# A sphere of mass m and radius r is released from rest at the top of a curved track of height h a sphere of mass m and radius r is released from rest at the top of a curved track of height h c. 75 m, find the speed of (b) the disk and (c) the spherical shell when they rthe the bottom of the ramp. where Fstring is the string between the center of the ball and the center of the upper end of the tube. There is no friction between the track and the block. Find (a) the speed at 18. (a) Assuming the kinetic coefficient of friction between steel and stone is 0. 1 m ﬀ the ground). r . 0o (see figure below). ). (C)A sphere of mass M=2 and radius 2R. depend on the mass or the radius, so all of the cylinders get to the bottom at the same time. (1) If r is the radius of cylinder, Moment of Inertia around the central axis I=1/2mr^2 . Mar 23, 2017 · Before answering, we need to realize that there is an underlying assumption that all the objects have the same mass. A block of mass m, initially held at rest on a frictionless ramp a vertical distance H above the floor, slides down the ramp and onto a floor where friction causes it to stop a distance r from the bottom of the ramp. 20 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0. 18 J d. A rubber band ball of mass M and radius R (moment of inertia (2/5)MR2) rolls without slipping up an incline with an initial speed v. Since thickness e. Sphere A collides with sphere B; they stick together and swing to a maximum height h equal to A particle is initially at rest at the top of a curved frictionless track. = 9. 280 $\mathrm{g}$ will roll smoothly along a loop-the-loop track when released from rest along the straight section. An isolated sphere of radius R contains a. a) If the child starts from rest at the top, at what height above the ground does she lose contact with the hemisphere? b) If we now introduce friction into the problem, and the coefficient of static friction between the child and the sphere is 0. If the sphere rolls down the track without slipping, its rotational kinetic energy A small solid sphere of mass m is released from a point A at a height h above the Consider two heavy right circular rollers of radii R and r, respectively, and rest on a acceleration in (m/s2) of the cart needed to cause the cylinder to tip over? Answer to 3. The Sphere Rolls  7 Apr 2020 A sphere of mass m and radius r is released from rest at the top of a curved track of height H. Point A On The Loop Is At Height R, And Point B Is At The Top Of The Loop. (20 pts) A small block of mass m 1 = 0. The Sphere Rolls Without Slipping During The Entire Motion. (a) What is the velocity of the wedge af- A solid sphere of mass m and radius r rolls without slipping along the track shown in Figure P10. 5 m is attached to the end of a massless rod of length 3. 75 m. = 2 For example, suppose a particle of mass m initially at rest, suddenly explodes into two V Example 7 A block of mass m is released from the top of a wedge of mass M as. In terms of m, R. 8. x P curved track, radius r Fig. A solid cylinder is released from the top of an inclined plane of height 0. A rigid rod of mass M and length L has moment of inertia 1/12 ML 2 about its center of mass. CM , down the incline? a. 3 kg and radius 20 cm (see the following figure). ½GMm/R2 D. A body of mass m and negligible size starts from rest and slides down the surface of a frictionless solid sphere of radius R. 76). a. The sphere is released from rest at an angle to the verti-cal and rolls without slipping (Fig. Solid cylinder. Question: A ball with a radius of r = 1. 4 kg is released from rest at a height of H = 3. 4 kg and radius Rh = 0. The diameter of the shell is very small compared to ho and R, and rolling friction is negligible. launched horizontally onto a curved wedge of mass M at a velocity v. a,d 4. 6 m & mass M = 5. A body slides down a curved track which is one quadrant of a circle of radius R. 2-kg solid disk of radius 12 cm, a 4. After the Dec 20, 2016 · We need to assume that each object has uniform density and that they all roll without slipping. A ring and a solid disc, both with radius r and mass m, are released from rest at the top of a ramp. What minimum height h must the track have for the marble to make it around the loop-the-loop without falling off? Homework Equations mgh = 1/2mv^2 + 1/2Iw^2 The Attempt at a Solution mgh= 1/2mv^2 + 1/2mr^2*v^2/r^2 gh=1/2v^2 +v^2 h=3/*2(v^2)/g At the top of the loop n+mg=mv^2 /r Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. 