The force can be calculated by simply rearranging Sep 12, 2022 · The gravitational force supplies the centripetal acceleration. (b) Nonuniform circular motion: An angular acceleration produces an inward centripetal acceleration that is changing in magnitude, plus a tangential acceleration a t. Step 3: Finally, the centripetal acceleration of the moving body will be displayed in the output field. Thus, the magnitude of centripetal force Fc F c is. A pendulum consists of a ball with a mass of 0. A minimum coefficient of friction is needed, or the car will move in a larger-radius curve and leave the roadway. If velocity and Centripetal acceleration is given, Radius is calculated as. Angular acceleration on the other hand is the change in the angular velocity with respect to time. 98 × 1024 kg, G=6. The ball is released from rest at some initial angle from vertical and freely swings back and forth. It has centripetal acceleration directed toward the center of Earth. Jan 18, 2022 · Centripetal Force vs Centripetal Acceleration Formula. ac = v2/r. There is a close connection between simple harmonic motion and uniform circular motion. a c = acceleration, centripetal, m/s 2. Invoking Newton's second law, we can pass from the centripetal force equation to find the Jan 16, 2020 · Its bob of mass 100 g performs a uniform circular motion in a horizontal plane in a circle of radius 30 cm. Step 2: Now click the button “Calculate the Unknown” to get the result. 25. Earth’s gravity is the only force acting, so Newton’s second law gives When an object moves in a circular path, it is constantly accelerating because its velocity is constantly changing direction. This is called the centripetal acceleration and is perpendicular to the direction of the linear speed. Find a) the angle made by the string with the vertical b) the tension in the string c) the period d) the speed of the bob e) centripetal acceleration of the bob f) centripetal and centrifugal force acting on the bob. If we know the angular velocity ω ω, then we can use. You must have seen various examples of centripetal acceleration in your everyday life. Therefore, you can rewrite the acceleration formula as. Sep 12, 2022 · Figure 10. Since the velocity vector (the direction) of a body changes when moved in a circle - there is an acceleration. ac = a c = v2 r v 2 r ; ac = rω2. ac = v2 r. 5 kg attached to the ceiling by a 3. 3). F_c=m\frac {v_t^2} {r} F c = m rvt2. where v is the velocity of the object, directed along a tangent line to the curve at any instant. 1) (6. v = √acR v = a c R. Where: a = Centripetal acceleration and is directed The direction of a centripetal force is toward the center of curvature, the same as the direction of centripetal acceleration. The centripetal acceleration ac has a magnitude equal to the square of the body’s speed v along the curve divided by the distance r from the centre of the circle to the moving body; that is, ac = v2 / r. Centripetal force is perpendicular to velocity and causes uniform circular motion. Also called radial acceleration. There is no tangential acceleration. We can model an atom like a circle, with its nucleus being its center. ac = v *ω. The centripetal-acceleration equation simplifies to. 4. ”. r r r is the curvature radius. 12). F = ma to Fc = mac. 3 years ago. Mar 26, 2016 · If an object is moving in uniform circular motion at speed v and radius r, you can find the magnitude of the centripetal acceleration with the following equation: Because force equals mass times acceleration, F = ma, and because centripetal acceleration is equal to v2 / r, you can determine the magnitude of the centripetal force needed to keep What I want to do in this video is a calculus proof of the famous centripetal acceleration formula that tells us the magnitude of centripetal acceleration, the actual direction will change it's always going to be pointing inwards, but the magnitude of centripetal acceleration is equal to the magnitude of the velocity-squared divided by the radius I want to be very clear, this is a scalar Feb 27, 2022 · The formula for centripetal force is given as: F c = mv 2 /r. is directed toward the center of a circle (center seeking) How Centripetal Acceleration Calculator works. It moves around a circular path of the radius (r) 80 cm. The formula for centripetal force is given by. In today's laboratory exercise the centripetal acceleration equation (1) will be Centripetal Acceleration: “Centripetal velocity represents the speed of the object revolving in a circular path” You can calculate the centripetal acceleration by following the centripetal acceleration formula below: $$ a = \frac{v^{2}}{r} $$ Derivation of Centripetal Acceleration: Apr 1, 2022 · There is a close connection between simple harmonic motion and uniform circular motion. This acceleration is named the centripetal