A 0.46-kg block is held in place against the spring by a 30-N horizontal external force. The external force is removed, and the block is projected with a velocity v1= 1.2 m/s upon separation from the spring, as shown in the figure. The block descends a ramp and has a velocity v= 1.5 m/s at the bottom. The track is frictionless between points A and B. The block enters a rough section at point B, extending to E. The coefficient of kinetic friction between the block and the rough surface is 0.38. The velocity of the block is v3 1.4 m/s at point C. The block moves on to D, where it stops. What distance does the block travel between points B and D? Smooth D B Rough 0.30 m 0.60 m 0.40 m 0.26 m 0.039 m
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- A glider of mass 0.240 kg is on a horizontal track, attached to a horizontal spring of force constant 6.00 N/m. There is friction between the track and the glider. Initially the spring (whose other end is fixed) is stretched by 0.100 m and the attached glider is moving at 0.400 m>s in the direction that causes the spring to stretch farther. The glider comes momentarily to rest when the spring is stretched by 0.112 m. (a) How much work does the force of friction do on the glider as the stretch of the spring increases from 0.100 m to 0.112 m? (b) What is the coefficient of kinetic friction between the glider and the track?To measure the static friction coefficient between a 1.40-kg block and a vertical wall, a spring (k = 770 N/m) is attached to the block, is pushed on the end in a direction perpendicular to the wall until the block does not slip downward (see figure). If the spring is compressed by 0.048 m, what is the coefficient of static friction?A 1.50-kg object slides to the right on a surface having a coefficient of kinetic friction 0.250 (Figure a). The object has a speed of vi = 3.30 m/s when it makes contact with a light spring (Figure b) that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distance d (Figure c). The object is then forced toward the left by the spring (Figure d) and continues to move in that direction beyond the spring's unstretched position. Finally, the object comes to rest a distance D to the left of the unstretched spring (Figure e). a) Find the distance of compression d (in m). b) Find the speed v (in m/s) at the unstretched position when the object is moving to the left (Figure d). c) Find the distance D (in m) where the object comes to rest. d) If the object becomes attached securely to the end of the spring when it makes contact, what is the new value of the distance D (in m) at which the object will come to rest after moving to the left?
- a 2 kg weight is fasten to a spring on an inclined plane. It has a spring constant of 20 N/m. When the spring is relaxed, the mass sits at the bottom of the incline. It is compressed 0.25 m from its relaxed position, and the weight is released. It goes down the incline, to the horizontal surface and up a second, identical incline. If there were kinetic friction between the weight and the right incline, but none between the weight and the left incline, what would be the coefficient of kinetic friction μk so the maximum height reachable is the same as the starting position (i.e. d=0.25m).A block with a mass of 30.0 kilograms (kg) is held against a spring with a force constant of k = 1.25×105 N/m. The spring is initially compressed 17.5 centimeters (cm) from equilibrium. Then the block is released, setting it into motion. The block initially slides along a frictionless surface, but then it encounters a 1.50 meter long rough patch where the coefficient of kinetic friction is 0.134. It then slides down a frictionless ramp, which is tilted at an angle of 19.5 degrees and has a length of 2.50 meters. How fast is the block moving when it reaches the bottom of the ramp? Give your answer in meters per second (m/s). Hint: use WNC = ΔK + ΔU.Consider the track shown in the figure below. Section AB is a quadrant of a circle of radius r = 2.00 m and is frictionless. From B to C is a horizontal section 3.0 m long with a coefficient of kinetic friction μk = 0.250. The section CD under the spring is frictionless. A block of mass m = 1.00 kg is released from rest at A. After sliding on the track, the block compresses 0.200 m the spring. Determine (using conservation of energy): (a) the speed of the block at point B. (b) the thermal energy (internal energy) produced when the block slips from B to C. (c) the velocity of the block at point C. (d) the stiffness constant k for the spring.
- The system is released from rest with no slack in the cable and with the spring stretched 200 mm. Determine the distance s traveled by the 3.6-kg cart before it comes to rest (a) if m approaches zero and (b) if m = 2.4 kg. Assume no mechanical interference and no friction. The distance s is positive if up the incline, negative if down. k = 105 N/m 3.6 kg 25° m Answers: (a) m = 0, S = (b) m = 2.4 kg, S = iA block with mass m = 19.1 kg is pressed against a spring with spring constant 2.720E+3 N/m, compressing the spring a distance of 0.130 m. It is then released from rest, moves across a frictionless horizontal surface, down a frictionless hill (vertical height h = 8.24 m), and onto a horizontal surface with friction μk = 0.287. How far (in m) will the block slide across the horizontal frictional surface before coming to rest?The cable of a 1170 kg elevator cab shown in the figure below snaps when the cab is at rest at a height ?=22.9m above a spring with spring constant ?=9.08×10^4N/m. Additionally a constant friction force created by the clamps sliding along the guide rails is experienced by the cab as it moves in the shaft with strength ?f=8.14×10^3N. (a) What isthe maximum distance xthe spring compresses? (b) What is the maximum acceleration experienced by the elevator during its movement described in the problem? Assume no static friction acting on the cab since we can imagine the clamps not engaging until the moment after the cab begins to fall. Also, note that the clamps stay engaged the whole time, including while the spring is being compressed and while the elevator is bouncing back up.
- One end of a horizontal spring with force constant 76.0 N/m is attached to a vertical post. A 2.00 kg block of frictionless ice is attached to the other end and rests on the floor. The spring is initially neither stretched nor compressed. A constant horizontal force of 54.0 N is then applied to the block, in the direction away from the post. (a) What is the speed of the block when the spring is stretched 0.400 m? (b) At that instant, what are the magnitude and direction of the acceleration of the block?A package of mass m = 6.00 kg is released on a 53.1° incline, a distance D = 4.00 m from a long spring with force constant 1.10 x 10² N/m that is attached at the bottom of the incline (Figure 1). The coefficients of friction between the package and incline are s = 0.400 and k = 0.200. The mass of the spring is negligible. (a) What is the maximum Figure m D www.k 0 = 53.1° 1 of 1 ▼ Part L Correct Find the total work done by the force of friction over the entire trip. Express your answer with the appropriate units. ► View Available Hint(s) W₁ = -75.1 J Submit Previous Answers Answer Requested As you can see, this is in accordance with your result from Part J. For the steps and strategies involved in solving this problem, you may view the Video Tutor Solution.5. Moumita is holding a mass m=0.50kg, which is connected to the bottom of a vertical spring with spring constant k=10.0ON/m. She is holding the mass in place at a height h=1.5m above the floor. The spring is relaxed in this condition. When Moumita lets go of the mass, how far will the mass fall before it turns around and starts to travel upwards?