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Let's consider the system given in Figure 2. The end of a flexible spring with spring constant k is attached to the wall and the other end to a block of mass m. There is no friction between the block and the inclined plane. When the spring is at its natural length, the block is first decelerated. The angle of inclination of the inclined plane is given as ß.
b) What will be the velocity (velocity component) of the block when the spring is extended by x?
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- Hanging Mass: A block of mass 14.1 kg is connected to a light cord of length 351.3 cm and a spring with an equilibrium length of 33.4 cm. The block hangs motionless as shown in the figure. The spring has a spring constant of 1799 N/ m. As the block hangs in equilibrium, the spring is horizontal and the cord makes an angle of 24 ° with respect to vertical. T k M (a) What is the tension in the cord? (b) How far is the spring stretched from its equilibrium length?A block of mass 2.9 kg is sitting on a frictionless ramp with a spring at the bottom that has a spring constant of 470 N/m (refer to the figure). The angle of the ramp with respect to the horizontal is 13°. a) The block, starting from rest, slides down the ramp a distance 54 cm before hitting the spring. How far, in centimeters, is the spring compressed as the block comes to momentary rest? b) After the block comes to rest, the spring pushes the block back up the ramp. How fast, in meters per second, is the block moving right after it comes off the spring? c) What is the change of the gravitational potential energy, in joules, between the original position of the block at the top of the ramp and the position of the block when the spring is fully compressed?A ball of mass 0.5kg is tied to a string of length 1.0 meters, and the other end of the string is tied to a rigid support. The ball is held straight out horizontally and is then released. a) What is the speed of the ball at the lowest point of its motion? b) What is the tension in the string at its joint? Solution FBD and Formula Required
- Tiny Spring: A tiny silica bead attached to a strand of DNA can be used to study the mechanical properties of DNA. The system can be approximated as a mass on a spring constrained to move in one dimension. In one such experiment, a bead of mass 7.8 × 10¬15 kg was attached to a strand of DNA with 1623 base pairs and observed for 720 seconds. (a) If the root mean square velocity of the bead is 7.56 x 10-4 m/s, at what temperature was the experiment carried out? (b) If the root mean square displacement of the particle is measured to be 1.18 × 10-7 m, what is the spring constant of the DNA molecule?Jum The mass of the block depicted in the image is 1.60 kg. The spring has a spring constant of 76.9 N/m. The coefficient of static friction between the block and the floor is 0.726. Assume that the spring makes no contact with the floor and therefore friction only acts on the block. How far must the block and spring assembly be compressed to just barely overcome the force of static friction acting on the block? Report your result in meters.AE is 182 ASAP
- A block of mass m is located on an inclined plane that makes an angle with the horizontal. The coefficient of kinetic friction between the block and the inclined plane is μ₁. The block presses against, but is not attached to, a spring with constant k₁. When the spring is at its equilibrium position, the block is at a height h above the ground, as shown. The initial position of the block, from which it is released, is a bit further up the inclined plane such that the spring is initially compressed by Ax. At the bottom of the inclined plane is a horizontal plane with a different coefficient of friction, μ2, for the first distance, d, after which the surface is frictionless, and the equilibrium position of a spring with constant k₂ is encountered. Part (a) Suppose that numeric values are such that block comes to rest before reaching the the ramp. Let x distance traveled from the equilibrium position of the block towards the bottom of the ramp. Enter an expression for x. Part (b) Suppose…A spring with spring constant k has an unstretched length L . A block of mass m is pushed against the spring to compress it to the unknown position x = A. The block is not attached to the spring and the ground is frictionless. Another force acts on the block, attracting it to the point x = 0, with a magnitude c /x2, where c is a known constant. The block is released from rest. Obtain an algebraic equation for the compressed position x = A, such that the block escapes from the attractive force. (To escape means it will go all the way to infinity where it will have zero velocity.)A 1120-kg car is being driven up a 7.03 ° hill. The frictional force is directed opposite to the motion of the car and has a magnitude of 490 N. A force F is applied to the car by the road and propels the car forward. In addition to these two forces, two other forces act on the car: its weight W and the normal force FN directed perpendicular to the road surface. The length of the road up the hill is 281 m. What should be the magnitude of F, in Newtons, so that the net work done by all the forces acting on the car is 188 kJ?
- 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?I am requesting help on the very last portion of this problem at the bottom as I have completed all other portions correct. I have previously answered 15.4J and 0J, which were both incorrect. Thank you.A 4.00 kg mass on a frictionless incline plane of angle 1 degrees is released and begins sliding down the incline. At the bottom of the incline is a spring (k=20 N/m) If the mass slides 0.10 m along the incline plane before it contacts the spring, how far is the spring compressed by the mass? (round to the nearest hundredth) How would the length of the spring compression change if there was friction between the incline plane and the mass? - The spring would be compressed the same length? -The spring would be compressed more? -The spring would be compressed less?