Minimum force required to prevent a ball weighing 29.6 pounds from rolling down a ramp which is inclined 14.9 degrees with the horizon?
To find the minimum force required to prevent the ball from rolling down the ramp, we need to consider the gravitational force pulling the ball downward and the component of this force that is acting parallel to the ramp.
First, let's break down the weight of the ball into its components. The weight W of an object can be calculated using the formula W = m * g, where m is the mass of the object and g is the acceleration due to gravity.
To find the mass of the ball, we need to convert the weight from pounds to kilograms. Since 1 lb is approximately 0.454 kg, the mass of the ball can be calculated as follows:
mass (m) = weight (W) / conversion factor
= 29.6 lb / 0.454 kg/lb
≈ 65.0 kg
Next, we need to determine the component of the weight parallel to the ramp. This can be calculated using the formula F = W * sin(θ), where F is the force acting parallel to the ramp, and θ is the angle of inclination of the ramp.
Substituting the known values into the formula:
F = 29.6 lb * sin(14.9 degrees)
However, before we proceed with the calculation, it's important to convert the angle from degrees to radians since the trigonometric functions in most programming languages work with radians. The conversion can be done using the formula:
theta_radians = theta_degrees * pi / 180
Substituting the angle of inclination into the formula:
theta_radians = 14.9 degrees * pi / 180
≈ 0.26 radians
Finally, we can calculate the force:
F = 29.6 lb * sin(0.26 radians)
≈ 8.0 lb
Therefore, the minimum force required to prevent the ball from rolling down the ramp is approximately 8.0 pounds.