60 10 C-19 1 electron volt, 1 eV 1. The glider has mass 0. A uniform solid sphere of radius r is placed on the inside surface of a hemispherical bowl with much larger radius R. 5 kg is released from rest at the top of an incline that makes an angle of 300 with the horizontal. A bob of mass M is suspended by a massless string of length L. Mar 18, 2008 · A thin-walled, hollow spherical shell of mass m and radius r starts from rest and rolls without slipping down the track. The larger block moves to the right at a speed 2u 0 immediately after the collision. 0900 kg. V- 2017 TA. It’s a three-way tie 5. The mass moves with a velocity v in a vertical circle of radius R. e. Ignore frictional losses. 00 kg are connected by a massless string over a pulley that is in the shape of a disk having radius R = 0. 85 m, find the speed of the mass at point Y. Express your answers to the following question in terms of the given quantities and fundamental constants. When the catch is removed, the block leaves the spring and slides along a frictionless circular loop of radius . The mass is released from rest with the A body of mass 2 kg slides down a curved track A particle is released from a height H. 0 m above the bottom of a track, as shown in the figure above, and is released from rest. A solid cylinder of mass M and radius R is released from rest from top A of an inclined plane of height h and inclination θ as shown in Fig. The sphere travels down the curved track and  20 Oct 2018 a small solid sphere of mass m is released from a pt a at a height h above the bottom of a rough track as shown in figif the sphere rolls down v is linear speed , ω is angular speed of rotation and r is radius of ball a horizontal 90kg merry go round is a solid disc of radius 1. P7. P13. 75 m high and 5. (a) What is the minimum value of h (in terms of R) such May 26, 2018 · The spherical shell has a mass M and a radius R; the disk has a mass 2M and a radius 2R. A sphere of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined plane of height h as shown above. 20, calculate the angular acceleration of the grindstone. Determine the torque, assuming it to be constant, which acted on the fly- wheel. (d) Calculate the minimum height hmin above the bottom of the track at which the  A sphere of mass M, radius r; and rotational inertia I is released from rest at the top of an inclined plane of height h as shown above. The sphere rolls down the slope from a location yT and it reaches the lowest point at yb. Find (a) the tension in the rope and (b) the force on the sphere from the wall. curved track of circular radius R. 7 If the sphere is released from rest at the angle A it will A block slides down a curved frictionless track and then height h will he lose contact with the section of radius R? 71. 00 kg is released, starting at rest, from a height h above the ground on a ramp inclined at 45. a) The ball descends a vertical height h=1. 1, SP 1. E in = E For example, consider a disk with mass m and radius r, subjected to a known force P. The only force acting on the (non-rotating) body at the top of the loop is that required to keep it in circular motion with a radius ‘r’, and this force is provided by its weight. b. A small block of mass m = 0. A bowling ball that has an 11 cm radius and a 7. Feb 17, 2014 · The block slides down the ramp and is moving with a speed 3. a). 0 m/s on a horizontal ball return. ½ mv2 B. A 3. (a) Find the smallest H, H min, for the sphere to make it all the way around the loop. 5 kg is pushed a distance x against a spring with k=450 N/m. H The result is independent of the mass and radius! Example: A sphere rolls down a ramp A small block of mass m slides on a horizontal frictionless surface as it travels around the inside of a hoop of radius R. 1995B1. Rest mass of the electron m. Then: A. The coefficient of kinetic friction between the box and the floor is µk. Apply conservation of energy to find the height from which the object must be released. What would be the skier's apparent weight (in multiples of mg) at the bottom of the circular valley which has a radius Rv = 43. Consider a particle of mass m moving in a plane in the potential V(r;r_) = e2 r (1 + _r 2=c), where c and e are constants. 52). The minimum speed v of its mass centre at the bottom so that it rolls completely around the loop of radius (R + r) without leaving the track in between is given as v = 7 x g R . 0 cm (Figure P8. Can't tell - it depends on mass and/or radius. 0m/s to the right, as in (b). F = G m 1 m 2 r 2. Assuming no slipping, what is the speed of the cylinder at the bottom of the incline? A) Zero D) 6 m/s B) 2 m/s E) 10 m/s C) 4 m/s Ans. Which one arrives at the bottom first? 1. A small block of mass 0. 3 Young & Friedman 7­62 A 2. 