Three-force equilibrium and force triangles · Short practice
Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.
Recall
Three-force equilibrium and force triangles — objective 1
Maths4U Original · Short practice
A 2 kg particle is held at rest by a string pulling up and left at acute angle α above the horizontal, a horizontal rightward force P, and its weight. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{5}{13},\quad\cos\alpha=\frac{12}{13}\). Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find the string tension in N.
Enter one exact number or fraction unless the question specifies rounding. Use the requested units and positive direction; enter the number without its unit. Angles here use degrees. Give full reasoning separately for written problems.
Fresh review variant
Three-force equilibrium and force triangles — objective 1
Maths4U Original · Short practice
A 3 kg particle is held at rest by a string pulling up and left at acute angle α above the horizontal, a horizontal rightward force P, and its weight. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{8}{17},\quad\cos\alpha=\frac{15}{17}\). Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find the string tension in N.
Enter one exact number or fraction unless the question specifies rounding. Use the requested units and positive direction; enter the number without its unit. Angles here use degrees. Give full reasoning separately for written problems.
Method
Three-force equilibrium and force triangles — objective 2
Maths4U Original · Short practice
A 3 kg particle is held at rest by a string pulling up and left at acute angle α above the horizontal, a horizontal rightward force P, and its weight. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{8}{17},\quad\cos\alpha=\frac{15}{17}\). Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find P in N.
Enter one exact number or fraction unless the question specifies rounding. Use the requested units and positive direction; enter the number without its unit. Angles here use degrees. Give full reasoning separately for written problems.
Fresh review variant
Three-force equilibrium and force triangles — objective 2
Maths4U Original · Short practice
A 4 kg particle is held at rest by a string pulling up and left at acute angle α above the horizontal, a horizontal rightward force P, and its weight. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{3}{5},\quad\cos\alpha=\frac{4}{5}\). Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find P in N.
Enter one exact number or fraction unless the question specifies rounding. Use the requested units and positive direction; enter the number without its unit. Angles here use degrees. Give full reasoning separately for written problems.
Apply
Three-force equilibrium and force triangles — objective 3
Maths4U Original · Short practice
A 4 kg particle is held at rest by a string pulling up and left at acute angle α above the horizontal, a horizontal rightward force P, and its weight. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{3}{5},\quad\cos\alpha=\frac{4}{5}\). Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find the ratio \(\displaystyle \frac{P}{T}\).
Enter one exact number or fraction unless the question specifies rounding. Use the requested units and positive direction; enter the number without its unit. Angles here use degrees. Give full reasoning separately for written problems.
Fresh review variant
Three-force equilibrium and force triangles — objective 3
Maths4U Original · Short practice
A 5 kg particle is held at rest by a string pulling up and left at acute angle α above the horizontal, a horizontal rightward force P, and its weight. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{5}{13},\quad\cos\alpha=\frac{12}{13}\). Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find the ratio \(\displaystyle \frac{P}{T}\).
Enter one exact number or fraction unless the question specifies rounding. Use the requested units and positive direction; enter the number without its unit. Angles here use degrees. Give full reasoning separately for written problems.
Check understanding
Three-force equilibrium and force triangles — objective 4
Maths4U Original · Short practice
A 5 kg particle is held at rest by a string pulling up and left at acute angle α above the horizontal, a horizontal rightward force P, and its weight. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{5}{13},\quad\cos\alpha=\frac{12}{13}\). Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find α in degrees, to 1 decimal place.
Enter one exact number or fraction unless the question specifies rounding. Use the requested units and positive direction; enter the number without its unit. Angles here use degrees. Give full reasoning separately for written problems.
Fresh review variant
Three-force equilibrium and force triangles — objective 4
Maths4U Original · Short practice
A 6 kg particle is held at rest by a string pulling up and left at acute angle α above the horizontal, a horizontal rightward force P, and its weight. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{8}{17},\quad\cos\alpha=\frac{15}{17}\). Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find α in degrees, to 1 decimal place.
Enter one exact number or fraction unless the question specifies rounding. Use the requested units and positive direction; enter the number without its unit. Angles here use degrees. Give full reasoning separately for written problems.