acceleration - and can be expressed as. Centripetal force formula is given by the mass, velocity and the radius. This is often written in the more familiar form. Sep 12, 2022 · The direction of the centripetal acceleration is toward the center of the circle. This connection is widely taught and included in standard textbooks. We call the acceleration of an object moving in uniform circular motion (resulting from a net external force) the centripetal acceleration ( ); centripetal means “toward the center” or “center seeking. is not a particular force, but the name given to whatever force or combination of forces is responsible for a centripetal acceleration. This describes how an object rotates faster and faster or slower and slower. Jul 3, 2024 · In the case of circular motion, the relevant acceleration is centripetal acceleration, which always points toward the center of the circle. Jul 16, 2020 · By using the expressions for centripetal acceleration ac from ac = v2 r; ac = rω2, we get two expressions for the centripetal force Fc in terms of mass, velocity, angular velocity, and radius of curvature: Fc = mv2 r; Fc = mrω2. Thus Fc = mv2 r = (900. Step 1: The object covers an arc length in a time interval , so . Figure 1. But I had read that with the increase in radius, there is increase in centripetal acceleration. R = v2 ac R = v 2 a c. According to Newton’s second law of motion, net force is mass times acceleration: F net = m a. Thus, the magnitude of centripetal force ( F c) is given as F c = m a c. 3 days ago · Putting v = rω, we get, Centripetal acceleration, a(c) = ω2r = v2 r a ( c) = ω 2 r = v 2 r. The object must therefore be accelerating. Centripetal force ( F c F c) is the force that keeps an object moving in a circular path. 1 meters/second. Nothing to it. It is directed towards the center of the ellipse and its magnitude is given by the equation a = v^2/r, where v is the velocity of the object and r is the radius of the circle at that point. where: Fc F c is centripetal force, m m is mass, v v is velocity, and r r is the radius of the path of motion. We call the acceleration of an object moving in uniform circular motion (resulting from a net external force) the centripetal acceleration ( ac ); centripetal means “toward the center” or “center seeking. Where the component, a (t) = r x α. Period (T ‍ ) Time needed for one revolution. Example 18. The result of doing this yields a centripetal acceleration equation of the form. For example, any point on a propeller spinning at a constant rate is executing uniform circular motion. A centripetal force ( Fc ) is the force that makes a moving object change direction. 00m / s)2 (500. 3. e. Centripetal force and acceleration are always directed towards the centre of the circle. Fc = mv2 r and Fc = mac. Where: ac = is the centripetal acceleration [m/s2] v = refers to tangential velocity [m/s]. The centripetal acceleration is caused by a Jun 6, 2024 · The acceleration is directed radially toward the centre of the circle. Nov 21, 2023 · The centripetal acceleration equation can be derived from a circular motion as the one displayed in figure 3. Example 2: A ball has a mass of 0. 1–3 Here, we exploit this connection to simultaneously derive two results from introductory mechanics: the period of a mass- spring system and the centripetal acceleration formula. Thus we have several alternative forms for the magnitude of the centripetal acceleration. Roller coaster physics, gravitational potential energy, and centripetal acceleration. 1) F c = m a c. The directions of the velocity of an object at two different points are shown, and the change in velocity Δv is seen to Centripetal Acceleration and Force Equations. Q. Figure 10. The formula used to find out the centripetal acceleration of a given object can be calculated as the tangential velocity squared over the radius or as follows: ac = v2/r. According to Newton’s second law of motion, net force is mass times acceleration: net F = ma. The centripetal ('center-seeking') acceleration is the motion inwards towards the center of a circle. If Radius and Centripetal acceleration is given, velocity is calculated as. Feb 20, 2022 · For uniform circular motion, the acceleration is the centripetal acceleration - a = ac a = a c. 9 The frictional force supplies the centripetal force and is numerically equal to it. As we know that resultant acceleration of the particle at P is given by, a = ω x v + r x α. 0 m) = 1125 N. In summary, the equation Mg=[1600∏2m(L+a)(1/t2)]- b represents an experiment to verify centripetal acceleration using a plastic tube, sticky tape, and slotted weight. Because the centripetal force. Jun 14, 2023 · Derivation of Centripetal Acceleration. The free body diagram of the ball when the pendulum makes an angle of 45 ° from the vertical Mar 26, 2016 · Centripetal acceleration is given