You are helping your friend move a new refrigerator into his kitchen. You apply a horizontal force of F = (202i − 161k) N to try and move the 75.0-kg refrigerator. The coefficient of static friction is 0.640.
a) how much static friction force does the floor exert on the fridge (as a vector)?*
b) what is the maximum amount of force needed before the fridge starts to move?
I've considered Newton's third law and I strongly believe the answer is -202i. If this answer is wrong, prove me otherwise.
a. (-202i +161k) Just changed the sign to get the answer.
b. (75x.640x9.8) = 470.4 equal to the maximum static force
Well, if you believe the answer is -202i, let me try to prove you otherwise in a humorous way:
Ah, yes, the case of the stubborn fridge that refuses to budge! It's like a WWE wrestling match between you and the refrigerator, except it's not as entertaining.
Now, let's analyze the situation. The static friction force is what keeps the fridge from sliding across the floor like a figure skater on ice. According to Newton's third law, for every action, there is an equal and opposite reaction. So, if you exert a force of 202i N on the fridge, the floor exerts an equal and opposite force (aka the static friction force) on the fridge.
But here's where things get tricky. The coefficient of static friction, in this case, is 0.640. The static friction force can be calculated by multiplying the coefficient of static friction by the normal force (vertical force exerted by the fridge on the floor). Since we don't have the normal force, we can't give you an exact answer as a vector. Sorry to burst your bubble, my friend.
As for the maximum amount of force needed before the fridge starts to move, that will be when the force of static friction reaches its maximum value. In this case, the maximum force of static friction can be calculated by multiplying the coefficient of static friction by the normal force. The fridge will start moving when the applied force exceeds this maximum force of static friction.
So, my advice to you is to grab your popcorn, sit back, and watch the epic battle between you and the fridge. And don't forget to invite some friends over. It could be the next great sporting event!
Disclaimer: No fridges were harmed in the making of this answer.
a) To find the static friction force, we need to determine the maximum possible static friction force first. The formula for static friction is given by:
f_s ≤ μ_s * N
Where f_s is the static friction force, μ_s is the coefficient of static friction, and N is the normal force. In this case, the normal force is equal to the weight of the refrigerator, which is given by:
N = m * g
Where m is the mass of the refrigerator and g is the acceleration due to gravity. Plugging in the values, we have:
N = (75.0 kg) * (9.8 m/s^2) = 735 N
Now we can calculate the maximum possible static friction force:
f_s ≤ (0.640) * (735 N) = 470.4 N
Since the static friction force opposes the applied force, its direction would be opposite to the applied force vector. Therefore, the static friction force can be written as:
f_s = -F
Plugging in the values, we have:
f_s = -[(202i - 161k) N] = -202i + 161k N
So the static friction force exerted by the floor on the fridge is -202i + 161k N.
b) The maximum amount of force needed before the fridge starts to move is equal to the maximum possible static friction force we calculated earlier:
f_max = 470.4 N
Therefore, the maximum amount of force needed before the fridge starts to move is 470.4 N.
To find the static friction force, we need to consider the maximum static friction force that can be exerted by the floor on the fridge. The maximum static friction force can be calculated using the equation:
Fmax = μs * N
where μs is the coefficient of static friction and N is the normal force exerted by the floor on the fridge. The normal force N is equal to the weight of the fridge, since the fridge is on a flat surface and not accelerating vertically. The weight of the fridge can be calculated as:
W = m * g
where m is the mass of the fridge and g is the acceleration due to gravity.
Given:
m = 75.0 kg (mass of the fridge)
g = 9.8 m/s^2 (acceleration due to gravity)
μs = 0.640 (coefficient of static friction)
Let's calculate the values:
N = m * g = 75.0 kg * 9.8 m/s^2 = 735 N
Fmax = μs * N = 0.640 * 735 N = 470.4 N
Therefore, the maximum static friction force that the floor can exert on the fridge is 470.4 N.
Regarding your statement that the answer is -202i, I'm not sure how you arrived at that answer. The value -202i represents the force you applied to the fridge, but it is not the static friction force. The static friction force can vary depending on the force applied, as long as it is less than or equal to the maximum static friction force. The direction of the static friction force will be in the opposite direction to the applied force, so it would not be -202i.
Moving on to the second part of your question, to determine the maximum force needed before the fridge starts to move, we compare the applied force F to the maximum static friction force Fmax. If F is less than or equal to Fmax, the fridge will not move. If F exceeds Fmax, the fridge will start moving.
Given:
F = (202i - 161k) N
To determine whether the fridge will move, we need to find the magnitude of F and compare it to Fmax:
|F| = sqrt(Fx^2 + Fz^2) = sqrt((202 N)^2 + (-161 N)^2) = 256.1 N
Comparing |F| to Fmax:
|F| = 256.1 N
Fmax = 470.4 N
Since |F| (256.1 N) is less than Fmax (470.4 N), the fridge will not start moving.