First we will find the speed of the ball just before it will hit the floor
so in order to find the speed of the cart we will first use energy conservation
![KE_i + PE_i = KE_f + PE_f](https://tex.z-dn.net/?f=KE_i%20%2B%20PE_i%20%3D%20KE_f%20%2B%20PE_f)
![\frac{1}{2}mv_i^2 + mgh = \frac{1}{2}mv_f^2 + 0](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7Dmv_i%5E2%20%2B%20mgh%20%3D%20%5Cfrac%7B1%7D%7B2%7Dmv_f%5E2%20%2B%200)
![\frac{1}{2}(1.25)(52)^2 + 1.25(9.8)(225) = \frac{1}{2}(1.25)v_f^2](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%281.25%29%2852%29%5E2%20%2B%201.25%289.8%29%28225%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%281.25%29v_f%5E2)
So by solving above equation we will have
![v_f = 84.3 m/s](https://tex.z-dn.net/?f=v_f%20%3D%2084.3%20m%2Fs)
now in order to find the momentum we can use
![P = mv](https://tex.z-dn.net/?f=P%20%3D%20mv)
![P = 1.25 \times 84.3](https://tex.z-dn.net/?f=P%20%3D%201.25%20%5Ctimes%2084.3)
![P = 105.4 kg m/s](https://tex.z-dn.net/?f=P%20%3D%20105.4%20kg%20m%2Fs)
Answer:
10.55111 m/s²
Explanation:
M = Mass of Saturn = ![95\times 5.972\times 10^{24}\ kg](https://tex.z-dn.net/?f=95%5Ctimes%205.972%5Ctimes%2010%5E%7B24%7D%5C%20kg)
r = Radius of Saturn = ![9.4\times 6.371\times 10^6\ m](https://tex.z-dn.net/?f=9.4%5Ctimes%206.371%5Ctimes%2010%5E6%5C%20m)
G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²
Acceleration due to gravity is given by
![g=\dfrac{GM}{r^2}\\\Rightarrow g=\dfrac{6.67\times 10^{-11}\times 95\times 5.972\times 10^{24}}{(9.4\times 6.371\times 10^6)^2}\\\Rightarrow g=10.55111\ m/s^2](https://tex.z-dn.net/?f=g%3D%5Cdfrac%7BGM%7D%7Br%5E2%7D%5C%5C%5CRightarrow%20g%3D%5Cdfrac%7B6.67%5Ctimes%2010%5E%7B-11%7D%5Ctimes%2095%5Ctimes%205.972%5Ctimes%2010%5E%7B24%7D%7D%7B%289.4%5Ctimes%206.371%5Ctimes%2010%5E6%29%5E2%7D%5C%5C%5CRightarrow%20g%3D10.55111%5C%20m%2Fs%5E2)
The acceleration due to gravity on Saturn is 10.55111 m/s²
Answer:
5 N acting in the same direction as the 10 N force
Explanation:
10+5=15
15=15
Answer:
Physical science, Earth science, and life science.
Answer:
F₃ = 122.88 N
θ₃ = 20.63°
Explanation:
First we find the components of F₁:
For x-component:
F₁ₓ = F₁ Cos θ₁
F₁ₓ = (50 N) Cos 60°
F₁ₓ = 25 N
For y-component:
F₁y = F₁ Sin θ₁
F₁y = (50 N) Sin 60°
F₁y = 43.3 N
Now, for F₂. As, F₂ acts along x-axis. Therefore, its y-component will be zero and its x-xomponent will be equal to the magnitude of force itself:
F₂ₓ = F₂ = 90 N
F₂y = 0 N
Now, for the resultant force on ball to be zero, the sum of x-components of the forces and the sum of the y-component of the forces must also be equal to zero:
F₁ₓ + F₂ₓ + F₃ₓ = 0 N
25 N + 90 N + F₃ₓ = 0 N
F₃ₓ = - 115 N
for y-components:
F₁y + F₂y + F₃y = 0 N
43.3 N + 0 N + F₃y = 0 N
F₃y = - 43.3 N
Now, the magnitude of F₃ can be found as:
F₃ = √F₃ₓ² + F₃y²
F₃ = √[(- 115 N)² + (- 43.3 N)²]
<u>F₃ = 122.88 N</u>
and the direction is given as:
θ₃ = tan⁻¹(F₃y/F₃ₓ) = tan⁻¹(-43.3 N/-115 N)
<u>θ₃ = 20.63°</u>