Question

Say you want to make a sling by swinging a mass M of 2.3 kg in a horizontal circle of radius 0.034 m, using a string of length 0.034 m. You wish the mass to have a kinetic energy of 13.0 Joules when released. How strong will the string need to be

Answer 1

T = 764.41 N

Step-by-step explanation:

In this case the tension of the string is determined by the centripetal force. The formula to calculate the centripetal force is given by:

`F_c=m(v^2)/(r)` (1)

m: mass object = 2.3 kg

r: radius of the circular orbit = 0.034 m

v: tangential speed of the object

However, it is necessary to calculate the velocity v first. To find v you use the formula for the kinetic energy:

`K=(1)/(2)mv^2`

You have the value of the kinetic energy (13.0 J), then, you replace the values of K and m, and solve for v^2:

`v^2=(2K)/(m)=(2(13.0J))/(2.3kg)=11.3(m^2)/(s^2)`

you replace this value of v in the equation (1). Also, you replace the values of r and m:

`F_c=(2.3kg)((11.3m^2/s^2)/(0.034))=764.41N`

hence, the tension in the string must be T = Fc = 764.41 N