The label has been scratched off a tuning fork and you need to know its frequency. From its size, you suspect that it is somewhe
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The mass M1 is 7.8 kg
Explanation:
Block M1 is hanging on the string while block M2 is on the frictionless ramp.
We have to write the equations of motion for the two blocks.
- For M1, the only two forces acting on it are the force of gravity (downward) and the tension in the string T (upward). So we can write
where
is the mass of the block
is the acceleration of gravity
is the acceleration of the system
- For M2, the only two forces acting on it are the tension in the string T (acting up along the ramp) and the component of the gravity acting down along the ramp, . So the equation of motion is
where
is the mass of the 2nd block
is the angle of the ramp
In order for the two blocks to be in equilibrium, the acceleration must be zero:
So the two equations become:
Isolating T from the 1st equation,
And substituting into the 2nd equation, we can find the value of the mass :
Learn more about acceleration and forces:
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m = mass of the ice added = ?
M = mass of water = 1.90 kg
= specific heat of the water = 4186 J/(kg ⁰C)
= specific heat of the ice = 2000 J/(kg ⁰C)
= latent heat of fusion of ice to water = 3.35 x 10⁵ J/kg
= initial temperature of ice = 0 ⁰C
= initial temperature of water = 79 ⁰C
T = final equilibrium temperature = 8 ⁰C
using conservation of heat
Heat gained by ice = Heat lost by water
m (T -
) + m
= M
(
- T)
inserting the values
m (4186) (8 - 0) + m (3.35 x 10⁵ ) = (1.90) (4186) (79 - 8)
m = 1.53 kg