A 240 g block on a 41 cm-long string swings in a circle on a horizontal, frictionless table at 73 rpm.
(a) What is the speed of the block?
(b) What is the tension in the string?
speed=w*r=73rev/min*2PIrad/rev*1min/60sec*.41 =73*2PI/60 * .41m
tension= massinKG*speed^2/radius
To answer these questions, we need to understand the concepts of circular motion, centripetal force, and the relationship between speed, radius, and angular velocity.
(a) To find the speed of the block, we can use the formula:
speed = radius × angular velocity
Here, the radius is given as the length of the string, which is 41 cm (0.41 m). The angular velocity is given as 73 rpm (revolutions per minute). However, we need to convert it to radians per second because the formula requires angular velocity in radians per second.
To convert rpm to radians per second, we use the following conversion factor:
1 revolution = 2π radians
1 minute = 60 seconds
To convert 73 rpm to radians per second:
angular velocity = 73 rpm × (2π radians / 1 revolution) × (1 revolution / 60 seconds)
Now we can calculate the speed:
speed = 0.41 m × [(73 rpm × 2π radians / 1 revolution × 1 revolution / 60 seconds)]
(b) To find the tension in the string, we need to consider the forces acting on the block in circular motion. The tension in the string provides the centripetal force required to keep the block moving in a circle.
The centripetal force (Fc) is given by the formula:
Fc = (mass × speed²) / radius
Here, the mass of the block is given as 240 g (0.240 kg), and we already calculated the speed and radius in part (a). Now we can substitute these values into the formula and solve for the tension.
Tension = (mass × speed²) / radius
Now we have the formula and the values needed to solve for both the speed and tension. Let's calculate the answers.