by the following equation: where v is the velocity and r is the radius. F_c = m * a_c. 00 m massless rope. The derivation of centripetal acceleration is provided below. Centripetal Acceleration Derivation. Step 2: The arc length can also be described in terms of the angle it subtends at the center of the circle: . . An astronaut on board the satellite may have a different point of view. The rotation around a fixed axis of a three-dimensional body involves the circular motion Aug 11, 2021 · The centripetal force causing the car to turn in a circular path is due to friction between the tires and the road. The unit of centripetal acceleration is m/s2. So there should be centripetal acceleration towards the center. F = mac = mv2 r F = m a c = m v 2 r. Otherwise either gravitational or centripetal acceleration will dominate and the probe will either fall to a lower Physics questions and answers. Click the “Calculate” button. The formula for the centripetal force is: F = \frac {m\cdot v^2} {r} F=rm⋅v2. 2) You may use whichever expression for centripetal force is more convenient. The first is that in Equation (6. The acceleration is the centripetal acceleration (peto – I desire). For uniform circular motion, the acceleration is the centripetal acceleration ( a c). So because we chose the centripetal direction, we're gonna be able to replace the centripetal acceleration with the formula for centripetal acceleration. May 5, 2015 · A probe in an orbit further out than geostationary will rotate more slowly because of the drop off in gravitational acceleration and a probe in an orbit closer to the earth will rotate more quickly because gravity is stronger. a c = centripetal acceleration (m/s 2, ft/s 2) Centripetal acceleration (a c ‍ ) Acceleration pointed towards the center of a curved path and perpendicular to the object’s velocity. a_c=\frac {v^2} {r};a_c=r\omega^2\\ ac=rv2;ac=rω2. 2. a = Fnet m a = F net m. Rearrange this formula to obtain the expression for velocity. r is the radius of the circular path. Calculate the period, frequency, angular speed and linear speed and centripetal acceleration acting on the mass. For uniform circular motion, the acceleration is the centripetal acceleration:. Where m is the of the body. The term rev/min stands for revolutions per minute. This agreement is approximate because the Moon’s orbit is slightly elliptical, and Earth is not stationary (rather the Earth-Moon system rotates about its center of mass, which is located some 1700 km Solution: Radius of the circular path = 4 km = 4 × 1000 m = 4000 m. This implies that for a given mass and velocity, a large centripetal force causes a small radius of curvature—that is, a tight curve. Input the mass of the rotating object (in kilograms) in the respective field. Where: F F F is the centripetal force; m m m is the mass; v v v is the speed; and. In the first scenario, ac is inversely proportional to the radius, whereas, in the second scenario, ac is directly proportional to the radius of the circular path. Previously published Jul 31, 2016 · 3. 2. F net = m a. Mar 9, 2017 · Centripetal Acceleration Changing the direction of velocity leads to the existence of acceleration called the centripetal acceleration ( a ) which is the acceleration acquired by an object moving in a circular path due to a continuous change in the direction of its velocity . Centripetal acceleration points towards the center of a circular path and is due to a centripetal force causing the circular motion. Where m is mass (Kg) and Fc is the centripetal force (N). A force that keeps an object moving in a circular path is a centripetal force. F = m a. Calculate the centripetal force given that it completes 1 round every 3 seconds. Because r is given, we can use the second expression in the equation. By converting this to radians per second, we obtain the angular velocity ω. fc= m v2 / r. Sep 8, 2013 · The centripetal acceleration of an ellipse is the acceleration experienced by an object moving in a circular path on the surface of an ellipse. The force in the opposite direction, pointing outward from the center of rotation, is called centrifugal force. Figure 6. In our case, we’ve been given the radius 𝑟, the speed 𝑣, and the mass of the car 𝑚. The acceleration is equal to the square of the velocity, divided by the radius of the circular path. Calculate the centripetal acceleration of the ball if its mass is doubled? So in other words, we're gonna write down that the centripetal acceleration is gonna be equal to the net centripetal force exerted on the mass that's going around in that circle. r = is the turning radius [m]. Centripetal Acceleration defines the distance that is covered and the direction of the movement. The centripetal acceleration in a uniform circular motion is m/s 2: Period of rotation calculation; T = t/N T = t/ T = Frequency