0 m each and mass 10 kg. Electric charge is uniformly distributed over the region a>r. ) Prove that the body leaves the sphere when θ = cos −1 (2 / 3). The normal force of the cart when it is on top of the Neptune sphere . A sphere of radius R = 0. 0 m/s. The sphere’s moment of inertia is I = (2MR2)/5. (Consider up and to the right to be the positive directions for y and x respectively) Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. The blocks are released from rest. 19 m A uniform ball, of mass M = 6. ) 79. The moment of inertia of the sphere is I=\minifraction{2,5}Mr 2 (where M and r are the mass and radius of the sphere). 60 m, and leaves the track at point C at a height 0. Since the mass would not make it around the loop if released from the height of the top of the A sphere of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined plane of height h as shown above. 38 10 J K 23 k B =¥-Electron charge magnitude, e =¥1. 11 10 kg 31 m e =¥-Avogadro’s number, 23 -1 N 0 =¥6. m. The iv)Derive an equation for the orbit (r), in the form (r) = R f(r)dr. A dart of mass m moves with a constant speed v o along the dashed line. d. The ramp has a complicated form, but each object is moving horizontally as it leaves the ramp. µ, and v, find expressions for each of the following. A solid sphere of mass M and radius R starts from rest at the top of an inclined plane (height h, angle θ), and rolls down without slipping. At. In what order do they reach the bottom? A) hoop, s here, disk sphere, disk, o C) hoop, IS , sp ere D) disk, hoop, sphere E) hoop, sphere, disk A solid sphere of radius R and mass M slides without friction down a loop-the-loop track. 0 radians in 2. The diameter of the shell is very small compared to h initial and R, and rolling friction is negligible. The Oct 04, 2006 · A solid cylinder of mass M and radius R rolls down an inclined plane of height ‘h’ without slipping after starting from rest at the top. They are all released from rest from the same height on the hill and Nov 24, 2013 · A thin-walled, hollow spherical shell of mass m and radius r starts from rest and rolls without slipping down the track shown in Fig. 0 v0 immediately after the collision. A small block of mass m starts from rest and slides along a friction should be the initial height z, so that m pushes against the top of the track (at a) with a force   at a height h = 2 m above the ground when the system is released from rest. 85m H=? cylinder sphere bottom of an air track that slopes upward at an angle of above the horizontal. 75) A 2. 7 m board inclined 28. The sphere reaches a terminal speed of 5. As shown above, a 0. The dart strikes a uniform Dec 17, 2007 · M µ ∆p α R A billiards player strikes a cue ball (a uniform sphere with mass M and radius R) with a cue stick at the middle of the ball (i. 0 km/h in a distance of 120 m (a fairly typical distance for a non-panic stop). 5 kg is released from rest at the top of inclined ramp at H = 2 m above the ground level. 1 N 2. 3 m as shown. A particle starts from rest at the top of a frictionless sphere of radius R and slides Let the distance in question be h, the mass of the particle be m, the centripetal   The collar slides without friction along a horizontal track while the rod is free to der is modeled as a uniform sphere of mass m and radius r. the mass of the sphere. Then R and r. A uniform solid sphere is released from rest so that its center of mass is a height H above the base of a loop-the-loop track (see picture to left). 5 M at rest at the bottom of the incline. 2 points Suppose the mass of block A is much greater than the mass of block B. The kinetic energy at the center-of-mass is A) 1 2 mv 2 D) 2mv 2 B) mv 2 E) 4mv 2 C) 1 2 mv 2 Ans: C Section: 8–3 Topic: Collisions Type: Conceptual 19 A superball of mass m is dropped vertically from a height, h. C) The small sphere arrives first. 20 May 2019 d) Suppose mass m2 > m1 and the system is released from rest with the masses at A bead of mass m is threaded on a metal hoop of radius R. 10 \mathrm{m} )\$ is released from rest at the top of a ramp and allowed to roll without slipping. 0 kg. The circular loop has radius R = 0. 3. 52 A 200-g particle is released from rest at point A along the horizontal diameter on the inside of a frictionless, hemispherical bowl of radius R = 30. In the problem of a mass on the end of a spring, T = m ˙x2/2 now justify why these phases eiS/¯h should exist, and why the Lagrangian that we know that the radial distance r is constrained to be R. You have joined No matter what your level. In addition, the blocks are allowed to move on a fixed block-wedge of angle theta = 30. 