the vertical meter stick on the left, has been placed at height of the loop's diameter. If the string is under tension, the force of tension will always be towards the center of the circle. So any projectile that has an initial vertical velocity of 14. T – m g cosθ = m v 2 ⁄ r. Sep 12, 2022 · Example 15. 0 m above its starting altitude spends 3. What is circular motion? Circular motion refers to the movement of an object along a circular path. In the case we are discussing here, velocity of the body is different at different points. T = m g cosθ + m v 2 ⁄ r. Nov 21, 2023 · The formula for normal (i. In the above graph, The velocity of the body changes from A to B in time t at a uniform rate. already dealt with uniform circular motion, it is sometimes easier to understand SHM using this idea of a reference circle. Given L is radius of circle. Along the y-axis: uniform acceleration, responsible for the vertical (downwards) motion of the particle. dr hm yi gh cg jm rf og ml he