What would be the force required to push a 100 lb. object along a ramp that is inclined 10 degrees with the horizontal?
To calculate the force required to push a 100 lb. object along a ramp inclined at 10 degrees with the horizontal, we can use the concept of force components.
Here's how you can solve it step by step:
Step 1: Convert weight from pounds to Newtons
The weight of the object is given as 100 lb. First, convert the weight from pounds to Newtons. The conversion factor is 1 lb ≈ 4.448 N. Therefore, 100 lb ≈ 100 * 4.448 N ≈ 444.8 N.
Step 2: Decompose the weight into components
Resolve the weight of the object into two components: one perpendicular to the ramp (normal force) and one parallel to the ramp (force due to gravity).
On an inclined plane, the weight (W) is resolved into two components:
- The component perpendicular to the ramp (N) is equal to the normal force acting vertically upwards.
- The component parallel to the ramp (G or Fg) is equal to the force due to gravity.
Step 3: Calculate the force due to gravity (Fg)
The force due to gravity acting parallel to the incline is given by the formula:
Fg = W * sin(θ),
where θ is the angle of inclination in degrees.
Substituting the values:
Fg = 444.8 N * sin(10°)
≈ 444.8 N * 0.1736
≈ 77.18 N.
Step 4: Determine the force required to push the object (Fr)
The force required to push the object up the ramp is equal to the force due to gravity acting parallel to the incline (Fg). Therefore, the force required is approximately 77.18 N.
Note: In this calculation, we assume an ideal situation neglecting other forces such as friction.
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To calculate the force required to push a 100 lb. object along a ramp inclined at 10 degrees with the horizontal, we need to consider the forces acting on the object. The force required can be determined using the formula:
Force (F) = Weight (W) * sin(θ)
First, convert the weight of the object from pounds to Newtons. Using the conversion factor of 1 pound = 4.44822 Newtons, we have:
Weight (W) = 100 lb. * 4.44822 N/lb. ≈ 444.82 N
Next, substitute the weight into the formula along with the angle θ of 10 degrees:
Force (F) = 444.82 N * sin(10 degrees)
Calculating sin(10 degrees) into a decimal:
sin(10 degrees) ≈ 0.173648
Finally, substitute the value into the formula to find the force:
Force (F) ≈ 444.82 N * 0.173648 ≈ 77.11 N
Therefore, the force required to push the 100 lb. object along the ramp inclined at 10 degrees with the horizontal is approximately 77.11 Newtons.