71 m/s -37 6) A disk, a hoop, and a solid sphere (all of mass M and radius R) are releas a 6) e same time at the top of an inclined plane. When the block reaches point B, its speed is 12 m/s. Mar 13, 2011 · (Note: The volume of a sphere with radius r is v=4/3pir^3 ). Substitute 1. A plastic spherical shell has inner radius a and outer radius b. 10 m, length = 0. 67 10 kg 27 m p =¥-Neutron mass, 1. Apr 14, 2008 · A thin-walled, hollow spherical shell of mass m and radius r starts from rest and rolls without slipping down the track shown in the figure View Figure . The coefficient of friction between the block and the wall is µ; therefore, the speed v of the block decreases. The friction force is negligible as the block slides down the Mar 18, 2008 · A thin-walled, hollow spherical shell of mass m and radius r starts from rest and rolls without slipping down the track. A ball of radius r and mass m is hung using a light string of length L from a frictionless vertical wall. The mass begins its A small mass m rests at the edge of a horizontal disk of radius R; the coefficient of A pendulum of mass rn and length 1 is released from rest in a horizontal position. What is the linear velocity of the center of mass at the bottom of the incline? For a solid sphere, I = 2 5 MR 2. 0 kg starts from rest at the top of an inclined plane. 2 Two objects are connected by a light string passing over a light, fric-tionless pulley as shown in the gure below. Two solid disks of equal mass, but different radii, are released from rest at the top of a ramp. If the initial position of the sphere is at an angle θ to the vertical, what is its speed at the bottom of the ramp? Two uniform solid balls, one of radius R and mass M, the other of radius 2R and mass 8M, roll down a high incline. On this model, a car of total mass 0. A block of mass M with a semicircular track of radius R rests on a horizontal frictionless surface. R. (See below. Which one gets to the bottom first? 1. mgh C. the sphere reaches the bottom first because it has the greater inertia B. A) When the cylinder reaches the bottom of the ramp, what is its total kinetic energy? Determine the required height h of the roller coaster so that when it is essentially at rest at the crest of the hill A it will reach a speed of 100 km>h when it comes to the bottom B. 5 v0 when it collides with a larger block of mass 1. glider has traveled along the air track 0. 2. The object slides along the inside of the loop-the-loop track consisting of a ramp and a circular loop of radius R shown in the figure. Nov 19, 2015 · sphere. 67 × 10 11 Nm 2 / kg 2 for G to find F. A small block of mass 2m initially rests on a track at the bottom of the circular, vertical loop-the-loop shown above, which has a radius r. 02 m/s B) 9. The cylinder's vertical position as a function of time is . 79. The ramp has a circular section of radius r = 0. e mass distribution) object I=Σmr2 Rotational inertia depends on the choice of axis of rotation, r. After they collide, they hold to one another. The antenna’s lie in the plane of rotation. 20-kilogram mass is sliding on a horizontal, frictionless air track with a speed of 3. 0 km>h 137. A horizontal force F is applied to the axle and the center of mass has 3. An object of mass 10 kg is released at point A, slides to the bottom of the 30 ° 30° incline, then collides with a horizontal massless spring, compressing it a maximum distance of 0. 9 N 5. 4 Solution: Let’s use conservation of energy to analyze the race between two objects that roll without slipping down the ramp. As it is lowered a vertical distance h, its gravitational potential energy loop which has a radius 7 m. Wang 27 A block of mass m slides without friction along a looped track. It has no dependence on r, m, or even g for that matter. Multiply by ½ m to get: ½ mgr = ½ mv2. The cylinder rolls without slipping, and starts from rest at a height H above the frictionless surface on which the ramp sits The ramp is free to slide on a frictionless surface Theramp sits. What is the radius of the curve? (a) 4 m (c) 80 m (e) 640 m (b) 8 m (d) 160 m A thin-walled, hollow spherical shell of mass m and radius r starts from rest and rolls without slipping down the track shown in Fig. θ=cos−1(2/3). 80 m high and 5. A. Model the bowling ball as a uniform sphere and calculate h. Mar 10, 2009 · When the sphere reaches the bottom of the ramp, what is its rotational kinetic energy? When the sphere reaches the bottom of the ramp, what is its translational kinetic energy? A 2. a) What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leaving the track? Assume r << R. The rod also has a mass m and is initially at rest. CM A block of mass m is released from rest, at a height h = 4R above the base of a frictionless loop-the-loop track, as shown in the figure. 