A man seeking to set a world record wants to tow a 110000-kg airplane along a runway by pulling horizontally on a cable attached to the airplane. The mass of the man is 70 kg, and the coefficient of static friction between his shoes and the runway is 0.76. What is the greatest acceleration the man can give the airplane? Assume that the airplane is on wheels that turn without any frictional resistance.
force friction on man=70*g*.76
greatest acceleration then
above force=110000*a
solve for a.
To find the greatest acceleration the man can give to the airplane, we need to consider the maximum static friction force that can be exerted between the man's shoes and the runway.
1. Calculate the maximum static friction force:
The maximum static friction force (F_max) can be calculated using the formula:
F_max = coefficient of static friction * normal force
The normal force (N) acting on the man is equal to his weight, which can be calculated as:
N = mass * gravity
Here, the mass of the man is 70 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.
Plugging in the values, we can calculate the normal force (N) and the maximum static friction force (F_max).
2. Calculate the force applied on the airplane:
The force applied on the airplane is equal to the product of mass and acceleration:
F_applied = mass * acceleration
Here, the mass of the airplane is given as 110000 kg. We need to find the acceleration.
3. Set up the equation:
To find the greatest acceleration, we need to equate the applied force to the maximum static friction force:
F_applied = F_max
Substitute the values for mass and acceleration to solve for acceleration.
Let's calculate the values step by step:
1. Calculate the maximum static friction force:
N = 70 kg * 9.8 m/s^2
F_max = 0.76 * N
2. Calculate the force applied on the airplane:
F_applied = 110000 kg * acceleration
3. Set up the equation:
F_applied = F_max
Now, substitute the values calculated in steps 1 and 2 into step 3, and solve for acceleration.