Hannah comes to a rest in <em>t</em> = 0.4 s, so her acceleration is
<em>a</em> = (0 - 25 m/s) / (0.4 s) = -62.5 m/s²
(that is, the acceleration points in the direction opposing her movement forward as she brakes)
Then the force exerted on her by the seatbelt has magnitude
<em>F</em> = (65 kg) (62.5 m/s²) = 4062.5 N ≈ 4063 N
Complete Question
The complete question is shown on the first uploaded image
Answer:
the change in energy of the block due to friction is ![E = -126 \ J](https://tex.z-dn.net/?f=E%20%3D%20-126%20%5C%20J)
Explanation:
From the question we are told that
The frictional force is ![F_f = 21 \ N](https://tex.z-dn.net/?f=F_f%20%20%3D%20%2021%20%5C%20N)
The mass of the block is ![m_b = 8 \ kg](https://tex.z-dn.net/?f=m_b%20%20%3D%208%20%5C%20kg)
The length of the ramp is ![l = 6 \ m](https://tex.z-dn.net/?f=l%20%3D%20%206%20%5C%20m)
The height of the block is ![h = 2 \ m](https://tex.z-dn.net/?f=h%20%3D%202%20%5C%20m)
The change in energy of the block due to friction is mathematically represented as
![\Delta E = - F_s * l](https://tex.z-dn.net/?f=%5CDelta%20E%20%20%3D%20%20-%20F_s%20%20%2A%20l)
The negative sign is to show that the frictional force is acting against the direction of the block movement
Now substituting values
![\Delta E = -(21)* 6](https://tex.z-dn.net/?f=%5CDelta%20E%20%20%3D%20%20-%2821%29%2A%20%206)
![\Delta E = -126 \ J](https://tex.z-dn.net/?f=%5CDelta%20E%20%3D%20-126%20%5C%20J)
Answer:
![36.4276\ m/s^2](https://tex.z-dn.net/?f=36.4276%5C%20m%2Fs%5E2)
Explanation:
m = Mass of stick
L = Length of stick = 1 m
h = Center of mass of stick = ![\dfrac{1}{2}=0.5\ m](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D%3D0.5%5C%20m)
g = Acceleration due to gravity
T = Time period = 0.85 s
Time period is given by
![T=2\pi\sqrt{\dfrac{I}{mgh}}](https://tex.z-dn.net/?f=T%3D2%5Cpi%5Csqrt%7B%5Cdfrac%7BI%7D%7Bmgh%7D%7D)
Moment of inertia is given by
![I=m\dfrac{L^2}{3}](https://tex.z-dn.net/?f=I%3Dm%5Cdfrac%7BL%5E2%7D%7B3%7D)
![T=2\pi\sqrt{\dfrac{m\dfrac{L^2}{3}}{mgh}}\\\Rightarrow T=2\pi\sqrt{\dfrac{L^2}{3gh}}\\\Rightarrow g=\dfrac{4\pi^2L^2}{3hT^2}\\\Rightarrow g=\dfrac{4\pi^2\times 1^2}{3\times 0.5\times 0.85^2}\\\Rightarrow g=36.4276\ m/s^2](https://tex.z-dn.net/?f=T%3D2%5Cpi%5Csqrt%7B%5Cdfrac%7Bm%5Cdfrac%7BL%5E2%7D%7B3%7D%7D%7Bmgh%7D%7D%5C%5C%5CRightarrow%20T%3D2%5Cpi%5Csqrt%7B%5Cdfrac%7BL%5E2%7D%7B3gh%7D%7D%5C%5C%5CRightarrow%20g%3D%5Cdfrac%7B4%5Cpi%5E2L%5E2%7D%7B3hT%5E2%7D%5C%5C%5CRightarrow%20g%3D%5Cdfrac%7B4%5Cpi%5E2%5Ctimes%201%5E2%7D%7B3%5Ctimes%200.5%5Ctimes%200.85%5E2%7D%5C%5C%5CRightarrow%20g%3D36.4276%5C%20m%2Fs%5E2)
The acceleration of gravity on this planet is ![36.4276\ m/s^2](https://tex.z-dn.net/?f=36.4276%5C%20m%2Fs%5E2)
A
The horizontal force cancels out. The two 4Ns go in opposite directions. So they don't affect the outcome.
The Vertical force is 6N up - 2 N down = 4 N Up
Answer 4 N up
B
The horizontal and vertical forces cancel out. Each gives 3N - 3N =0
The net force is 0
C
You only have horizontal forces on this one
5N - 3N = 2N
The answer is 2N to the right.