Answer:
f' = 2 f
Explanation:
The frequency of the pendulum that swings in simple harmonic motion is given by :
Where
l is the length of pendulum
g is the acceleration due to gravity
If the length of the thread is increased by a factor of 4, such that, l' = 4 l, let f' is the new frequency such that,
f' = 2 f
So, the new frequency of the pendulum will become 2 time of initial frequency. Hence, the correct option is (b) "2f"
Answer:
68.8 N 13.8°N of W
Explanation:
F₁ is 50 N 30°N of W. The terminal angle is 150°.
F₂ is 25 N 20°S of W. The terminal angle is -160°.
Graphically, you can add the vectors using head-to-tail method. Move F₂ so that the tail of the vector is at the head of F₁. The resultant vector will be from the tail of F₁ to the head of F₂.
Algebraically, find the x and y components of each vector.
F₁ₓ = 50 N cos(150°) = -43.3 N
F₁ᵧ = 50 N sin(150°) = 25 N
F₂ₓ = 25 N cos(-160°) = -23.5 N
F₂ᵧ = 25 N sin(-160°) = -8.6 N
The x and y components of the resultant vector are the sums:
Fₓ = -43.3 N + -23.5 N = -66.8 N
Fᵧ = 25 N + -8.6 N = 16.4 N
The magnitude of the resultant force is:
F = √(Fₓ² + Fᵧ²)
F = √((-66.8 N)² + (16.4 N)²)
F = 68.8 N
The direction of the resultant force is:
θ = tan⁻¹(Fᵧ / Fₓ)
θ = tan⁻¹(16.4 N / -66.8 N)
θ = 166.2°
θ = 13.8°N of W
Answer:
a) 20 seconds
b) 600 m
Explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration
a) Speeder acceleration is 0 as the speed is constant
Police car
The distance they travel will be equal
Time required by the police car to catch the speeder is 20 seconds
b) The distance traveled by the police car will be 1.5×20² = 600 m
