Answer to Question #157322 in Classical Mechanics for Diego Hernandez

Question

. A 3 kg object travels in a uniform circle at a constant speed of 10 m/s. The centripetal force acting on the object is 150 Newtons.

a.     Calculate the weight of the object.

 

 

 

 

 

b.     Calculate the centripetal acceleration of the object. 

 

 

 

 

 

c.    Calculate the radius of the circle.

 

 

 

 

 

d.     Calculate the circumference of the circle.

 

  

 

 

e.     Calculate the time required for the object to complete one full circle.

Answer 1

a) We can find the weight of the object from the formula:

$$W=mg=3\ kg\cdot9.8\ \dfrac{m}{s^2}=29.4\ N.$$

b)-c) Let's first find the radius of the circle:

$$F_c=\dfrac{mv^2}{r},$$ $$r=\dfrac{mv^2}{F_c}=\dfrac{3\ kg\cdot(10\ \dfrac{m}{s})^2}{150\ N}=2\ m.$$

Finally, we can find the centripetal acceleration:

$$a_c=\dfrac{v^2}{r}=\dfrac{(10\ \dfrac{m}{s})^2}{2\ m}=50\ \dfrac{m}{s^2}.$$

d) We can find the circumference of the circle from the formula:

$$C=2\pi r=2\pi\cdot2\ m=12.56\ m.$$

e) We can find the time required for the object to complete one full circle from the formula:

$$T=\dfrac{C}{v}=\dfrac{12.56\ m}{10\ \dfrac{m}{s}}=1.26\ s.$$