of rotation calculation; f = N/t f = / f = Angular displacement calculation; φ = N × 2 × π φ = × 2 × φ = Angular velocity calculation; ω = N × 2 × π/t ω = × 2 × / ω = / ω = Tangential velocity calculation Consider an object moving in a circle with radius at a constant speed – i. (6. We solve this for μs, noting that mass Step 1: Identify and list the given values such as mass, radius, and centripetal force of the object. The directions of the velocity of an object at two different points are shown, and the change in velocity Δv is seen to Centripetal Acceleration Formula. to calculate the centripetal acceleration. The directions of the velocity of an object at two different points are shown, and the change in velocity Δv is seen to Since the velocity vector (the direction) of a body changes when moved in a circle - there is an acceleration. Velocity = 10 km/sec = 10 × 1000 m/sec = 10,000 m/sec. 67x10-11m3⋅kg−1⋅s−2, use the centripetal force and centripetal acceleration formula to calculate the speed of satellite use the value of r you measured in step 3. The larger the F c, the smaller the radius of curvature r and the sharper the curve. The We proved that this centrally directed acceleration, called centripetal acceleration, is given by the formula. Centripetal (radial) acceleration is the acceleration that causes an object to move along a circular path, or turn. The formula for finding centripetal acceleration is given as: a c = v 2 /r. 3) (5. Another variation of the equation for centripetal acceleration is one that comes from combining two centripetal force equations. , at 90 degrees), it cannot do any work on the object horizontally because none of the net force component is in the same direction as the object's motion. Derive an expression for centripetal acceleration in uniform circular motion. That is what we see from Newton's 2nd law. Sudhanwa Garud. Now we have a relationship between centripetal force and the coefficient of friction. ; F c = m r ω 2. Whereas ordinary (tangential) acceleration points along (or opposite to) an object's direction of motion, centripetal acceleration points radially inward from the object's position, making a right angle with the object's velocity vector. Apr 10, 2024 · 1. Substituting the expression for ac a c into the above equation, we get: F c = m× v2 r F c = m × v 2 r. Strategy. This acceleration is what we refer to as centripetal acceleration because it points towards the center of the circle. The formula for centripetal acceleration: \(a_c=\frac{v^2}{r}\) Any net force causing uniform circular motion is called a centripetal force. v is the linear velocity of the body. m is the mass of the body; v is the linear velocity of the body; r is the radius of the circular path; Read More: Types of Generators and A ball of mass m is attached with the string of length R, rotating in a circular motion, with instantaneous velocity v and centripetal acceleration a. Jul 12, 2015 · $\begingroup$ Notice that after one full turn the change in position is also zero. Previously published derivations of the centripetal Aug 16, 2022 · Centripetal force and centripetal acceleration equation. a c = v 2 / r = ω 2 r = (2 π n rps ) 2 r = (2 π n rpm / 60) 2 r (π n rpm / 30) 2 r (1) where . When a force ( F ) acts on a body of mass ( m ) moving at Mar 7, 2022 · The radius (r) of this circle is equal to the mass (m) times the square of the velocity (v) divided by the centripetal force (F), or r = mv^2/F. where F_c is the centripetal force, and m is the mass of the object. The magnitude of this force is determined by the equation: F c = m×ac F c = m × a c. The centripetal force keeps a body constantly moving with the same velocity in a curved path. 8 meters/second squared, and the maximum speed at which these slot cars can run without flying off the track is: V = 1. Where. The direction of a centripetal force is toward the center of curvature, the same as the direction of centripetal acceleration. For a rotating body, the centripetal and centrifugal forces are equal in magnitude, but opposite in direction. Mar 12, 2024 · The acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass. Previously published derivations of the centripetal Jan 25, 2023 · Ans: According to Newton’s second law of motion, the net force is mass times acceleration: F n e t = m a. The centripetal acceleration of the Moon found in (b) differs by less than 1% from the acceleration due to Earth’s gravity found in (a). The formula of centripetal force is given by \(F_c=\frac{mv^2}{r}\) Where. 