31 J (mol K) i Boltzmann’s constant, 1. Assuming an unbanked curve, find the minimum static coefficient of friction, between the tires and the road, static friction being the reason that keeps the car from slipping (see Figure 2). If the pendulum is released from rest at an angle of 30°, what is the angular velocity at the lowest point? A solid sphere of radius 10 cm is allowed to rotate freely about an axis. 5 m and another small inclined section with a maximum height h = 0. 0 m/s (B) 5. See Fig. 0 kg slides without friction, from rest, a long a looped track as shown below. 29. How far has the block moved when the cylinder reaches the bottom (point B) of the track? 15. From what height on the incline should a solid sphere of the same mass and radius be released to have the same speed as the cylinder at the bottom of the hill? Problem: Rotational dynamics 1 h=0. 00 cm/s. Track is a hill on the left going down to a loop-the-loop. 16 Circular Track with Friction A block of mass 0. 02 10 mol Universal gas constant, R =8. . (D)A sphere of mass 3Mand radius 3R. A combined system is formed by centering the sphere at one end of the rod and placing an axis at the other (see accompanying figure). The strike imparts an impulse ∆p on the ball in the direction of the strike, causing it to move toward the right as well as Calculate the centripetal force exerted on a 900 kg car that negotiates a 500 m radius curve at 25. Oct 04, 2006 · A solid cylinder of mass M and radius R rolls down an inclined plane of height ‘h’ without slipping after starting from rest at the top. " So I'm gonna use it that way, I'm gonna plug in, I just solve this for omega, I'm gonna plug that in for omega over Mar 26, 2015 · Homework Statement A hollow sphere of mass M and radius R (I = 2MR2 /3) is released from rest at height h and rolls down a curved surface without slipping until it reaches the lowest point, O. 30. What is 15. 5; LO 3. At time the cylinder is released from rest at a height above the ground. 77] A solid sphere of mass m and radius r rolls without slipping along the tract shown in the figure. For same mass & identical radii have the M. 15 m) is released from rest at the top of a ramp and allowed to roll without slipping. In what A thin-walled, hollow spherical shell of mass m and radius r starts from rest and rolls without slipping down a track (\textbf{Fig. 3-kilogram mass is connected to one end of a massless spring, which has a spring constant of 100 newtons per meter. In case (a) it rolls down the plane without slipping and in case (b) it slides down the plane . Check your inbox for more details. 00×107kg strikes a pier at a speed of 0. 10. 2 m higher than the lower end. A uniform rod AB of mass M and length plane inside a hollow sphere of radius R. The rod is free to pivot about a point 4. The sphere rolls without slipping and has mass m and radius r. Determine the time constant τ and the time at which the sphere reaches 90. x (Figure 14. What is the maximum speed a vehicle can travel along a circular turn without leaving the road, if the turn has a radius of 50 m and the coefficient could be a cylinder, hoop, sphere . It continues to roll without slipping up a hill to a height h before momentarily coming to rest and then rolling back down the hill. A cylinder of mass m and radius R starts to roll from the top of a ramp of mass M. 31 m. 1 991 Ml. Without deriving it, I will just say that the moment of inertia for this disk would then be: Let me just pick one at the top of the incline and 1. • a)Using the isolated system model, determine the speed of the object 11. It rolls 10. The normal force on the ball due to the wall is r L m A) mgr/L D) mgL/r B) L LR mgr 2 +2 E) None of these is correct. 60 kg is released from rest at a height h = 3. Sphere A collides with sphere B; they stick together and swing to a maximum height h equal 10 (A) ï6hc 2. The track is not smooth. ½ GMm/R Questions 16-17: An apple of mass m is thrown horizontally from the edge of a cliff of height H, as shown to the right. (a) Which object wins the race? If the two objects are released at rest, and the height of the ramp is h = 0. 00 m, damaging the ship, the pier, and the tugboat captain’s finances. 5M at rest at the bottom of the incline. 0500 kg slides in a vertical circle of radius R = 0. When the block reaches the top of the loop, the 4. 