Answer:
Distance is 100m, displacement is 0m
Explanation:
Distance is how much you travelled in total (100m)
Displacement is when you compare your final and initial positions.
It is usually Final position - Initial position.
Since you start and finish at the same point, it would be 0 - 0 = 0m
So the displacement is 0m.
Answer:
a) τ = 4.47746 * 10^25 N-m
b) E = 2.06301 * 10^13 J
c) P = 3.25511*10^21 W
Explanation:
Given:
- The radius of earth r = 6.3781×10^6 m
- The angular speed of earth w = 7.27*10^-5 rad/s
- The time taken to reach above speed t = 5 yrs = 1.57784760 * 10^8 s
- The mass of earth m = 5.972 × 10^24 kg
- The inertia of sphere I = 2/5 * m* r^2
Solution:
- The angular acceleration of the earth from rest to w is given by α:
α = w / t
α = (7.27*10^-5) / (1.57784760 * 10^8)
α = 4.60754*10^-13 rad/s^2
- The required torque τ is given by:
τ = I*α
τ = 2/5 * m* r^2 * α
τ = 2/5 *(5.972 × 10^24) * (6.3781×10^6)^2 * (4.60754*10^-13)
τ = 4.47746 * 10^25 N-m
- The power required P to turn the earth to the speed w is:
P = τ*w
P = (4.47746 * 10^25)*(7.27*10^-5)
P = 3.25511*10^21 W
- The energy E required is :
E = P / t
E = (3.25511*10^21) / (1.57784760 * 10^8)
E = 2.06301 * 10^13 J
Answer:
ω = √(2T / (mL))
Explanation:
(a) Draw a free body diagram of the mass. There are two tension forces, one pulling down and left, the other pulling down and right.
The x-components of the tension forces cancel each other out, so the net force is in the y direction:
∑F = -2T sin θ, where θ is the angle from the horizontal.
For small angles, sin θ ≈ tan θ.
∑F = -2T tan θ
∑F = -2T (Δy / L)
(b) For a spring, the restoring force is F = -kx, and the frequency is ω = √(k/m). (This is derived by solving a second order differential equation.)
In this case, k = 2T/L, so the frequency is:
ω = √((2T/L) / m)
ω = √(2T / (mL))
"watt" means "Joule of energy per second"
"60 watts" means "60 Joules per second"
(60 joules per second) x (5 seconds) = <em>300 Joules of energy</em>
Left. Opposite of the direction the box is pushed.
