How much work is it to push a box (mass 190 kg) up an incline (angle 16 degrees with the horizontal) that is 8.3 meters long, if the coefficient of kinetic friction between the box and the incline is 0.6?
My doubt is how do I find force?
To find the force required to push the box up the incline, we can break it down into two components: the force needed to overcome gravity and the force needed to overcome friction.
1. Force to overcome gravity:
The force required to overcome gravity can be calculated using the formula:
Force_gravity = mass * acceleration_due_to_gravity
In this case, the mass of the box is given as 190 kg, and the acceleration due to gravity is approximately 9.8 m/s^2. Therefore:
Force_gravity = 190 kg * 9.8 m/s^2
2. Force to overcome friction:
The force required to overcome friction can be calculated using the formula:
Force_friction = coefficient_of_friction * force_normal
The force normal is the normal force experienced by the box, which can be calculated using the formula:
Force_normal = mass * acceleration_due_to_gravity * cos(angle_of_incline)
The angle of the incline is given as 16 degrees, so the angle in radians is (16 * π) / 180.
Force_normal = 190 kg * 9.8 m/s^2 * cos(16 * π / 180)
Now we can calculate the force of friction:
Force_friction = 0.6 * Force_normal
3. Total force required:
Finally, we can calculate the total force required to push the box up the incline by adding the force required to overcome gravity and the force required to overcome friction:
Total_force = Force_gravity + Force_friction
Now you can substitute the values into these equations and calculate the force required to push the box up the incline.
To find the force required to push the box up the incline, you need to consider several factors. Here's a step-by-step explanation on how to calculate the force:
Step 1: Calculate the gravitational force acting on the box.
The gravitational force can be calculated using the formula Fg = m * g, where Fg is the force, m is the mass of the box, and g is the acceleration due to gravity (approximately 9.8 m/s^2). In this case, the mass of the box is given as 190 kg, so the gravitational force is 190 kg * 9.8 m/s^2 = 1862 Newtons.
Step 2: Determine the component of the gravitational force acting parallel to the incline.
Since the incline is at an angle of 16 degrees with the horizontal, you need to find the component of the gravitational force acting parallel to the incline. This component is equal to Fg * sin(θ), where θ is the angle of the incline. Therefore, the component of the gravitational force is 1862 N * sin(16 degrees) = 509 Newtons.
Step 3: Calculate the frictional force.
The coefficient of kinetic friction (μ) between the box and the incline is given as 0.6. The frictional force can be calculated using the formula Ff = μ * Fn, where Ff is the frictional force and Fn is the normal force. The normal force can be determined using the formula Fn = mg * cos(θ), where m is the mass of the box, g is the acceleration due to gravity, and θ is the angle of the incline. Therefore, the normal force is 190 kg * 9.8 m/s^2 * cos(16 degrees) = 1801 Newtons. The frictional force is then 0.6 * 1801 N = 1081 Newtons.
Step 4: Calculate the net force required.
The net force required to push the box up the incline is the sum of the component of the gravitational force acting parallel to the incline and the frictional force. In this case, it is 509 N + 1081 N = 1590 Newtons.
So, the force required to push the box up the incline is 1590 Newtons.
work=force up*distance
forceup=friction+gravity
= mgCosTheta*mu+mgSinTheta
distance=8.3m
solve fod work.