𝑚 is the mass of the object. In the previous example, if the mass of the object is 2 kilograms, the centripetal force can Centripetal acceleration ac a c is the acceleration experienced while in uniform circular motion. It is perpendicular to the linear velocity v v and has the magnitude. We use this and the magnitude of the centripetal acceleration to find the total acceleration. The force of a moving object can be Dec 9, 2019 · Centripetal force is the force on a body moving in a circle that points inward toward the point around which the object moves. Consider a satellite of mass m in a circular orbit about Earth at distance \(r\) from the center of Earth (Figure \(\PageIndex{1}\)). ac = v2 R a c = v 2 R. The procedure to use the centripetal acceleration calculator is as follows: Step 1: Enter the velocity, radius and x for the unknown value in the respective input field. 1: The frictional force supplies the centripetal force and is numerically equal to it. If velocity and radius is given, Centripetal acceleration is calculated as. By using the expressions for centripetal acceleration ac a c from ac = v2 r; ac = rω2 a c = v 2 r; a c = r ω 2, we get two expressions for the centripetal The centripetal acceleration of the Moon found in (b) differs by less than 1% from the acceleration due to Earth’s gravity found in (a). ac = rω2. Jun 16, 2022 · The centripetal acceleration formula a = ω^2r is derived by substituting v = ωr into the original formula a = v^2/r. Given the value of Mass of earth, Me=5. It always points toward the center of rotation. From Newton’s second law F = m ⋅ a F = m ⋅ a, we can see that centripetal acceleration is: Thus the centripetal force in this situation is. We call the acceleration of an object moving in uniform circular motion (resulting from a net external force) the centripetal acceleration ( [latex]\boldsymbol {a_ {\textbf {c}}} [/latex]); centripetal means “toward the center” or “center seeking. The directions of the velocity of an object at two different points are shown, and the change in velocity Δv is seen to In summary, the physics of roller coasters (in general) is a combination of gravitational potential energy converted into kinetic energy (high speed), and using this speed to create centripetal acceleration around different portions of the track. is directed tangentially to the object's motion (i. 31} and evaluating it at t = 2. Jan 21, 2024 · The formula for centripetal acceleration for a body moving in a circular path is given by. Example 3 Dec 28, 2020 · Centripetal Force, Mathematically. Where fc = centripetal force; m=mass; v= velocity; r= radius. Solve the equation for the centripetal acceleration for the radius and then insert these quantities in it. uniform circular motion. In equation form, Newton’s second law of motion is. Therefore,v 2 = F c r/m. Step 3: Equating the two expressions for gives , which simplifies to . Solution: The equation for centripetal force is as follows: Fc = mv2 r (5. ; a c = r ω 2. SI units are m s 2 ‍ . The maximum centripetal acceleration we have is a = 3. So, we’re ready to plug in and solve for 𝐹. In the question, mass of the stone (m), radius of the circle (r), and total centripetal force F c = m a c. Follow these steps: Enter the centripetal force (in Newtons) in the designated field. Doing this changes the equation of. 0 s. 1: (a) Uniform circular motion: The centripetal acceleration a c has its vector inward toward the axis of rotation. Any object that is moving in a circle and has an acceleration vector pointed towards the centre of that circle is known as Centripetal acceleration. Uniform circular motion is a specific type of motion in which an object travels in a circle with a constant speed. Centripetal means it acts towards the centre of the circular path. The simulator you are using seems to adjust the force. Using the first expression for Fc from the equation. Consider a satellite of mass m in a circular orbit about Earth at distance r from the center of Earth (Figure 13. acts at right angles to the velocity at any instant. This agreement is approximate because the Moon’s orbit is slightly elliptical, and Earth is not stationary (rather the Earth-Moon system rotates about its center of mass, which is located some 1700 km Centripetal acceleration is defined as the property of the motion of an object traversing a circular path. 1. The frictional force supplies the centripetal force and is numerically equal to it. In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular arc. Now you want to decrease the radius of the circle, so someone should apply more centripetal acceleration in order to decrease your radius. a = v 2 / r r = v 2 / a v = (ar) 1/2. If an object of mass m is rotating with constant speed v about a circle of radius r, then the centripetal acceleration on the object has the magnitude: a = v2/r (1) This equation is derived in Randall Knight, Physics for Scientists and Engineers, Section 7. The angular velocity ω can be calculated using the formula ω = 2π/T, where T is the The centripetal force is exerted at right angles to the velocity as well as along the radius of the circular path towards the center. Suppose you are moving in circle of radius r r. The directions of the velocity of an object at two different points are shown Jul 20, 2022 · The magnitude of the radial component of the acceleration can be expressed in several equivalent forms since both the magnitudes of the velocity and angular velocity are related by v = rω . 