Can someone please help me with this? A steel ball bearing is 5 cm in diameter a
ID: 2252532 • Letter: C
Question
Can someone please help me with this?A steel ball bearing is 5 cm in diameter at 29 degrees Celsius. A bronze plate has a hole that is 4.995 cm. in diameter at 29 degrees Celsius. What common temperature must they have in order for the ball to just squeeze through the hole? Answer in units of degrees Celsius. Can someone please help me with this?
A steel ball bearing is 5 cm in diameter at 29 degrees Celsius. A bronze plate has a hole that is 4.995 cm. in diameter at 29 degrees Celsius. What common temperature must they have in order for the ball to just squeeze through the hole? Answer in units of degrees Celsius.
Explanation / Answer
As the metals heat up, they expand. The bronze plate expands, making the hole bigger, but steel ball will also get bigger. The amount that they expand depends on a characterstic value called the "coefficient of linear expansion". It is about 13E-6/K for steel and about 18E-6/K for bronze. Since the bronze number is more than steel, it the ring will grow faster than the ball as the temperature rises. At some point, the hole size will "catch up" to the ball size.
Use the equation L1 = L0 (1 + a(T1-T0)),
where L1 is the resulting length, L0 is the starting length, a is the coefficient, and T1-T0 is the change in temperature.
For bronze L1 = 4.995(1 + 18E-6(T-30)),
for steel L1 = 5(1 + 13E-6(T-30).
Set the equal and solve for T
4.995(1 + 18E-6(T-30)) = 5(1 + 13E-6(T-30))
T = 230.723 degrees