How much work is needed to push a 142- kg packing crate a distance of 2.45 m up an inclined plane that makes an angle of 20 o with the horizontal, when
inclined plane is frictionless?
Work = M*g*H , where H is the vertical rise. M = 142 kg and g = 9.8 m/s^2.
Trigonometry tells you that
H = 2.45 sin20 meters
Now do the calculation.
Thank You!!!!
To find the work done in pushing the packing crate up the inclined plane, you can use the following steps:
1. Calculate the gravitational force acting on the crate.
Weight (W) = mass (m) * gravitational acceleration (g)
W = 142 kg * 9.8 m/s^2 (acceleration due to gravity)
W = 1391.6 N
2. Determine the component of the gravitational force along the direction of the incline.
Force along the incline (F) = Weight (W) * sin(angle of the incline)
F = 1391.6 N * sin(20°)
F = 472.1 N
3. Calculate the work done.
Work (W) = Force (F) * distance (d)
W = 472.1 N * 2.45 m
W = 1155.6 J
Therefore, the work needed to push the 142 kg packing crate a distance of 2.45 m up the frictionless inclined plane is 1155.6 Joules.
To calculate the work required to push the packing crate up an inclined plane, we need to use the formula for work:
Work = Force x Distance x cos(θ)
Where:
- Work is the amount of work done (in joules)
- Force is the force applied to move the crate (in newtons)
- Distance is the distance the crate is moved (in meters)
- θ is the angle between the force and the displacement (in degrees)
First, let's calculate the force needed to move the crate up the inclined plane. We'll use the component of the weight of the crate that is parallel to the inclined plane:
Force = Weight x sin(θ)
Where:
- Weight is the force due to gravity acting on the crate (in newtons)
- θ is the angle of inclination (in degrees)
Weight = mass x gravity
Where:
- Mass is the mass of the crate (in kilograms)
- Gravity is the acceleration due to gravity (approximately 9.8 m/s^2)
Let's calculate the force first:
Weight = 142 kg x 9.8 m/s^2
Next, calculate the force parallel to the inclined plane:
Force = Weight x sin(20°)
Now that we have the force, we can calculate the work:
Work = Force x Distance x cos(θ)
Since the inclined plane is frictionless, the angle between the force and the displacement is the same as the angle of inclination:
Work = Force x Distance x cos(20°)
Now, substitute the values and calculate the work.