Weight = (mass) x (gravity) = (100 kg) x (1.62 m/s^2) = 162 newtons.
Hi there!
(a)
Recall that:
![W = F \cdot d = Fdcos\theta](https://tex.z-dn.net/?f=W%20%3D%20F%20%5Ccdot%20d%20%3D%20Fdcos%5Ctheta)
W = Work (J)
F = Force (N)
d = Displacement (m)
Since this is a dot product, we only use the component of force that is IN the direction of the displacement. We can use the horizontal component of the given force to solve for the work.
![W =248(56)cos(30) = 12027.36 J](https://tex.z-dn.net/?f=W%20%3D248%2856%29cos%2830%29%20%3D%2012027.36%20J)
To the nearest multiple of ten:
![W_A = \boxed{12030 J}](https://tex.z-dn.net/?f=W_A%20%3D%20%5Cboxed%7B12030%20J%7D)
(b)
The object is not being displaced vertically. Since the displacement (horizontal) is perpendicular to the force of gravity (vertical), cos(90°) = 0, and there is NO work done by gravity.
Thus:
![\boxed{W_g = 0 J}](https://tex.z-dn.net/?f=%5Cboxed%7BW_g%20%3D%200%20J%7D)
(c)
Similarly, the normal force is perpendicular to the displacement, so:
![\boxed{W_N = 0 J}](https://tex.z-dn.net/?f=%5Cboxed%7BW_N%20%3D%200%20J%7D)
(d)
Recall that the force of kinetic friction is given by:
![F_{f} =\mu_k mg](https://tex.z-dn.net/?f=F_%7Bf%7D%20%3D%5Cmu_k%20mg)
Since the force of friction resists the applied force (assigned the positive direction), the work due to friction is NEGATIVE because energy is being LOST. Thus:
![W_f = -\mu_k mgd\\W_f = - (0.1)(56)(9.8)(56) = -3073.28 J](https://tex.z-dn.net/?f=W_f%20%3D%20-%5Cmu_k%20mgd%5C%5CW_f%20%3D%20-%20%280.1%29%2856%29%289.8%29%2856%29%20%3D%20-3073.28%20J)
In multiples of ten:
![\boxed{W_f = -3070 J}](https://tex.z-dn.net/?f=%5Cboxed%7BW_f%20%3D%20-3070%20J%7D)
(e)
Simply add up the above values of work to find the net work.
![W_{net} = W_A + W_f \\\\W_{net} = 12027.36 + (-3073.28) = 8954.08 J](https://tex.z-dn.net/?f=W_%7Bnet%7D%20%3D%20W_A%20%2B%20W_f%20%5C%5C%5C%5CW_%7Bnet%7D%20%3D%2012027.36%20%2B%20%28-3073.28%29%20%3D%208954.08%20J)
Nearest multiple of ten:
![\boxed{W_{net} = 8950 J}}](https://tex.z-dn.net/?f=%5Cboxed%7BW_%7Bnet%7D%20%3D%208950%20J%7D%7D)
(f)
Similarly, we can use a summation of forces in the HORIZONTAL direction. (cosine of the applied force)
![F_{net} = F_{Ax} - F_f](https://tex.z-dn.net/?f=F_%7Bnet%7D%20%3D%20F_%7BAx%7D%20-%20F_f)
![W = F_{net} \cdot d = (F_{Ax} - F_f)](https://tex.z-dn.net/?f=W%20%3D%20F_%7Bnet%7D%20%5Ccdot%20d%20%3D%20%28F_%7BAx%7D%20-%20F_f%29)
![W = (F_Acos(30) - \mu_k mg)d\\W = (248cos(30) - 0.1(56)(9.8)) * 56 \\\\W = 8954.08 J](https://tex.z-dn.net/?f=W%20%3D%20%28F_Acos%2830%29%20-%20%5Cmu_k%20mg%29d%5C%5CW%20%3D%20%28248cos%2830%29%20-%200.1%2856%29%289.8%29%29%20%2A%2056%20%5C%5C%5C%5CW%20%3D%208954.08%20J)
Nearest multiple of ten:
![\boxed{W_{net} = 8950 J}](https://tex.z-dn.net/?f=%5Cboxed%7BW_%7Bnet%7D%20%3D%208950%20J%7D)
Answer:
![E=88200\ J](https://tex.z-dn.net/?f=E%3D88200%5C%20J)
Explanation:
Given:
- mass of car,
![m=1500\ kg](https://tex.z-dn.net/?f=m%3D1500%5C%20kg)
- distance of skidding after the application of brakes,
![d=15\ m](https://tex.z-dn.net/?f=d%3D15%5C%20m)
- coefficient of kinetic friction,
![\mu_k=0.4](https://tex.z-dn.net/?f=%5Cmu_k%3D0.4)
<u>So, the energy dissipated during the skidding of car:</u>
<em>Frictional force:</em>
![f=\mu_k.N](https://tex.z-dn.net/?f=f%3D%5Cmu_k.N)
where N = normal reaction by ground on the car
![f=0.4\ties 1500\times 9.8](https://tex.z-dn.net/?f=f%3D0.4%5Cties%201500%5Ctimes%209.8)
![f=5880\ N](https://tex.z-dn.net/?f=%20f%3D5880%5C%20N)
<em>Now from the work-energy equivalence:</em>
![E=f.d](https://tex.z-dn.net/?f=E%3Df.d)
![E=5880\times 15](https://tex.z-dn.net/?f=E%3D5880%5Ctimes%2015)
is the dissipated energy.
Es el conjunto de longitudes de onda de todas las radiaciones electromagnéticas
Answer:
The kinetic energy of the mass at the instant it passes back through the equilibrium position is 0.06500 J.
Explanation:
Given that,
Mass = 2.15 kg
Distance = 0.0895 m
Amplitude = 0.0235 m
We need to calculate the spring constant
Using newton's second law
![F= mg](https://tex.z-dn.net/?f=F%3D%20mg)
Where, f = restoring force
![kx=mg](https://tex.z-dn.net/?f=kx%3Dmg)
![k=\dfrac{mg}{x}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7Bmg%7D%7Bx%7D)
Put the value into the formula
![k=\dfrac{2.15\times9.8}{0.0895}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7B2.15%5Ctimes9.8%7D%7B0.0895%7D)
![k=235.41\ N/m](https://tex.z-dn.net/?f=k%3D235.41%5C%20N%2Fm)
We need to calculate the kinetic energy of the mass
Using formula of kinetic energy
![K.E=\dfrac{1}{2}mv^2](https://tex.z-dn.net/?f=K.E%3D%5Cdfrac%7B1%7D%7B2%7Dmv%5E2)
Here, ![v = A\omega](https://tex.z-dn.net/?f=v%20%3D%20A%5Comega)
![K.E=\dfrac{1}{2}m\times(A\omega)^2](https://tex.z-dn.net/?f=K.E%3D%5Cdfrac%7B1%7D%7B2%7Dm%5Ctimes%28A%5Comega%29%5E2)
Here, ![\omega=\sqrt{\dfrac{k}{m}}^2](https://tex.z-dn.net/?f=%5Comega%3D%5Csqrt%7B%5Cdfrac%7Bk%7D%7Bm%7D%7D%5E2)
![K.E=\dfrac{1}{2}m\times A^2\sqrt{\dfrac{k}{m}}^2](https://tex.z-dn.net/?f=K.E%3D%5Cdfrac%7B1%7D%7B2%7Dm%5Ctimes%20A%5E2%5Csqrt%7B%5Cdfrac%7Bk%7D%7Bm%7D%7D%5E2)
![K.E=\dfrac{1}{2}kA^2](https://tex.z-dn.net/?f=K.E%3D%5Cdfrac%7B1%7D%7B2%7DkA%5E2)
Put the value into the formula
![K.E=\dfrac{1}{2}\times235.41\times(0.0235)^2](https://tex.z-dn.net/?f=K.E%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes235.41%5Ctimes%280.0235%29%5E2)
![K.E=0.06500\ J](https://tex.z-dn.net/?f=K.E%3D0.06500%5C%20J)
Hence, The kinetic energy of the mass at the instant it passes back through the equilibrium position is 0.06500 J.