This question involves the concepts of centripetal force and centripetal acceleration.
a) The centripetal acceleration for the piece of gum stuck to the outside edge of the record will be "6.67 m/s²".
b) The gum will have to overcome "0.033 N" centripetal force to remain stuck to the vinyl.
a)
The centripetal acceleration of the gum can be found using the following formula:
[tex]a_c=\frac{v^2}{r}[/tex]
where,
[tex]a_c[/tex] = centripetal acceleration = ?
v = linear speed of record = 1 m/s
r = radius of the record = [tex]\frac{diameter}{2}=\frac{0.3\ m}{2}=0.15\ m[/tex]
Therefore,
[tex]a_c=\frac{(1\ m/s)^2}{0.15\ m}\\\\a_c = 6.67\ m/s^2[/tex]
b)
Now, the centripetal force can be given as follows:
[tex]F_c=ma_c\\F_c=(0.005\ kg)(6.67\ m/s^2)\\F_c=0.033\ N[/tex]
Learn more about centripetal force here:
brainly.com/question/11324711?referrer=searchResults
The attached picture shows the centripetal force.
