Two masses (m1 = 532 grams, m2 = 114 grams) are connected with a rope through a frictionless pulley
The ramp has an elevation angle θ = 65.3° and a coefficient of friction μ = 0.184.
What are Fll and Fperpendicular for m1?
What is the normal force on m1?
To find Fll and Fperpendicular for m1, we first need to understand the forces acting on m1.
1. Fll (force along the ramp): This force is parallel to the inclined plane. It can be calculated using the formula: Fll = m1 * g * sin(θ), where g is the acceleration due to gravity (approximately 9.8 m/s²) and θ is the angle of elevation (65.3°).
2. Fperpendicular (force perpendicular to the ramp): This force is perpendicular to the inclined plane. It can be calculated using the formula: Fperpendicular = m1 * g * cos(θ), where θ is the angle of elevation (65.3°), and g is the acceleration due to gravity (approximately 9.8 m/s²).
Now let's calculate Fll and Fperpendicular for m1:
1. Fll = m1 * g * sin(θ)
= 532 g * 9.8 m/s² * sin(65.3°)
To calculate the sine of an angle, you can use a scientific calculator or an online calculator. The sine of 65.3° is approximately 0.9063.
Fll = 532 g * 9.8 m/s² * 0.9063
Fll ≈ 4883.3264 g m/s²
2. Fperpendicular = m1 * g * cos(θ)
= 532 g * 9.8 m/s² * cos(65.3°)
You can again use a scientific calculator or an online calculator to calculate the cosine of 65.3°, which is approximately 0.4226.
Fperpendicular = 532 g * 9.8 m/s² * 0.4226
Fperpendicular ≈ 2146.2824 g m/s²
To find the normal force on m1, let's break it down:
The normal force (N) is the force exerted by a surface to support the weight of an object resting on it. In this case, the surface is the inclined plane.
The normal force on m1 (N1) balances the component of m1's weight perpendicular to the ramp (Fperpendicular). Therefore, N1 = Fperpendicular.
Substituting the values we calculated earlier, we have:
N1 ≈ 2146.2824 g m/s²
Please note that the values given above are in terms of grams multiplied by g (acceleration due to gravity) and meters per second squared.