Question

İn a situation where the kinetic friction force in air is 10 N, a stationary block with a mass of 2 kg falls from a height y onto a spring with spring constant k = 400 N/m. Since the maximum compression in the spring is 3 m, find the height y. Solve it using the energy method

Answer 1

To find the height y when a stationary block with a mass of 2 kg falls onto a spring with a spring constant of 400 N/m, we can use the energy method. By equating the potential energy of the block to the elastic potential energy of the spring, we can solve for the height y. The height y is approximately 0.51 m.

Step-by-step explanation:

To find the height y when a stationary block with a mass of 2 kg falls from a height and compresses a spring, we can use the energy method. In this problem, we have kinetic friction force in air and a spring with a spring constant. Here's how we can solve it step by step:

1. 
   
2. First, let's find the potential energy of the block when it is at height y. The potential energy is given by PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. Since the block is stationary, its speed is zero, so the potential energy is equal to the kinetic friction force: PE = 10 N.
3. 
   
4. Next, let's find the compression of the spring when the block falls. The potential energy is converted into elastic potential energy as the spring compresses. The elastic potential energy is given by PE = (1/2)kx^2, where k is the spring constant and x is the compression of the spring. We are given the maximum compression of the spring, which is 3 m, so the potential energy is PE = (1/2)(400 N/m)(3 m)^2 = 1800 J.
5. 
   
6. Finally, we can equate the potential energy of the block to the elastic potential energy of the spring to find the height y. We have PE = mgh and PE = 1800 J, so 10 N = 2 kg x 9.8 m/s^2 x y. Solving for y, we get y = 10 N / (2 kg x 9.8 m/s^2) = 0.51 m.

Therefore, the height y is approximately 0.51 m.