In the above diagram, a cart, which has a mass of 6.44 kg, is moving to the right at a speed of2.75 m/s. If the elastic constant for the bumper is 3.75.x 10,3N/m, what is the mechanical energy in thesystem when the bumper is compressed a distance of 22.5 cm?a. 119J C. 88.4 Jb. 70.6J d. 24.4 J
Question
In the above diagram, a cart, which has a mass of 6.44 kg, is moving to the right at a speed of2.75 m/s. If the elastic constant for the bumper is 3.75.x 10,3N/m, what is the mechanical energy in thesystem when the bumper is compressed a distance of 22.5 cm?a. 119J C. 88.4 Jb. 70.6J d. 24.4 J
Solution
The mechanical energy in the system can be calculated by adding the kinetic energy of the cart and the potential energy stored in the compressed bumper.
Step 1: Calculate the kinetic energy (KE) of the cart using the formula KE = 1/2 * m * v^2, where m is the mass and v is the velocity. KE = 1/2 * 6.44 kg * (2.75 m/s)^2 = 24.4 J
Step 2: Calculate the potential energy (PE) stored in the compressed bumper using the formula PE = 1/2 * k * x^2, where k is the spring constant and x is the displacement. PE = 1/2 * 3.75 * 10^3 N/m * (0.225 m)^2 = 95 J
Step 3: Add the kinetic energy and potential energy to get the total mechanical energy in the system. Total mechanical energy = KE + PE = 24.4 J + 95 J = 119.4 J
So, the mechanical energy in the system when the bumper is compressed a distance of 22.5 cm is approximately 119 J.
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