Physics, 16.11.2019 09:31 latoyatuggle23

Ablock of wood with the density of 780 kg/m^3 has a cubic shape with sides 0.259m long. a cord of negligible mass is used to tie a piece of lead to the bottom of the wood. the lead pulls the wood into the water until it is just completely covered with water. what is the mass of lead? density of water 1000kg/m^3 and density of lead 11300 kg/m^3

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Answer from: barbar12345

3.828 kg

Explanation:

m - mass of lead

gravitational acceleration =9.81 ms⁻²

Vwood - volume of the wood cube

d(water) - density of water

d(wood) - density of wood

Vwood= $(0.259 m)^{3} =0.0174 m^{3}$

Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces

assuming the equillibrium state

weight of lead + weight of wood = upthrust for the cube

$\\m*g+Vwood*d_(wood)*g=Vwood*d(water)*g\\m*9.81 + 0.0174*780*9.81 = 0.0174*1000*9.81 \\m=3.828 kg$

Answer from: Quest

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

$f\alpha \frac{dp}{dt}$

⇒ $f= k \frac{dp}{dt}$

here k is the proportionality constant whose value is 1.

$f=\frac{dp}{dt}$

$f= \frac{d[mv]}{dt}$

$f= m\frac{dv}{dt} +v\frac{dm}{dt}$

$f=ma+v\frac{dm}{dt}$ [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

Answer from: Quest

answer: 31, 5556. 952 seconds

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