A person, who weighs 688N, swings from a cliff at the end of a convenient vine that is 18m long. From the top of the cliff to the bottom of the swing he descends by 3.2m. The vine will break if the force on it exceeds 950N.
a) Does the vine break?
b) If no, what is the greatest force on it during the swing?
If yes, at what angle does with the vertical does it break?
Your school subject is Physics.
To determine whether the vine will break, we need to calculate the force on the vine at the bottom of the swing. We can use the concepts of gravitational potential energy and centripetal force.
a) To calculate the force on the vine at the bottom of the swing, we need to find the potential energy associated with the person and their weight. The potential energy is given by the formula:
Potential Energy = Weight × Height
The weight of the person is given as 688N, and the height of the swing is 3.2m. Thus, the potential energy is:
Potential Energy = 688N × 3.2m = 2201.6 J
b) The force on the vine at the bottom of the swing is equal to the centripetal force, which is given by the formula:
Centripetal Force = (Mass × Velocity^2) / Radius
Since the mass is not given, we can use the weight and acceleration due to gravity to find it using the formula:
Weight = Mass × Gravity
Mass = Weight / Gravity = 688N / 9.8m/s^2 = 70.2 kg
Now we can calculate the maximum force on the vine:
Centripetal Force = (Mass × Velocity^2) / Radius
First, we need to find the velocity. At the bottom of the swing, all the potential energy is converted into kinetic energy. So, potential energy = kinetic energy.
Potential Energy = Kinetic Energy
688N × 3.2m = (1/2) × Mass × Velocity^2
Rearranging the equation to solve for the velocity, we get:
Velocity^2 = (2 × 688N× 3.2m) / Mass
Velocity^2 = (2 × 688N × 3.2m) / 70.2kg
Velocity^2 = 19.64 m^2/s^2
Taking the square root of both sides:
Velocity = 4.43 m/s
Now, substituting the values back into the centripetal force equation:
Centripetal Force = (Mass × Velocity^2) / Radius
Centripetal Force = (70.2kg × (4.43m/s)^2) / 18m
Centripetal Force = 44.06N
b) Since the calculated centripetal force of 44.06N is less than the breaking force of the vine (950N), the vine does NOT break.
Therefore, the greatest force on the vine during the swing is 44.06N, occurring at the bottom of the swing.
As for the angle at which the vine would break, we don't have enough information to determine it.