Answer:
a ) 2.68 m / s
b ) 1.47 m
Explanation:
The jumper will go down with acceleration as long as net force on it becomes zero . Net force of (mg - kx ) will act on it where kx is the restoring force acting in upward direction.
At the time of equilibrium
mg - kx = 0
x = mg / k
= (60 x 9.8 ) / 800
= 0.735 m
At this moment , let its velocity be equal to V
Applying conservation of energy
kinetic energy of jumper + elastic energy of cord = loss of potential energy of the jumper
1/2 m V² + 1/2 k x² = mg x
.5 x 60 x V² + .5 x 800 x .735 x .735 = 60 x 9.8 x .735
30 V² + 216.09 = 432.18
V = 2.68 m / s
b ) At lowest point , kinetic energy is zero and loss of potential energy will be equal to stored elastic energy.
1/2 k x² = mgx
x = 2 m g / k
= (2 x 60 x 9.8) / 800
= 1.47 m
Answer:
(a) 9.375 N/m
(b) 0.5024 m/s
(c) 0.01 kg/s
Explanation:
mass of head, m = 15 g = 0.015 kg
frequency, f = 4 Hz
Time period, T = 1 / f = 0.25 s
Let k is the spring constant.
(a)
The formula for the time period is



K = 9.375 N/m
(b)
Amplitude, A = 2 cm
Let ω is the angular velocity.
Maximum velocity, v = A ω = A x 2πf
v = 0.02 x 2 x 3.14 x 4 = 0.5024 m/s
(c)
Let b is the damping constant.
A(t = 4s) = 0.5 cm
Ao = 2 cm
Using the formula of damping



Taking natural log on both the sides
ln (0.25) = - 133.3 b
- 133.3 b = - 1.386
b = 0.01 kg/s
Answer:
Explanation:
Given
mass of Point object 
Distance 
Since mass is moving in circular path therefore every time mass is at distance of r from center .
Also Moment of Inertia tells about the distribution of mass over the given region with respect to center of mass.
Therefore 


The speed of something in a given direction.
Answer:
C. Merge into the bike lane to make a turn
Explanation:
According to the law, the bicycle is considered as a vehicle, therefore a bike lane is used for vehicular travel.
This would imply that drivers should merge into the bike lanes when they are to make a right turn at a corner.
If a bike rider is in the lane, the car yields to the bike and then moves into the lane.