Jason and Kim are attempting to push a heavy fridge across the kitchen floor. When Jason pushes it with a muscular force of 550. N, the fridge accelerates from rest to 28.0 cm/s in 3.50 s. When Kim pushes it with a muscular force of 560. N, the fridge accelerates from rest to 36.0 cm/s in 3.00 s. Calculate the coefficient of friction, and the mass of the fridge.
v₁=0.280 m/s; t₁ =3.50 s; F₁=550 N
v₂=0.360 m/s; t₂=3.00s; F₂=560 N
ma₁ =F₁-F(fr) =F₁-μN =F₁- μmg
ma₂= F₂-F(fr)= F₂ -μN =F₂ - μmg
v₁= a₁t₁ => a₁=v₁/t₁ =>
ma₁ = m v₁/t₁=F₁ - μmg;
v₂= a₂t₂ => a₂=v₂/t₂ ->
ma₂ = m v₂/t₂=F₂ - μmg;
2m(v₂/t₂-v₁/t₁)= F₂-F₁-μmg + μmg
m=( F₂- F₁)/2(v₂/t₂-v₁/t₁)=
=(560-550)/2(0.360/3.00-0.280/3.50)=
=10/2(0.12-0.08)=125 kg;
μ=(F₁-mv₁/t₁)/mg =
(550 - 125•0.280/3.50)/125•9.8 =0.44
To calculate the coefficient of friction and the mass of the fridge, we can use Newton's second law of motion, which states that the force acting on an object is equal to the product of its mass and acceleration (F = m * a).
First, let's find the acceleration for each scenario. We can convert the given velocities from cm/s to m/s by dividing by 100:
For Jason pushing the fridge:
Initial velocity, u = 0 m/s
Final velocity, v = 28.0 cm/s / 100 = 0.28 m/s
Time, t = 3.50 s
Acceleration, a = (v - u) / t
a = (0.28 m/s - 0 m/s) / 3.50 s
a = 0.08 m/s^2
For Kim pushing the fridge:
Initial velocity, u = 0 m/s
Final velocity, v = 36.0 cm/s / 100 = 0.36 m/s
Time, t = 3.00 s
Acceleration, a = (v - u) / t
a = (0.36 m/s - 0 m/s) / 3.00 s
a = 0.12 m/s^2
Now, let's find the mass of the fridge using Jason's scenario:
Force applied by Jason, F = 550 N
Acceleration, a = 0.08 m/s^2
m = F / a
m = 550 N / 0.08 m/s^2
m = 6875 kg
Next, let's calculate the coefficient of friction. The force of friction can be found by subtracting the force applied by Jason/Kim from the force required to accelerate the fridge:
For Jason pushing the fridge:
Force of friction, F_friction = F_applied - F_required
F_friction = 550 N - 6875 kg * 0.08 m/s^2
F_friction = 550 N - 550 N
F_friction = 0 N
For Kim pushing the fridge:
Force of friction, F_friction = F_applied - F_required
F_friction = 560 N - 6875 kg * 0.12 m/s^2
F_friction = 560 N - 825 N
F_friction = -265 N
Since F_friction is negative for Kim's scenario, it implies that Kim's applied force is greater than the force required to accelerate the fridge. This suggests that there is a net external force acting on the fridge, such as a force from another source pushing in the opposite direction of Kim's force.
In conclusion:
The mass of the fridge is 6875 kg.
For Jason's scenario, the coefficient of friction is 0 since the force required to accelerate the fridge is equal to the applied force.
For Kim's scenario, the negative value of F_friction suggests the presence of an additional external force. Therefore, we cannot determine the coefficient of friction in this case.