A stone of mass m = 1.05 kg is released from a height of h = 2.1 m into a pool of water. At a time of t = 1.83 s after hitting the surface of the water, the stone's velocity has decreased by 50%.
What is the magnitude of the average force the stone experiences, in newtons, during the time t?

Answer:

Explanation:

ignoring air resistance, the kinetic energy at water impact will equal the potential energy converted

½mv² = mgh

v = √(2gh)

v = √(2(9.81)2.1) = 6.4188... m/s

after impact, an impulse will result in a change of momentum.

There is a downward impulse due to gravity equal to the weight of the stone and an upward average force due to water resistance and buoyancy force.

FΔt = mΔv

(F - mg)Δt = m(vf - vi)

(F - mg) = m(vf - vi)/Δt

F = m(vf - vi)/Δt + mg

F = m((vf - vi)/Δt + g)

F = 1.05(((½(-6.4188) - -6.4188)/ 1.83) + 9.81)

F = 12.14198...

F = 12.1 N

The magnitude of the average force the stone experiences, will be 12.1 N.

Force is defined as the push or pulls applied to the body. Sometimes it is used to change the shape, size, and direction of the body. Force is defined as the product of mass and acceleration. Its unit is Newton.

The given data in the problem is;

m is the stone mass = 1.05 kg

The height is h, = 2.1 m i

The time is, t = 1.83 s

Velocity decreased by 50%.

From the law of conservation of energy the kinetic energy is equal to the potential energy;

[tex]\rm \frac{1}{2} mv^2 = mgh \\\\ v = \sqrt{2gh}\\\\ v = \sqrt{2 \times 9.81 \times 2.1 } \\\\ v= 64188 \ m/sec.[/tex]

From Newton's second law of motion, the impulsive force is equal to the change in momentum;

[tex]\rm F \triangle T = m \traingle v \\\\ (F - mg) = \frac{v_f-v_i}{\triangle t } \\\\ F = \frac{v_f-v_i}{\triangle t } + mg \\\\ F =m\frac{v_f-v_i}{\triangle t + g} \\\\ F= 12.14 98 \\\\ F=12.1 N[/tex]

Hence the magnitude of the average force the stone experiences, will be 12.1 N.

To learn more about the force refer to the link;

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1. A roller coaster with a mass of 800 kg sits stationary at the top of a section of track, 75 m above

the ground as shown. When the brake is released, it starts to roll down the track


2. For each height represented in the diagram, calculate the gravitational potential energy using

Ep = mgh. Show ONE SAMPLE calculation in the calculations section below and fill in Table 1 for

each of the heights of the roller coaster. (6 marks)


3. Assuming there is no friction, determine the mechanical kinetic energy using Ek = Etotal - Ep.

Show ONE SAMPLE calculation in the calculations section below and fill in Table 1 for each of

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4. For each height represented in the diagram, calculate the velocity using = �2

. Show ONE

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6. Repeat steps 1 – 5 above for a roller coaster cart that has a mass of 300 kg and enter your

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800 kg roller coaster cart:

Sample calculation for gravitational potential energy:

Sample calculation for Mechanical kinetic energy:

Sample calculation for velocity:


300 kg roller coaster cart:

Sample calculation for gravitational potential energy:

Sample calculation for mechanical kinetic energy:

Sample calculation for velocity:


Results:

Table 1: Potential energy, kinetic energy, total energy, and velocity of the 800 kg roller coaster cart


Table 2: Potential energy, kinetic energy, total energy, velocity of the 300 kg roller coaster cart.


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1. Describe the relationship between the gravitational potential energy and the mechanical kinetic

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2. Describe the shapes of each of the three lines in the graph. Explain why the velocity is different.

(4 marks)

3. Describe how mass affects the speed at the bottom of the roller coaster. (2 marks)

4. Describe how mass affects the gravitational potential energy and the mechanical kinetic energy

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5. At what point does the roller coaster have a maximum value for the following? Justify your

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a. Gravitational potential energy

b. Mechanical energy

c. Velocity

6. In your calculations, you assumed that the roller coaster was frictionless. All real roller coasters

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from your calculated values for a real roller coaster. (Hint: what form of energy would some of

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