One day while moving boxes you get tired and decide to use a rocket instead. You attach a small rocket of negligible mass to a 74.2 kg box. When you turn the rocket on, it provides a constant thrust of 271 N, and the sbox begins sliding across the pavement. If the magnitude of acceleration of the box is 1.72 m/s2, what is the coefficient of kinetic friction between the soapbox and pavement?
M*g = 74.2 * 9.8 = 727 N. = Wt. of box = Normal force, Fn.
u*Fn = 727u = Force of kinetic friction.
Ft - u*Fn = M*a.
271 - 727u = 74.2*1.72.
u =
To find the coefficient of kinetic friction between the soapbox and the pavement, we can use the following equation:
μk = (T - m * g) / (m * a)
Where:
μk = coefficient of kinetic friction
T = applied force (thrust from the rocket) = 271 N
m = mass of the box = 74.2 kg
g = acceleration due to gravity = 9.8 m/s^2
a = acceleration of the box = 1.72 m/s^2
Let's calculate the coefficient of kinetic friction:
μk = (271 N - 74.2 kg * 9.8 m/s^2) / (74.2 kg * 1.72 m/s^2)
μk = (271 N - 726.76 N) / (127.504 kg * m/s^2)
μk = -455.76 N / (127.504 kg * m/s^2)
μk = -3.572
However, a coefficient of friction cannot be negative. The negative sign indicates a direction, but we are only interested in magnitude. Therefore, we take the absolute value of the expression:
μk = 3.572
So, the coefficient of kinetic friction between the soapbox and the pavement is approximately 3.572.
To find the coefficient of kinetic friction between the soapbox and pavement, we can use the equation:
μk = (Ff / Fn)
Where:
- μk is the coefficient of kinetic friction
- Ff is the force of kinetic friction
- Fn is the normal force
In this case, the force of kinetic friction is equal to the product of the coefficient of kinetic friction and the normal force:
Ff = μk * Fn
The normal force can be calculated by multiplying the mass of the box by the acceleration due to gravity:
Fn = m * g
Where:
- m is the mass of the box
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
Given values in the problem:
- Mass of the box (m) = 74.2 kg
- Magnitude of acceleration (a) = 1.72 m/s^2
- Thrust provided by the rocket (Ft) = 271 N
First, we need to determine the normal force by using the weight formula:
Fn = m * g
Fn = (74.2 kg) * (9.8 m/s^2)
Fn = 727.96 N
Next, we can calculate the force of kinetic friction:
Ff = μk * Fn
271 N = μk * 727.96 N
Simplifying the equation, we can solve for μk:
μk = 271 N / 727.96 N
μk ≈ 0.3728
Therefore, the coefficient of kinetic friction between the soapbox and pavement is approximately 0.3728.