A dead dog of mass 2.2 kg and an initial speed of 5.5 m.s-1 slides along a rough horizontal surface and stops after travelling 4.2 m. calculate the frictional force between the dog and the surface (Think of the work the friction has to do to stop the dog – the Ek of the dog will be changed into heat energy by this work).
F * 4.2 = work done by friction
Ke at start = (1/2)(2.2)(5.5)^2
Ke at finsh = 0
chnge in potential energy = 0 because level
so
4.2 F = 1.1* 5.5^2
To find the frictional force between the dog and the surface, we need to calculate the change in kinetic energy and then use the work-energy principle.
1. Calculate the initial kinetic energy (Ek_initial) of the dog:
Ek_initial = (1/2) * mass * velocity^2
Ek_initial = (1/2) * 2.2 kg * (5.5 m/s)^2
2. Calculate the final kinetic energy (Ek_final) of the dog, which is zero since the dog slides to a stop:
Ek_final = 0
3. Calculate the change in kinetic energy (ΔEk):
ΔEk = Ek_final - Ek_initial
ΔEk = 0 - [(1/2) * 2.2 kg * (5.5 m/s)^2]
4. Apply the work-energy principle:
Work_done = ΔEk
5. The work done by the frictional force is equal to the negative of the change in kinetic energy:
Work_done = -ΔEk
6. The work done by friction can be calculated using the formula:
Work_done = Frictional_Force * Distance
7. Rearrange the equation to solve for the frictional force:
Frictional_Force = Work_done / Distance
8. Substitute the values into the equation to find the frictional force:
Frictional_Force = (-ΔEk) / Distance
9. Calculate the value:
Frictional_Force = [-(1/2) * 2.2 kg * (5.5 m/s)^2] / 4.2 m
Using a calculator, we can determine the value of the frictional force between the dog and the surface.
To calculate the frictional force between the dog and the surface, we need to use the concept of work and energy. The work done by the frictional force is equal to the change in kinetic energy of the dog.
The initial kinetic energy (Ek) of the dog is given by the equation:
Ek = (1/2) * m * v^2
Where:
Ek is the initial kinetic energy
m is the mass of the dog (2.2 kg)
v is the initial speed (5.5 m/s)
Plugging in the values into the equation, we get:
Ek = (1/2) * 2.2 kg * (5.5 m/s)^2
Ek = 33.33 Joules
The final kinetic energy is zero since the dog stops completely. Therefore, the change in kinetic energy (ΔEk) is:
ΔEk = 0 - 33.33 Joules
ΔEk = -33.33 Joules
Now, as the dog stops, the frictional force does the work -ΔEk to change the dog's kinetic energy into heat energy. The work done by the frictional force is given by:
Work = -ΔEk
Therefore, the frictional force is the negative value of the change in kinetic energy, which is:
Frictional Force = - (-33.33 Joules)
Frictional Force = 33.33 Joules
So, the frictional force between the dog and the surface is 33.33 Joules.