Answer:
x₂=2×1
Explanation:
According to the work-energy theorem, we can assume that the gravitational potential energy at the lowest point of compression is zero since the kinetic energy change is 0;
mgx-(kx)²/2 =0 where m refers to the object's mass, g indicates the acceleration due to gravity, k denotes spring constant, and x represents the spring's compression.
mgx=(kx)²/2
x=2mg/k----------------compression when the object is at rest
However, ΔK.E =-1/2mv²⇒kx²=mv² -----------where v symbolizes the object's velocity and K.E signifies kinetic energy
Thus, if kx²=mv² then
v=x *√(k/m) ----------------where v=0
<pDoubling v results in multiplying x *√(k/m) by 2, leading to x₂ being double x₁
Response:
The new resistance is half of the original resistance.
Explanation:
Resistance in a wire is represented by:
= resistivity of the material
L and A are the physical dimensions
If a wire is exchanged for one where all linear dimensions are doubled, i.e. l' = 2l and r' = 2r
The updated resistance of the wire can be calculated as follows:
The new resistance equals half of the original resistance. Thus, this provides the solution needed.
Assuming that the mass of the empty wagon is "M," according to Newton's second law, we can derive the following relationships. Given that the empty wagon accelerates at 1.4 m/s², we proceed with this information. If a child weighing three times the mass of the wagon is on it, we can establish the relevant equations.
1 hour = 3,600 seconds
1 km = 1,000 meters
75 km/hour = (75,000/3,600) m/s = 20-5/6 m/s
The mean speed during the deceleration is
(1/2)(20-5/6 + 0) = 10-5/12 m/s.
Traveling at this average speed for 21 seconds,
the bus covers
(10-5/12) × (21) = 218.75 meters.
Answer:
a) The jogger's acceleration is 1.5 m/s²
b) The car's acceleration is also 1.5 m/s²
c) Yes, the car covers a distance 76 m greater than the jogger.
Explanation:
a) Acceleration is the change in velocity over a given time interval:
a = (final velocity - initial velocity) / time
For the jogger:
a = (3.0 m/s - 0 m/s) / 2.0 s = 1.5 m/s²
b) For the car:
a = (41.0 m/s - 38.0 m/s) / 2.0 s = 1.5 m/s²
c) To find how far the car has traveled after 2 seconds, use the formula for position under acceleration along a straight path:
x = x₀ + v₀ t + ½ a t²
where
x = position at time t
x₀ = initial position
v₀ = initial velocity
t = elapsed time
a = acceleration
Assuming x₀ = 0 (origin at car's starting point):
x = 38.0 m/s × 2 s + ½ × 1.5 m/s² × (2.0 s)²
x = 79 m
Similarly, position of the jogger after 2 seconds is:
x = 0 m/s × 2 s + ½ × 1.5 m/s² × (2.0 s)² = 3 m
The difference traveled by the car compared to the jogger is 79 m - 3 m = 76 m