0kg)(25. ω = is the angular velocity that is May 31, 2021 · If you change the mass, then either the acceleration or the centripetal force must change as well (or both). This formula allows us to calculate the centripetal acceleration of a pendulum based on its angular velocity and the length of the pendulum. 𝑣 is the velocity of the object. And it’s equal to the mass of the object times its speed squared over the radius of the circle it moves in. A 1000 kg mass travels in a circle of radius 5 m and completes 4 revolutions in 2 seconds. Centripetal Acceleration Formula. It can be uniform, with a constant rate of rotation and constant tangential speed, or non-uniform with a changing rate of rotation. Sep 17, 2023 · Radial or Centripetal Force. 3) F c = m v 2 r. Evaluate centripetal and tangential acceleration in nonuniform circular motion, and find the total acceleration vector. We find the magnitude of the tangential acceleration by taking the derivative with respect to time of |v(t)| using Equation \ref{4. Causes an object to change its direction and not its speed along a circular pathway. Apr 1, 2022 · Here, we exploit this connection to simultaneously derive two results from introductory mechanics: the period of a mass- spring system and the centripetal acceleration formula. (Note that you do not need the mass of satellite). 1 10. The calculator will instantly compute and display the centripetal acceleration (in meters per second squared) based on the provided values. Example 2. 5. Possible Answers: Correct answer: Explanation: The formula for centripetal force is: Where is the mass of the object, is its velocity, and is the radius of the circle made by the motion of the object around the center. By Newton's first law, if there is acceleration, there must be a net force. The constants a and b account for the radius of the tape and static friction in the tube, respectively. m/s 2. The mathematical explanation of centripetal acceleration was first provided by Christian Huygens in the year 1659. a c is the centripetal acceleration. ac = v2 r a c = v 2 r. (5. Centripetal acceleration has units of metre per second squared. Substitute 500 N for F c, 25 m for r and 200 kg for m into the formula to find the velocity. Earth’s gravity is the only force acting, so Newton’s second law gives We proved that this centrally directed acceleration, called centripetal acceleration, is given by the formula. By using the expressions for centripetal acceleration ac a c from ac = v2 r; ac = rω2, a c = v 2 r; a c = r ω 2, we get two expressions for the centripetal force Fc F c in terms of mass, velocity, angular velocity, and radius of curvature: Fc = m F c = m v2 r v 2 r ; Fc = mrω2. {Fc = mv2 r Fc = mrω2, mv2 r =μsmg { F c = m v 2 r F c = m r ω 2, m v 2 r = μ s m g. What we are interested in here really the average value of the instantaneous acceleration, but to get it requires calculus (or at least the machinery of limits), which the OP doesn't want. a c = r ω 2. Centripetal acceleration and centripetal force. The centripetal force formula is mathematically expressed as 𝐹꜀ = 𝑚 x (𝑣²/𝑟) 𝐹꜀ is the centripetal force. Linear velocity is easy enough to tie to angular velocity because. A body moving in a circle experiences a continual change in direction, which causes a change in velocity, which results in acceleration. Jun 24, 2022 · The relationship between centripetal acceleration and centripetal force is given by the formula: See also How to Find Velocity of Seismic Waves: A Comprehensive Guide. In fact, because of its The satellite, being in a circular orbit, is accelerating towards the centre of the circle, and all is as expected - \( F = ma\). Then the result will be: a = \(\frac{v^{2}}{r}\) This means the centripetal force acting on the motorcycle remains unchanged and so does its radius. Fc = mac. Therefore, centripetal acceleration. a = a c. F c = f = μsN = μsmg. The acceleration of an object moving along a circular path is referred to as centripetal acceleration. Here, we exploit this connection to simultaneously derive two results from introductory mechanics: the period of a mass- spring system and the centripetal acceleration formula. He is at a constant distance from Earth, not 6. So is the centripetal acceleration directly or inversely proportional to the radius of the circular path, since ac=v^2/r=w^2*r. We must be aware of the fact that this formula is something that is similar to the conventional formula of the force. 2 kg. mi tq st vt ry mb yj dg xs nu