# Physics

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?

1. 👍 1
2. 👎 0
3. 👁 2,218
1. 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)=...

1. 👍 1
2. 👎 0

## Similar Questions

1. ### Physics

A batter hits a ball and it is caught 4 seconds later 100 meters from home plate. What is the initial velocity of the ball?

2. ### Physics

A tennis player hits a ball at ground level, giving it an initial velocity of 24 m/s at 57 degrees above the horizontal. (a) what are the horizontal and verticla components of the ball;s initial velocity? (b) how high above the

3. ### PHYSICS

A batter hits a fly ball which leaves the bat 0.90 m above the ground at an angle of 61 degrees with an initial speed of 28 m/s heading towards center field. Ignore air resistance. (a) How far from the home plate would the ball

4. ### physics

when babe ruth hit a homer over the 7.5-m-high right field fence 95 m from home plate, roughly what wa the minimum speed of the ball when it left the bat? Assume the ball wa hit 1.0 m above the ground and it path initially made a

1. ### Physics

A soccer ball is kicked with an initial horizonal velocity of 18 m/s and an initial vertical velocity of 18 m/s. 1) What is the initial speed of the ball? 2)What is the initial angle of the ball with respect to the ground? 3)What

2. ### PHYSICS

The figure shows a ball with mass m = 0.405 kg attached to the end of a thin rod with length L = 0.516 m and negligible mass. The other end of the rod is pivoted so that the ball can move in a vertical circle. The rod is held

3. ### Physics

Ted Williams hits a baseball with an initial velocity of 120 miles per hour (176 ft/s) at an angle of θ = 35 degrees to the horizontal. The ball is struck 3 feet above home plate. You watch as the ball goes over the outfield wall

4. ### PHYSICS CENTER OF MASS

A thin rectangular plate of uniform areal density σ = 2.79 kg/m2 has length of 37.0 cm and width of 23.0 cm. The lower left hand corner is located at the origin, (x,y)= (0,0) and the length is along the x-axis. (a)There is a

1. ### Calculus 1

A ball is thrown vertically upward from ground level with initial velocity of 96 feet per second. Assume the acceleration of the ball is a(t) = -32 ft^2 per second. (Neglect air Resistance.) (a) How long will it take the ball to

2. ### 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?

3. ### physics

A baseball player hits a home run over the left-field fence, which is 104 m from home plate. The ball is hit at a point 1.04 m directly above home plate, with an initial velocity directed 28.5° above the horizontal. By what

4. ### 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.