You are watching a YouTube video to prepare for a physics exam. The 'teacher' in the video states that a ball is elastic because it deforms when it collides with a wall or floor. Are they correct? Carefully explain your answer, and include definitions of deformation and elasticity. (b) [7 marks]A 25.0 cm tall spring is compressed by 12 mm when a 1.00 kg mass is placed on it.(i) (1 mark)Determine the spring constant of the spring.(ii) (1 mark)Calculate the elastic potential energy stored in the spring.(iii) (1 mark)Where did the energy stored in the spring 'come from'?(iv) (2 marks)The spring is now placed horizontally on a frictionless surface with one end attached to a wall and a 740 g mass attached to the other end. The mass is given a push to set it oscillating. What is the frequency of oscillation?(v) (2 marks)A pendulum is placed above the mass-spring system and the bob oscillates back and forth exactly in time with the mass. How long is the pendulum?
Question
You are watching a YouTube video to prepare for a physics exam. The 'teacher' in the video states that a ball is elastic because it deforms when it collides with a wall or floor. Are they correct? Carefully explain your answer, and include definitions of deformation and elasticity. (b) [7 marks]A 25.0 cm tall spring is compressed by 12 mm when a 1.00 kg mass is placed on it.(i) (1 mark)Determine the spring constant of the spring.(ii) (1 mark)Calculate the elastic potential energy stored in the spring.(iii) (1 mark)Where did the energy stored in the spring 'come from'?(iv) (2 marks)The spring is now placed horizontally on a frictionless surface with one end attached to a wall and a 740 g mass attached to the other end. The mass is given a push to set it oscillating. What is the frequency of oscillation?(v) (2 marks)A pendulum is placed above the mass-spring system and the bob oscillates back and forth exactly in time with the mass. How long is the pendulum?
Solution
The 'teacher' in the video is partially correct. When a ball collides with a wall or floor, it does deform, meaning it changes shape. However, this alone does not make the ball elastic. Elasticity refers to the ability of an object to return to its original shape after being deformed. So, if the ball returns to its original shape after the collision, then it can be considered elastic.
(i) The spring constant (k) can be determined using Hooke's Law, which states that the force (F) exerted by a spring is equal to the displacement (x) times the spring constant (k). In this case, the force is the weight of the 1.00 kg mass, which is 9.8 N (1 kg * 9.8 m/s^2), and the displacement is 12 mm or 0.012 m. So, k = F/x = 9.8 N / 0.012 m = 816.67 N/m.
(ii) The elastic potential energy (U) stored in the spring can be calculated using the formula U = 1/2 * k * x^2. Substituting the values, we get U = 1/2 * 816.67 N/m * (0.012 m)^2 = 0.059 Nm or 0.059 J.
(iii) The energy stored in the spring came from the work done to compress the spring, which is equal to the force applied times the displacement.
(iv) The frequency of oscillation (f) can be calculated using the formula f = 1/(2π) * sqrt(k/m), where m is the mass of the object. Substituting the values, we get f = 1/(2π) * sqrt(816.67 N/m / 0.74 kg) = 1.36 Hz.
(v) The period of oscillation (T) of the pendulum is equal to the period of the mass-spring system, which is the reciprocal of the frequency. So, T = 1/f = 1/1.36 s = 0.735 s. The length (L) of the pendulum can be calculated using the formula T = 2π * sqrt(L/g), where g is the acceleration due to gravity. Solving for L, we get L = (T^2 * g) / (4π^2) = (0.735 s)^2 * 9.8 m/s^2 / (4π^2) = 0.44 m.
Similar Questions
A 25.0 cm tall spring is compressed by 12 mm when a 1.00 kg mass is placed on it.(i) (1 mark)Determine the spring constant of the spring.(ii) (1 mark)Calculate the elastic potential energy stored in the spring.(iii) (1 mark)Where did the energy stored in the spring 'come from'?(iv) (2 marks)The spring is now placed horizontally on a frictionless surface with one end attached to a wall and a 740 g mass attached to the other end. The mass is given a push to set it oscillating. What is the frequency of oscillation?(v) (2 marks)A pendulum is placed above the mass-spring system and the bob oscillates back and forth exactly in time with the mass. How long is the pendulum?
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