Consider the upward direction of motion as positive and downward direction of motion as negative.
a = acceleration due to gravity in downward direction = - 9.8 ![\frac{m }{s^{2}}](https://tex.z-dn.net/?f=%5Cfrac%7Bm%20%7D%7Bs%5E%7B2%7D%7D)
v₀ = initial velocity of rock in upward direction = ?
v = final velocity of rock at the highest point = 0 ![\frac{m }{s}](https://tex.z-dn.net/?f=%5Cfrac%7Bm%20%7D%7Bs%7D)
t = time to reach the maximum height = 4.2 sec
Using the kinematics equation
v = v₀ + a t
inserting the values
0 = v₀ + (- 9.8) (4.2)
v₀ = 41.2 ![\frac{m }{s}](https://tex.z-dn.net/?f=%5Cfrac%7Bm%20%7D%7Bs%7D)
Answer:
![f2/f1 = \sqrt{2}](https://tex.z-dn.net/?f=%20f2%2Ff1%20%3D%20%5Csqrt%7B2%7D%20)
Explanation:
From frequency of oscillation
![f = 1/2pi *\sqrt{k/m}](https://tex.z-dn.net/?f=%20f%20%3D%201%2F2pi%20%2A%5Csqrt%7Bk%2Fm%7D%20)
Initially with the suspended string, the above equation is correct for the relation, hence
![f1 = 1/2pi *\sqrt{k/m}](https://tex.z-dn.net/?f=%20f1%20%3D%201%2F2pi%20%2A%5Csqrt%7Bk%2Fm%7D%20)
where k is force constant and m is the mass
When the spring is cut into half, by physics, the force constant will be doubled as they are inversely proportional
![f2 = 1/2pi *\sqrt{2k/m}](https://tex.z-dn.net/?f=%20f2%20%3D%201%2F2pi%20%2A%5Csqrt%7B2k%2Fm%7D%20)
Employing f2/ f1, we have
![f2/f1 = \sqrt{2}](https://tex.z-dn.net/?f=%20f2%2Ff1%20%3D%20%5Csqrt%7B2%7D%20)
Answer:
Initial concentration of the reactant = 3.34 × 10^(-2)M
Explanation:
Rate of reaction = 2.30×10−4 M/s,
Time of reaction = 80s
Final concentration = 1.50×10−2 M
Initial concentration = Rate of reaction × Time of reaction + Final concentration
= 2.30×10−4 M/s × 80s + 1.50×10−2 M = 3.34 × 10^(-2)M
Initial concentration = 3.34 × 10^(-2)M
Answer:
Loss, ![\Delta E=-10.63\ J](https://tex.z-dn.net/?f=%5CDelta%20E%3D-10.63%5C%20J)
Explanation:
Given that,
Mass of particle 1, ![m_1=m =0.66\ kg](https://tex.z-dn.net/?f=m_1%3Dm%20%3D0.66%5C%20kg)
Mass of particle 2, ![m_2=7.4m =4.884\ kg](https://tex.z-dn.net/?f=m_2%3D7.4m%20%3D4.884%5C%20kg)
Speed of particle 1, ![v_1=2v_o=2\times 6=12\ m/s](https://tex.z-dn.net/?f=v_1%3D2v_o%3D2%5Ctimes%206%3D12%5C%20m%2Fs)
Speed of particle 2, ![v_2=v_o=6\ m/s](https://tex.z-dn.net/?f=v_2%3Dv_o%3D6%5C%20m%2Fs)
To find,
The magnitude of the loss in kinetic energy after the collision.
Solve,
Two particles stick together in case of inelastic collision. Due to this, some of the kinetic energy gets lost.
Applying the conservation of momentum to find the speed of two particles after the collision.
![m_1v_1+m_2v_2=(m_1+m_2)V](https://tex.z-dn.net/?f=m_1v_1%2Bm_2v_2%3D%28m_1%2Bm_2%29V)
![V=\dfrac{m_1v_1+m_2v_2}{(m_1+m_2)}](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7Bm_1v_1%2Bm_2v_2%7D%7B%28m_1%2Bm_2%29%7D)
![V=\dfrac{0.66\times 12+4.884\times 6}{(0.66+4.884)}](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7B0.66%5Ctimes%2012%2B4.884%5Ctimes%206%7D%7B%280.66%2B4.884%29%7D)
V = 6.71 m/s
Initial kinetic energy before the collision,
![K_i=\dfrac{1}{2}(m_1v_1^2+m_2v_2^2)](https://tex.z-dn.net/?f=K_i%3D%5Cdfrac%7B1%7D%7B2%7D%28m_1v_1%5E2%2Bm_2v_2%5E2%29)
![K_i=\dfrac{1}{2}(0.66\times 12^2+4.884\times 6^2)](https://tex.z-dn.net/?f=K_i%3D%5Cdfrac%7B1%7D%7B2%7D%280.66%5Ctimes%2012%5E2%2B4.884%5Ctimes%206%5E2%29)
![K_i=135.43\ J](https://tex.z-dn.net/?f=K_i%3D135.43%5C%20J)
Final kinetic energy after the collision,
![K_f=\dfrac{1}{2}(m_1+m_2)V^2](https://tex.z-dn.net/?f=K_f%3D%5Cdfrac%7B1%7D%7B2%7D%28m_1%2Bm_2%29V%5E2)
![K_f=\dfrac{1}{2}(0.66+4.884)\times 6.71^2](https://tex.z-dn.net/?f=K_f%3D%5Cdfrac%7B1%7D%7B2%7D%280.66%2B4.884%29%5Ctimes%206.71%5E2)
![K_f=124.80\ J](https://tex.z-dn.net/?f=K_f%3D124.80%5C%20J)
Lost in kinetic energy,
![\Delta K=K_f-K_i](https://tex.z-dn.net/?f=%5CDelta%20K%3DK_f-K_i)
![\Delta K=124.80-135.43](https://tex.z-dn.net/?f=%5CDelta%20K%3D124.80-135.43)
![\Delta E=-10.63\ J](https://tex.z-dn.net/?f=%5CDelta%20E%3D-10.63%5C%20J)
Therefore, the magnitude of the loss in kinetic energy after the collision is 10.63 Joules.
Answer:
10N to the left side towards you
Explanation:
The net force is the resultant force that acts on a body.
Force is a push or pull on a body.
Push to left side = 25N
Pull to the right = 15N
Net force = Push to left side - Pull to the right = 25N - 15N
Net force = 10N to the left side towards you
The net force is therefore 10N to the left side towards you