A ball on the end of a string is whirled around in a horizontal circle of radius 0.467 m. The plane of the circle is 1.24 m above the ground. The string breaks and the ball lands 2.49 m away from the point on the ground directly beneath the ball’s location when the string breaks.
The acceleration of gravity is 9.8 m/s2 .
Find the centripetal acceleration of the ball during its circular motion.
Answer in units of m/s2
5.8kg bag of groceries is in equilibrium on an incline of 34deg. the acceleration of gravity is 9.81m/s^2. What is the magnitude of the normal force on the bag?
To find the centripetal acceleration of the ball during its circular motion, we need to apply the following formula:
centripetal acceleration (ac) = (velocity squared) / radius
However, we don't have the velocity directly given in the question. To find it, we can use the concept of conservation of energy.
The potential energy at the maximum height is converted into kinetic energy at the lowest point of its circular motion. The potential energy can be calculated using the formula:
potential energy (PE) = mass × gravity × height
Given:
height = 1.24 m
gravity = 9.8 m/s^2
Now, we need to convert the potential energy to kinetic energy:
potential energy (PE) = kinetic energy (KE)
Kinetic energy (KE) can be calculated using the formula:
kinetic energy (KE) = (1/2) × mass × velocity^2
Since the mass cancels out, we can equate the equations:
mass × gravity × height = (1/2) × mass × velocity^2
Simplifying the equation:
gravity × height = (1/2) × velocity^2
Now, solve for velocity:
velocity^2 = (2 × gravity × height)
velocity = sqrt(2 × gravity × height)
Substitute the given values:
gravity = 9.8 m/s^2
height = 1.24 m
velocity = sqrt(2 × 9.8 × 1.24)
Now that we have the velocity, we can calculate the centripetal acceleration using the formula mentioned earlier:
centripetal acceleration (ac) = (velocity^2) / radius
Substitute the given value:
radius = 0.467 m
centripetal acceleration (ac) = (sqrt(2 × 9.8 × 1.24)^2) / 0.467
Simplify and calculate the value to get the answer in units of m/s^2.