m₁ = 2.3 kg <span>
θ₁ = 70° </span><span>
θ₂ = 17° </span><span>
g = 9.8 m/s²
->The component of the gravitational force on m₁ that is parallel down the incline is: </span><span>
F₁ = m₁ × g × sin(θ₁) </span><span>
F₁ = (2.3
kg) × (9.8 m/s²) × sin(70°) = 21.18 N </span><span>
->The component of the gravitational force on m₂ that is parallel down the incline is: </span><span>
F₂ = m₂ × g × sin(θ₂) </span><span>
F₂ = m₂ × (9.8 m/s²) × sin(70°) = m₂ × (2.86 m/s²) </span><span>
Then the total mass of the system is:
m = m₁ + m₂ </span><span>
m = (2.3 kg) + m₂ </span><span>
If it is given that m₂ slides down the incline, then F₂ must be bigger than F₁, </span><span>
and so the net force on the system must be:
F = m₂×(2.86
m/s²) - (21.18 N) </span><span>
Using Newton's second law, we know that
F = m × a
So if we want the acceleration to be 0.64 m/s², then
m₂×(2.86
m/s²) - (21.18 N) = [(2.3 kg) + m₂] ×
(0.64 m/s²) </span><span>
m₂×(2.86
m/s²) - (21.18 N) = (1.47 N) + m₂×(0.64
m/s²) </span><span>
m₂×(2.22
m/s²) = (22.65 N) </span><span>
m₂<span> = 10.2
kg</span></span>
Answer:
See below ~
Explanation:
An object will sink in water when its density is greater than that of water, which is 1 g/cm³.
Volume of the box is <u>1331 cm³</u>. (11³)
Maximum mass of sand will be 1331 g. [because 1331/1331 = 1 g/cm³]
- Volume of sand = Mass of sand / Density of sand
- Volume (sand) = 1331/3.5
- Volume (sand) = 380.29 cm³
If the volume of sand is <u>greater than 380.29 cm³</u>, the box will sink in water.
Answer:
The conservation of energy should be used to answer this question.
a)
At the position where the spring is unstretched, the elastic potential energy of the spring is zero.
since 
and 
is equal to zero.
The roots of this quadratic equation can be solved by using discriminant.
We should use the positive root, so
x = 0.292 m.
b)
We should use energy conservation between the point where the spring is momentarily at rest, and the point where the spring is unstretched.
since the kinetic energy at point 2 and the potential energy at point 3 is equal to zero.
Explanation:
In questions with springs, the important thing is to figure out the points where kinetic or potential energy terms would be zero. When the spring is unstretched, the elastic potential energy is zero. And when the spring is at rest, naturally the kinetic energy is equal to zero.
In part b) the cookie slides back to its original position, so the distance traveled, x, is equal to the distance in part a). The frictional force is constant in the system, so it is quite simple to solve part b) after solving part a).
