As a bowling ball of radius 15.9 cm rolls down the alley to the right, a frictional force of magnitude 1.46 N, directed to the left, acts on it. Find the frictional torque with respect to an axis through the center of the ball.
torque= force (N) x radius (m)
To find the frictional torque with respect to an axis through the center of the ball, we need to determine the moment arm and the magnitude of the torque.
The moment arm is the perpendicular distance from the axis of rotation to the line of action of the force. In this case, since the force is directed to the left, the moment arm is the radius of the ball, which is 15.9 cm or 0.159 meters.
The magnitude of the torque can be calculated using the formula:
Torque = Force x Moment Arm
Substituting the given values:
Torque = 1.46 N x 0.159 m = 0.23214 Nm (rounded to five decimal places)
Therefore, the frictional torque with respect to an axis through the center of the ball is approximately 0.23214 Nm.
To find the frictional torque with respect to an axis through the center of the ball, we need to use the concept of torque, which is the rotational equivalent of force. Torque is given by the product of force and the perpendicular distance from the axis of rotation.
In this case, the frictional force is acting on the bowling ball, causing it to rotate. The torque due to friction can be calculated as follows:
Torque = force x distance
The force acting on the ball due to friction is given as 1.46 N and is directed to the left. However, since torque is a vector quantity, we also need to consider the direction of the torque. In this case, the torque will be directed clockwise since the frictional force is acting to oppose the forward rotation of the ball.
Now, we need to find the perpendicular distance from the axis of rotation to the line of action of the force. Since the axis of rotation is through the center of the ball, this distance is equal to the radius of the ball.
Radius of the ball = 15.9 cm = 0.159 m
Thus, the frictional torque with respect to an axis through the center of the ball can be calculated as:
Torque = force x distance
= 1.46 N x 0.159 m
= 0.23214 N·m
Therefore, the frictional torque with respect to an axis through the center of the ball is 0.23214 N·m, directed clockwise.