To solve this problem it is necessary to apply the concepts related to the Force from Hooke's law, the force since Newton's second law and the potential elastic energy.
Since the forces are balanced the Spring force is equal to the force of the weight that is


Where,
k = Spring constant
x = Displacement
m = Mass
g = Gravitational Acceleration
Re-arrange to find the spring constant



Just before launch the compression is 40cm, then from Potential Elastic Energy definition



Therefore the energy stored in the spring is 63.72J
A heat pump absorbs heat from the cold outdoors at 3 C and supplies heat to a
house at 20 C at a rate of 30,000 kJ/h. If the power consumed by the heat pump
<span>is 3 kW, find the coefficient of performance of the heat pump.</span>
Answer:

Explanation:
We know that speed is given by dividing distance by time or multiplying length and frequency. The speed of the father will be given by Lf where L is the length of the father’s leg ad f is the frequency.
We know that frequency of simple pendulum follows that 
Now, the speed of the father will be
while for the child the speed will be 
The ratio of the father’s speed to the child’s speed will be

Emily throws the ball at 30 degree below the horizontal
so here the speed is 14 m/s and hence we will find its horizontal and vertical components


vertical distance between them

now we will use kinematics in order to find the time taken by the ball to reach at Allison

here acceleration is due to gravity

now we will have

now solving above quadratic equation we have

now in order to find the horizontal distance where ball will fall is given as

here it shows that horizontal motion is uniform motion and it is not accelerated so we can use distance = speed * time

so the distance at which Allison is standing to catch the ball will be 5.33 m
Answer:
Explanation:
We shall apply Pascal's Law in fluid mechanics
According to it , pressure is transmitted in liquid from one point to another without any change .
25 cm diameter = 12.5 x 10⁻² m radius
Area = 3.14 x (12.5 x 10⁻²)²
= 490.625 x 10⁻⁴ m²
Pressure by vehicle
Force / area
13000 / 490.625 x 10⁻⁴
= 26.497 x 10⁴ Pa
5 cm diameter = 2.5 x 10⁻² radius
area = 3.14 x (2.5 x 10⁻²)²
= 19.625 x 10⁻⁴ m²
If we assume required force F on this area
Pressure = F / 19.625 x 10⁻⁴ Pa
According to Pascal Law
F / 19.625 x 10⁻⁴ = 26.497 x 10⁴
F = 19.625 x 26.497
= 520 N