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.

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.

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.

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.

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.

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.

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.

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.