Question

Ex: A hockey puck having a mass of 0.30 kg slides on the horizontal, frictionless surface of an ice rink. Two hockey sticks strike the puck simultaneously, exerting the forces on the puck. The force F? has a magnitude of 5.0 N, and is directed at ? = 20° below the x-axis and the force F? has a magnitude of 8.0 N and is directed at ? = 60° above the x-axis. Determine both the magnitude and the direction of the puck’s acceleration. Soln: ? F_x = F_1x + F_2x = F_1 cos (-20°) + F_2 cos 60° = (5.0 N)(0.940) + (8.0 N)(0.500) = 8.7 N ? F_y = F_1y + F_2y = F_1 sin (-20°) + F_2 sin 60° = (5.0 N)(-0.342) + (8.0 N)(0.866) = 5.2 N a_x = ? F_x / m = 8.7 N / 0.30 kg = 29 m/s² a_y = ? F_y / m = 5.2 N / 0.30 kg = 17 m/s² a = ?((29 m/s²)² + (17 m/s²)²) = 34 m/s² ? = tan?¹ (a_y / a_x) = tan?¹ (17 / 29) = 30°

          Ex: A hockey puck having a mass of 0.30 kg slides on the horizontal, frictionless surface of an ice rink. Two hockey sticks strike the puck simultaneously, exerting the forces on the puck. The force F? has a magnitude of 5.0 N, and is directed at ? = 20° below the x-axis and the force F? has a magnitude of 8.0 N and is directed at ? = 60° above the x-axis. Determine both the magnitude and the direction of the puck’s acceleration.

Soln:
? F_x = F_1x + F_2x = F_1 cos (-20°) + F_2 cos 60°
= (5.0 N)(0.940) + (8.0 N)(0.500) = 8.7 N
? F_y = F_1y + F_2y = F_1 sin (-20°) + F_2 sin 60°
= (5.0 N)(-0.342) + (8.0 N)(0.866) = 5.2 N
a_x = ? F_x / m = 8.7 N / 0.30 kg = 29 m/s²
a_y = ? F_y / m = 5.2 N / 0.30 kg = 17 m/s²
a = ?((29 m/s²)² + (17 m/s²)²) = 34 m/s²
? = tan?¹ (a_y / a_x) = tan?¹ (17 / 29) = 30°

Ex: A hockey puck having a mass of 0.30 kg slides on the horizontal, frictionless surface of an ice rink. Two hockey sticks strike the puck simultaneously, exerting the forces on the puck. The force F? has a magnitude of 5.0 N, and is directed at ? = 20° below the x-axis and the force F? has a magnitude of 8.0 N and is directed at ? = 60° above the x-axis. Determine both the magnitude and the direction of the puck’s acceleration.

Soln:
? Fx = F1x + F2x = F1 cos (-20°) + F2 cos 60°
= (5.0 N)(0.940) + (8.0 N)(0.500) = 8.7 N
? Fy = F1y + F2y = F1 sin (-20°) + F2 sin 60°
= (5.0 N)(-0.342) + (8.0 N)(0.866) = 5.2 N
ax = ? Fx / m = 8.7 N / 0.30 kg = 29 m/s²
ay = ? Fy / m = 5.2 N / 0.30 kg = 17 m/s²
a = ?((29 m/s²)² + (17 m/s²)²) = 34 m/s²
? = tan?¹ (ay / ax) = tan?¹ (17 / 29) = 30°

Added by Richard C.

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