A bowling ball encounters a 0.76m vertical rise on the way back to the ball rack, as the drawing illustrates. Ignore frictional losses and assume that the mass of the ball is distributed uniformly. If the translational speed of the ball is 3.80m/s at the bottom of the rise, find the translational speed at the top.
Take the initial KEnergy, subtract the graviatational potential energy on the rise, and the remainder is KE. From that, compute speed.
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.