You need to move a 135-kg sofa to a different location in the room. It takes a force of 92 N to start it moving. What is the coefficient of static friction between the sofa and the carpet?
92/(M*g)= ___
M is the mass and g is the acceleration of gravity.
.07
To answer this question, we can use Newton's second law of motion, which states that the force (F) required to move an object is equal to the product of its mass (m) and its acceleration (a). In this case, the acceleration can be assumed to be zero since we're dealing with static friction, which means the sofa is not moving yet.
Newton's second law can be written as:
F = m * a
In this case, the force required to start the sofa moving (F) is given as 92 N, and the mass of the sofa (m) is given as 135 kg. Therefore, we can rearrange the equation to solve for acceleration:
a = F / m
Plugging in the values, we get:
a = 92 N / 135 kg
Calculating this, we find that the acceleration is approximately 0.681 m/s^2. Since the sofa is not moving yet, this value represents the maximum static friction force between the sofa and the carpet.
The formula for static friction is given by:
F(static friction) = µ(static friction) * N
Where:
F(static friction) is the static friction force,
µ(static friction) is the coefficient of static friction, and
N is the normal force between the two surfaces in contact.
In this case, the normal force is equal to the weight of the sofa, which can be calculated as:
N = m * g
Where:
m is the mass of the sofa, and
g is the acceleration due to gravity, approximately equal to 9.8 m/s^2.
Plugging in the values, we have:
N = 135 kg * 9.8 m/s^2
Calculating this, we find that the normal force is approximately 1323 N.
Now, we can rearrange the static friction formula to solve for the coefficient of static friction (µ(static friction)):
µ(static friction) = F(static friction) / N
Plugging in the known values, we get:
µ(static friction) = 92 N / 1323 N
Calculating this, we find that the coefficient of static friction between the sofa and the carpet is approximately 0.069.