Physics

posted by .

A ball and a thin plate are made from different materials and have the same initial temperature. The ball does not fit through a hole in the plate, because the diameter of the ball is slightly larger than the diameter of the hole. However, the ball will pass through the hole when the ball and the plate are both heated to a common higher temperature. In each of the arrangements in the drawing the diameter of the ball is 1.00 10-5 m larger than the diameter of the hole in the thin plate, which has a diameter of 0.09 m. The initial temperature of each arrangement is 27.3°C. At what temperature will the ball fall through the hole in each arrangement?
Please HELP!!!

  • Physics -

    hole d=0.09 m
    ball D=d+Δd=d+10⁻⁵m=0.09001 m
    t=27.3℃
    ΔL=αLΔT
    D+ΔD = d+Δd
    D+ α1•D•ΔT =d + α2•d•ΔT
    D-d = α2•d•ΔT - α1•D•ΔT= ΔT(α2•d- α1•D)
    ΔT = (D-d)/(α2•d- α1•D)= Δd/(α2•d- α1•D)
    Arrangement A:
    ball: Gold α1=14•10⁻⁶ (℃⁻)¹
    hole: Lead α2 = 29•10⁻⁶ (℃⁻)¹
    ΔT = Δd/(α2•d- α1•D) =
    =10⁻⁵/(29•10⁻⁶•0.09 - 14•10⁻⁶•0.09001) =
    =7.408°.
    t=27.3+7.408=34.708℃

    Arrangement B:
    Steel α1=12•10⁻⁶ (℃⁻)¹
    Aluminium α2 = 23•10⁻⁶ (℃⁻)¹
    ΔT = Δd/(α2•d- α1•D)=...
    Arramgment C:
    Quartz α1=0.5•10⁻⁶ (℃⁻)¹
    Silver α2 = 19•10⁻⁶ (℃⁻)¹
    ΔT = Δd/(α2•d- α1•D)=...

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. physics

    a crane drops a .3 kg steel ball onto a steel plate. the ball's speeds just before impact and after are 4.5 m/s and 4.2 m/s respectively. If the ball is in contact with the plate for .03 s, what is the magnitude of the average force …
  2. PHysics

    A baseball pitcher throws a ball horizontally under negligible air resistance. The ball falls 83cm in travelling 18.4 m to the home plate. Determine the ball's initial horizontal speed.
  3. Physics

    How do i get the answer A steel ball of diameter Lb = 4.196 cm is placed on a hole of diameter Lh = 4.042 cm on an aluminium plate. The initial temperature is 14 ¢XC. What would be the minimum temperature so that the ball will fit …
  4. Physics: urgent help needed

    i have a test on monday 1 A beach ball is thrown straight up with a speed of 10m/s from a point 2 m above the ground a) Assuming no air reistance, calculate how far up the ball will go b)At what speed will the ball eventually hit the …
  5. physics

    You are playing right field for the baseball team. Your team is up by one run in the bottom of the last inning of the game when a ground ball slips through the infield and comes straight toward you. As you pick up the ball 62 m from …
  6. Physics

    A 20lb ball is 1 ft. in diameter and has a angular velocity of 300 rpm when it is 2 ft. away from the plate. The coefficient of rolling friction between the surface and the ball is μs = 0.3. It strikes the 1-ft. high, 10-lb plate …
  7. Physics

    In a quality control test a steel ball with mass M falls a distance of H and bounces off a steel plate and through a hole in the wall into the ok bucket. If the ball bounces up a distance of 9/10H after hitting that plate and has a …
  8. Physics

    A 4.55 kg steel ball is dropped onto a copper plate from a height of 10.0 m. If the ball leaves a dent 2.80 mm deep in the plate, what is the average force exerted by the plate on the ball during the impact?
  9. Physics

    I have a few physics questions that I don't understand. Two are thermal expansion problems and the other is an ideal gas law problem. 1. Two rods, one made of iron and the other of aluminum, have the same initial length at 64.00 deg. …
  10. Physics

    A plate made of steel has a 18.9979 mm diameter hole cut into it. A 19.0000 mm diameter ball made of glass is sitting in the hole. Both are at an initial temperature of 9.00 deg. C. If the plate and ball are both heated, at what temperature …

More Similar Questions