What is the gravitational component of weight along the plane for a 3 kg mass on a 60° incline?

What is the gravitational component of weight along the plane for a 3 kg mass on a 60° incline?

• A. 25.4 N
• B. 12.7 N
• C. 43.0 N
• D. 9.8 N

Answer: (A)

When a mass sits on an incline, gravity can be split into two components: one pulling straight down along the plane and one perpendicular to the plane. The component along the plane is mg sin(theta), where theta is the incline angle. Here, m = 3 kg, g = 9.8 m/s^2, and theta = 60°. The weight is mg = 3 × 9.8 = 29.4 N. The along-the-plane component is 29.4 × sin(60°). Since sin(60°) ≈ 0.866, this is about 29.4 × 0.866 ≈ 25.4 N. So the gravitational component along the plane is about 25.4 N. The other numbers don’t come from mg sin(60°): for example, 43.0 N would exceed the total weight, and 9.8 N would be the weight of 1 kg, not our 3 kg mass.

When a mass sits on an incline, gravity can be split into two components: one pulling straight down along the plane and one perpendicular to the plane. The component along the plane is mg sin(theta), where theta is the incline angle.

Here, m = 3 kg, g = 9.8 m/s^2, and theta = 60°. The weight is mg = 3 × 9.8 = 29.4 N. The along-the-plane component is 29.4 × sin(60°). Since sin(60°) ≈ 0.866, this is about 29.4 × 0.866 ≈ 25.4 N.

So the gravitational component along the plane is about 25.4 N. The other numbers don’t come from mg sin(60°): for example, 43.0 N would exceed the total weight, and 9.8 N would be the weight of 1 kg, not our 3 kg mass.