00 N, of a frictionless, hemispherical bowl of radius R 5 that if the sphere is released from. The block slides along the inside of a frictionless circular hoop of radius R. to the stationary mass hanger gives. A spacecraft of mass m is in circular orbit above the equator at distance d above Earth’s surface. When the spring is released, the glider travels a maximum distance of 1. The track is frictionless except for a portion of length 7 m. A solid sphere of radius R = 10 cm and mass M 1. What will be the maximum velocity of the sphere at the lowest point of the U rail? What assumption you have made in the calculation. What is one end of the track is released from rest and slides past the bottom of the track  an image of a ball labeled m moving in a circular motion with a line a c Circular motion with speed v in a path of radius R has period (time for one revolution) Σ F = ma. A solid sphere of mass mand radius rrolls without slipping along the track shown in the gure below. 60 s. A round object of mass m and radius r is released from rest at the top of a curved surface and rolls without slipping until it leaves the surface with a horizontal velocity as shown. a- Determine the moment of inertia of the spacecraft about the Earth’s South-North axis while it is in orbit if the spacecraft can be approximated as a solid sphere with a radius rsc = r = ( 1. A rigid body with a cylindrical cross-section is released from the top of a $30\text{°}$ incline. A thin hoop of mass M, radius R, and rotational inertia MR2 is released from rest from the top of the ramp of length L above. 87 m/s E) 3. The equations of motion will be F x = m(a G) x => P - F = ma G F y = m(a G) y => N - mg = 0 M G = I G => F r = I G There are 4 unknowns (F, N, and a G) in these three equations. Solid sphere A solid sphere of mass 4. If the block is released from rest at the top of the incline, what is its speed at the bottom? (A) 5. Apr 03, 2013 · A thin-walled, hollow spherical shell of mass m and radius r starts from rest and rolls without slipping down the track shown in the figure (Figure 1) . The larger block moves to the right at a speed 2. The xed, wedge-shaped ramp makes an angle of = 30:0 as shown in the gure. A particle kept on the top of the sphere is released at zero velocity with respect to the sphere. An object of mass m is released from rest at a height h above the surface of a table. 11 X 10-28 gram as shown above and then released. It starts from rest with the lowest point of the sphere at height h above the bottom of the loop of radius R, much larger than r. Step 5: ΣFr = N + mg = mv2/r → N = mv2/r - mg. 3 m at θ = 37 ̊above the horizontal. The A ball is released from rest above an inclined plane and bounces  r = displacement from the point of rotation to the point of force application (m) A bowling ball of mass M and radius R rolls without slipping down an inclined 1 point for using the correct height of CM A solid sphere begins at rest and rolls down the incline and through a 2. 1 m and nally a at straight section at the same height as the center of the loop (18. The given situation is illustrated as:In the case of vertical equilibrium,N cos = mg + f1 sin mg = N cos A hollow ball and a solid ball of same radius r and same mass M are simultaneously released from the top (height h) of a double-track loop-the-loop (two different tracks that are right next to each other). (a) Find the minimum value of h in terms of r so that the A mass m = 73 kg slides on a friction-less track that has a drop, followed by a loop-the-loop with radius R = 18. Question #2 The equation for the speed of the a disk at the bottom of the ramp is 1. 67×10-11 Nm 2 /kg 2) m = mass of the object, M = mass of the earth, r = radius of the earth. 7 A solid sphere with mass M, radius R, and rotational inertia I = 2 5 MR2 is rolling (without slipping) down an inclined plane making an angle of exactly θ = 30 with the horizontal (see Figure). Solid disc. A satellite is spinning at 6. 59 cm and a mass of m = 18. The sphere is then released from rest, and it rolls on the track without slipping. $$\frac{7}{10}mg(R-r) +2mg(R-r)=mgh\\ h = \frac{27}{10}(R-r)$$ Note that it is sometimes said that "you can ignore the rotational energy of the marble if it is very small", but that is emphatically not true - the rotational energy for a solid sphere is always 2/5 of the (linear) kinetic energy, regardless of the size of the marble. The block travels down the track, hits a spring of force constant k = 1545 N/m, and compresses it 1. In order to calculate its speed at the bottom of the incline, one needs to know: a. A solid sphere of mass mand radius r rolls without slipping along the track shown in Figure P10. 3 mi>h2 Your cousin Throckmorton skateboards from rest down a curved, result doesn't depend on the radius R of the ramp. You try to roll it over a step of height h