PhysicsUK Connections

A spring obeys Hooke's law and has a spring constant of 25 N m⁻¹. (a) Calculate the extension produced by a force of 5.0 N. (2) (b) Calculate the elastic potential energy stored in the spring at this extension. (2)

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A technician calibrates the spring bumper of a small instrument trolley. Figure 1 shows the force F needed to compress the spring by x from its natural length. The graph is a straight line through (0, 0), (0.020 m, 1.2 N), (0.040 m, 2.4 N) and (0.060 m, 3.6 N). The trolley has mass 0.60 kg. It is released from rest against the spring at compression 0.060 m on a horizontal track. A constant resistive force of 0.60 N opposes the motion as soon as the trolley moves. The spring's mass is negligible and its deformation is elastic. The trolley loses contact with the spring at its natural length. There are no other energy losses. (a) Use the gradient of the force-compression graph to determine the spring constant. [2] (b) Use the graph to calculate the work needed to compress the spring from its natural length to 0.060 m. [2] (c) Calculate the acceleration just after release, stating its direction relative to the bumper. [3] (d) Calculate the speed when the trolley loses contact with the spring. Account for the work done against resistance. [3] (e) Explain why a single constant-acceleration equation cannot describe the whole interval while the trolley is in contact with the spring. [2] (f) Calculate the distance travelled after losing contact before the trolley stops. Use a constant-acceleration equation for this part. [3]

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A sensor is suspended from a small ring by a light vertical cord. The ring is held by an inclined spring on its left and a light horizontal cord on its right, as shown in Figure 2. The spring slopes upwards to the left at 40.0° above the horizontal. The sensor's weight is 12.0 N. The ring and cords have negligible mass. All forces act in one plane through the centre of the ring, which is at rest. The spring constant is 80.0 N m⁻¹ and the spring obeys Hooke's law for extensions up to 0.300 m. (a) Use vertical equilibrium to calculate the tension in the inclined spring. [3] (b) Calculate the tension in the horizontal cord. [2] (c) Calculate the spring's extension and check whether using Hooke's law is consistent with the stated proportional range. [3] (d) A pupil claims that the spring tension is 12.0 N because the sensor is at rest. Explain why this claim is incorrect. [2]

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