Initially, the spring stretches by 3 cm under a force of 15 N. From these data, we can find the value of the spring constant, given by Hook's law:

where F is the force applied, and

is the stretch of the spring with respect to its equilibrium position. Using the data, we find

Now a force of 30 N is applied to the same spring, with constant k=5.0 N/cm. Using again Hook's law, we can find the new stretch of the spring:
Answer:
d = 10.2 m
Explanation:
When the car travels up the inclined plane, its kinetic energy will be used to do the work in climbing up. So according to the law of conservation of energy, we can write that:

where,
m = mass of car
v = speed of car at the start of plane = (36 km/h)(1000 m/1 km)(1 h/3600 s)
v = 10 m/s
F = force on the car in direction of inclination = W Sin θ
W = weight of car = mg
θ = Angle of inclinition = 30°
d = distance covered up the ramp = ?
Therefore,

<u>d = 10.2 m</u>
Answer:
82 degrees
Explanation:
consider your staying point to be the center of a circle. this center has the coordinates (0, 0).
the radius of the circle is the distance you walked East (14 miles).
I assume your teacher means as "angle of displacement" the angle between the East-West line going through your starting point and the direct line from your starting point to your current position.
then the 100 miles North is tan(displacement angle)×14.
as it is the same, if you first went North and then East, or the other way around. you end up at the same point, with the same coordinates.
so, again.
100 = 14×tan(angle)
tan(angle) = 100/14 = 50/7 = 7.142857...
the displacement angle is then 82 degrees.
Answer:
The answer is below
Explanation:
The length of the rope is equal to the radius of the circle formed by the complete rotation of the rope. Therefore the radius = 1.50 m.
a) The distance covered by the rope when completing one rotation is the same as the perimeter of the circle. Hence:
Distance covered in one rotation = 2π * radius = 2π * 1.5 = 3π meters
The velocity of the ball = Distance / time = 3π meters / 3.4 seconds = 2.77 m/s
b) The initial velocity (u) is 0 m/s, the final velocity is 2.77 m/s during time (t) = 3.4 s. Hence acceleration (a):
v = u + at
2.77 = 3.4a
a = 0.82 m/s²
c) Force on ball = mass * acceleration = 4 * 0.82 = 3.28 N