An object of mass 0.5 kg is whirled at the end of a string 0.8 m long.If the string makes three revolution in 1.2 s,find the tension in the string.
To find the tension in the string, we can use the centripetal force equation:
F = (m * v^2) / r
Where:
F = tension in the string
m = mass of the object (0.5 kg)
v = velocity of the object
r = radius of the circular path (0.8 m)
To find the velocity of the object, we need to determine the circumference of the circular path. Since the object makes three revolutions in 1.2 seconds, we can calculate the time it takes for one revolution:
Time for one revolution = Total Time / Number of Revolutions
Time for one revolution = 1.2 s / 3 revolutions
Time for one revolution = 0.4 s
The velocity of the object is equal to the circumference of the circular path divided by the time for one revolution:
v = 2πr / (Time for one revolution)
v = 2 * 3.14 * 0.8 / 0.4
v = 12.56 m/s
Now we can substitute the values into the centripetal force equation to find the tension:
F = (m * v^2) / r
F = (0.5 kg * (12.56 m/s)^2) / 0.8 m
F = (0.5 kg * 157.7536 m^2/s^2) / 0.8 m
F = 78.8768 N
Therefore, the tension in the string is approximately 78.88 N.
To find the tension in the string, we need to apply Newton's second law of motion. Newton's second law states that the net force acting on an object is equal to the product of its mass and acceleration.
In this case, the acceleration of the object can be calculated using the centripetal acceleration formula:
a = (v^2) / r
Where:
a is the centripetal acceleration,
v is the linear velocity of the object, and
r is the radius of the circular path (which is equal to the length of the string).
First, let's calculate the linear velocity of the object. The number of revolutions made by the string in a given time indicates the number of complete circles that the object makes in that time. So in this case, the string makes three complete revolutions in 1.2 seconds.
To find the linear velocity, we can use the formula:
v = (2πr * n) / t
Where:
v is the linear velocity,
r is the radius,
n is the number of revolutions, and
t is the time.
Let's substitute the given values into the formula:
v = (2π * 0.8 m * 3) / 1.2 s
Simplifying the expression, we get:
v = 4π m/s
Now that we have the linear velocity, let's calculate the centripetal acceleration:
a = (v^2) / r
a = (4π)^2 m/s^2 / 0.8 m
a = 16π^2 m/s^2
Finally, we can determine the tension in the string using the equation:
F = m * a
Where:
F is the force (tension),
m is the mass of the object, and
a is the centripetal acceleration.
Substituting the given values:
F = 0.5 kg * 16π^2 m/s^2
Calculating the expression:
F ≈ 251.33 N
Therefore, the tension in the string is approximately 251.33 Newtons.
The tension in the string provides the centripetal force for objects tied to a string & movin in a circular path.
Ft = mv^2/r
where m=mass of d object, v=uniform velocity of d movin body & r=radius of d circle formed by d moving string
1 revolution = 360¡ã or 2pie radians
so 3rev = 2pie * 3radians = 6pie radians
time for 3rev = 1.2secs
angular vel. = ¦È/t
6pie / 1.2 = 5pie radians per sec
since pie = 3.142, so
5 * 3.14 = 15.7radians.sec
Tension = Mv^2/r
=0.5 * 15.7 / 0.8
= 9.81newtons
am not so sure bout d answer but try dis link to understand more wikihow-com/Calculate-Tension-in-Physics