The incline is frictionless, this means we can use the conservation of energy: the initial kinetic energy of the block
![K= \frac{1}{2}mv^2](https://tex.z-dn.net/?f=K%3D%20%5Cfrac%7B1%7D%7B2%7Dmv%5E2%20)
is converted into gravitational potential energy
![U=mgh](https://tex.z-dn.net/?f=U%3Dmgh)
where h is the height reached by the block as it stops. By equalizing the two formulas, we get
![\frac{1}{2} mv^2=mgh](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20mv%5E2%3Dmgh)
![h= \frac{v^2}{2g}= \frac{(12.0 m/s)^2}{2(9.81 m/s^2)} =7.3 m](https://tex.z-dn.net/?f=h%3D%20%5Cfrac%7Bv%5E2%7D%7B2g%7D%3D%20%5Cfrac%7B%2812.0%20m%2Fs%29%5E2%7D%7B2%289.81%20m%2Fs%5E2%29%7D%20%3D7.3%20m%20)
However, this is the maximum height reached by the block. The distance along the surface of the plane is given by:
Answer:
24cm from the surface
Explanation:
Equation for refraction
n2/v- n1/u = n2-n1/R
= u = infinity ( parallel)
2/v= (2-1)/R
V = 2R
V= 24cm
Answer:
decrease
Explanation:
Rate of production of heat = 100 J/s
Rate of heat flowing out = 200 J/s
As the rate of flowing heat is more than the rate of generating heat so the temperature of body will decrease.
Answer:
x = D (M/M-m) 2.41
Explanation:
a) Let's apply Newton's second law to find the summation of force, where each force is given by the law of universal gravitation
F = g m₁m₂ / r²
Σ F = 0
F1- F2 = 0
F1 = F2
We set the reference system in the body of greatest mass (M) the planet
F1 = g m₁ M / x²
F2 = G m1 m / (D-x)²
G m₁ M / x² = G m₁ m / (D-x)²
M (D-x)² = m x²
MD² -2MD x + M x² = m x²
x² (M-m) -2MD x + MD² = 0
We solve the second degree equation
x = [2MD ±√ (4M²D² - 4 (M-m) MD²)] / 2 (M-m)
x = {2MD ± 2D √ (M² + (M-m) M)} / 2 (M-m)
x = D {M ± Ra (2M²-mM)} / (M-m)
x = D (M ± M √ (2-m/M)) / (M-m)
x = D (M / (M-m)) (1 ±√ (2-m/M)
Let's analyze this result, the value of M-m >> 1, so if we take the negative root, the value of x would be negative, it is out of the point between the two bodies, so the correct result must be taken with the positive root
x = D (M / (M-m)) (1 + √2)
x = D (M/M-m) 2.41
b) X = 2/3 D
x = D (M/M-m) 2.41
2/3 D = D (M/(M-m)) 2.41
2/3 (M-m) = M 2.41
2/3 M - 2/3 m = 2.41 M
1.743 M = 0.667 m
M/m = 0.667/1.743
M/m = 0.38