To find the translational speed of the bowling ball at the top of the 0.76m vertical rise, you can follow these steps:
Step 1: Determine the initial kinetic energy (KE) of the bowling ball. The formula for kinetic energy is given by KE = (1/2) * m * v^2, where m is the mass of the ball and v is the initial translational speed. In this case, the initial translational speed is given as 3.80m/s.
Step 2: Calculate the gravitational potential energy (PE) at the bottom of the rise. The formula for gravitational potential energy is given by PE = m * g * h, where m is the mass of the ball, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the vertical height (0.76m in this case).
Step 3: Subtract the gravitational potential energy from the initial kinetic energy to obtain the remaining kinetic energy. Let's call this KE_remainder. Therefore, KE_remainder = KE - PE.
Step 4: Compute the speed at the top of the rise using the remaining kinetic energy. The formula to calculate speed is given by v_top = √(2 * KE_remainder / m), where m is the mass of the ball.
By following these steps, you can find the translational speed of the bowling ball at the top of the 0.76m vertical rise.