Which has the greater kinetic energy: a bowling ball that slides down the lane without rolloing, or one of the exact same mass that moves at the same translational speed but rolls without slipping?
The rolling ball has additional rotational kinetic energy. It makes the total kinetic energy 0.6 M V^2 instead of 0.5 M V^2.
To determine which object has greater kinetic energy, we need to consider the rotational kinetic energy for the rolling object in addition to its translational kinetic energy.
For the bowling ball sliding down the lane without rolling, it only has translational kinetic energy. The equation for translational kinetic energy (KEtrans) is given by:
KEtrans = 0.5 * mass * velocity^2
For the bowling ball that rolls without slipping, we need to calculate both translational and rotational kinetic energy. The equation for rotational kinetic energy (KErot) is given by:
KErot = 0.5 * moment of inertia * angular velocity^2
Since the bowling ball is rolling without slipping, the angular velocity is related to its translational velocity (v) and radius (r) by the equation:
v = r * angular velocity
To compare the kinetic energy of the two scenarios, we need to equate their translational velocities:
v (sliding) = v (rolling)
Therefore:
mass * v^2 (sliding) = mass * v^2 (rolling)
Since the mass is the same, we can ignore it in the comparison.
Comparing the kinetic energy of the objects, we find:
KEtrans (sliding) = KEtrans (rolling) + KErot (rolling)
Since the rolling object has both translational and rotational kinetic energy, it will have a greater total kinetic energy compared to the sliding object.
Therefore, the bowling ball that rolls without slipping has greater kinetic energy than the bowling ball that slides down the lane without rolling.
To determine which object has greater kinetic energy, let's start by understanding the concept of kinetic energy. Kinetic energy is the energy possessed by an object due to its motion. It depends on both the mass of the object and its speed.
In this case, we have two scenarios: a bowling ball sliding down the lane without rolling and a bowling ball rolling without slipping, both having the same mass and translational speed. Let's analyze each scenario separately:
1. Bowling ball sliding down the lane without rolling:
In this case, the bowling ball is moving solely due to the force of gravity, which causes it to slide along the lane. When an object slides, its kinetic energy is also influenced by the friction between the object and the surface. In this case, since the ball is sliding and not rolling, the frictional force opposes its motion, causing a loss of energy. As a result, the kinetic energy of the sliding ball will be less than its translational kinetic energy.
2. Bowling ball rolling without slipping:
In this scenario, the bowling ball is rolling along the lane without slipping. When an object rolls, its kinetic energy is determined by both its translational motion and its rotational motion. The rotational motion adds an additional contribution to the ball's kinetic energy. As a result, the rolling ball will have a higher kinetic energy compared to the sliding ball.
In conclusion, the bowling ball that rolls without slipping will have greater kinetic energy compared to the bowling ball that slides down the lane without rolling, given that both have the same mass and translational speed.