The above diagram shows a cart with a mass of 9.50 kg that has collided with and compressed a springbumper with an elastic constant of 2.40 x 10 3N/m. When the spring is compressed a distance of8.75 cm, the cart still has a speed of 1.22 m/s. What is the mechanical energy of the cart at that instant?a. .8.13 c. 7.07Jb. 9.12J d. 16.3J
Question
The above diagram shows a cart with a mass of 9.50 kg that has collided with and compressed a springbumper with an elastic constant of 2.40 x 10 3N/m. When the spring is compressed a distance of8.75 cm, the cart still has a speed of 1.22 m/s. What is the mechanical energy of the cart at that instant?a. .8.13 c. 7.07Jb. 9.12J d. 16.3J
Solution
The mechanical energy of the cart at that instant can be calculated by adding the kinetic energy and the potential energy of the spring.
The kinetic energy (KE) can be calculated using the formula:
KE = 0.5 * m * v^2
where: m = mass of the cart = 9.50 kg v = speed of the cart = 1.22 m/s
The potential energy (PE) stored in the spring can be calculated using the formula:
PE = 0.5 * k * x^2
where: k = spring constant = 2.40 x 10^3 N/m x = compression distance = 8.75 cm = 0.0875 m (since 1 cm = 0.01 m)
Let's calculate these:
KE = 0.5 * 9.50 kg * (1.22 m/s)^2 = 7.07 J
PE = 0.5 * 2.40 x 10^3 N/m * (0.0875 m)^2 = 9.12 J
The total mechanical energy is the sum of the kinetic and potential energies:
ME = KE + PE = 7.07 J + 9.12 J = 16.19 J
So, the closest answer is d. 16.3J.
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