Answer:
approximately 0.607.
Step-by-step explanation:
To find the coefficient of friction, we'll first calculate the force of friction acting on the body.
1. Break the 18N pull force into horizontal and vertical components. The horizontal component can be found using trigonometry:
Horizontal component (F_horizontal) = 18N * cos(14°)
2. Now, calculate the net horizontal force acting on the body:
Net horizontal force (F_net_horizontal) = Pull force - Friction force = F_horizontal - Friction force
We know that F_net_horizontal is responsible for accelerating the body horizontally, so it equals the mass of the body (m) times its acceleration (a). In this case, the acceleration is zero since the body is being dragged at a constant speed.
F_net_horizontal = m * a
Since a = 0, we have:
F_net_horizontal = 0
3. Rearrange the equation to solve for the friction force (F_friction):
F_friction = F_horizontal
4. Now, calculate the coefficient of friction (μ) using the formula:
μ = F_friction / Weight
μ = F_horizontal / Weight
μ = (18N * cos(14°)) / 50N
μ ≈ 0.607
So, the coefficient of friction (μ) is approximately 0.607.
To Further Explain
Certainly! Let's break down the problem step by step and explain it in more detail.
You have a body with a weight of 50 Newtons (N) being dragged along a rough horizontal plane by a pull force of 18 Newtons (N) acting at an angle of 14 degrees with the horizontal. You want to find the coefficient of friction.
1. **Resolve the Pull Force:**
First, you need to find the horizontal component of the 18N pull force. Since the force is at an angle of 14 degrees to the horizontal, you can use trigonometry to calculate it:
Horizontal component (F_horizontal) = Pull force * cos(14°)
F_horizontal = 18N * cos(14°)
2. **Net Horizontal Force:**
The net horizontal force (F_net_horizontal) is the force responsible for accelerating or maintaining the body's motion along the horizontal plane. Since you mentioned that the body is being dragged at a constant speed, the acceleration is zero. Therefore, F_net_horizontal is also zero.
F_net_horizontal = 0
3. **Friction Force:**
The friction force (F_friction) opposes the motion of the body and is equal in magnitude to the horizontal component of the pull force:
F_friction = F_horizontal
4. **Coefficient of Friction:**
Finally, you can calculate the coefficient of friction (μ) using the formula:
μ = F_friction / Weight
μ = F_horizontal / Weight
Plug in the values:
μ = (18N * cos(14°)) / 50N
Now, you can calculate μ:
μ ≈ (18N * 0.9703) / 50N ≈ 0.607
So, the coefficient of friction (μ) is approximately 0.607.
This coefficient of friction represents the ratio of the frictional force (which opposes motion) to the normal force (which is equal to the weight of the body). It quantifies the roughness of the surface and how much resistance the surface provides to the sliding motion of the body. In this case, μ ≈ 0.607 indicates a relatively high level of friction on the rough horizontal plane.