Maths4U Original · Short practice

A 10 kg particle is held at rest by two separate light taut strings. The left string makes acute angle α above the leftward horizontal, with \(\displaystyle \sin\alpha=\frac{8}{17},\ \cos\alpha=\frac{15}{17}\). The right string makes acute angle β above the rightward horizontal, with \(\displaystyle \sin\beta=\frac{3}{5},\ \cos\beta=\frac{4}{5}\). Let \(\displaystyle T_{1}\) be the left-string tension and \(\displaystyle T_{2}\) the right-string tension. No other forces except weight act. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

Find the left-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 two separate light taut strings. The left string makes acute angle α above the leftward horizontal, with \(\displaystyle \sin\alpha=\frac{3}{5},\ \cos\alpha=\frac{4}{5}\). The right string makes acute angle β above the rightward horizontal, with \(\displaystyle \sin\beta=\frac{5}{13},\ \cos\beta=\frac{12}{13}\). Let \(\displaystyle T_{1}\) be the left-string tension and \(\displaystyle T_{2}\) the right-string tension. No other forces except weight act. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

Find the left-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 two separate light taut strings. The left string makes acute angle α above the leftward horizontal, with \(\displaystyle \sin\alpha=\frac{3}{5},\ \cos\alpha=\frac{4}{5}\). The right string makes acute angle β above the rightward horizontal, with \(\displaystyle \sin\beta=\frac{5}{13},\ \cos\beta=\frac{12}{13}\). Let \(\displaystyle T_{1}\) be the left-string tension and \(\displaystyle T_{2}\) the right-string tension. No other forces except weight act. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

Find the right-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 4 kg particle is held at rest by two separate light taut strings. The left string makes acute angle α above the leftward horizontal, with \(\displaystyle \sin\alpha=\frac{5}{13},\ \cos\alpha=\frac{12}{13}\). The right string makes acute angle β above the rightward horizontal, with \(\displaystyle \sin\beta=\frac{8}{17},\ \cos\beta=\frac{15}{17}\). Let \(\displaystyle T_{1}\) be the left-string tension and \(\displaystyle T_{2}\) the right-string tension. No other forces except weight act. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

Find the right-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 4 kg particle is held at rest by two separate light taut strings. The left string makes acute angle α above the leftward horizontal, with \(\displaystyle \sin\alpha=\frac{5}{13},\ \cos\alpha=\frac{12}{13}\). The right string makes acute angle β above the rightward horizontal, with \(\displaystyle \sin\beta=\frac{8}{17},\ \cos\beta=\frac{15}{17}\). Let \(\displaystyle T_{1}\) be the left-string tension and \(\displaystyle T_{2}\) the right-string tension. No other forces except weight act. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

Find the left-string horizontal component magnitude 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 5 kg particle is held at rest by two separate light taut strings. The left string makes acute angle α above the leftward horizontal, with \(\displaystyle \sin\alpha=\frac{8}{17},\ \cos\alpha=\frac{15}{17}\). The right string makes acute angle β above the rightward horizontal, with \(\displaystyle \sin\beta=\frac{3}{5},\ \cos\beta=\frac{4}{5}\). Let \(\displaystyle T_{1}\) be the left-string tension and \(\displaystyle T_{2}\) the right-string tension. No other forces except weight act. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

Find the left-string horizontal component magnitude 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 5 kg particle is held at rest by two separate light taut strings. The left string makes acute angle α above the leftward horizontal, with \(\displaystyle \sin\alpha=\frac{8}{17},\ \cos\alpha=\frac{15}{17}\). The right string makes acute angle β above the rightward horizontal, with \(\displaystyle \sin\beta=\frac{3}{5},\ \cos\beta=\frac{4}{5}\). Let \(\displaystyle T_{1}\) be the left-string tension and \(\displaystyle T_{2}\) the right-string tension. No other forces except weight act. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

Find the sum of the upward tension components 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 6 kg particle is held at rest by two separate light taut strings. The left string makes acute angle α above the leftward horizontal, with \(\displaystyle \sin\alpha=\frac{3}{5},\ \cos\alpha=\frac{4}{5}\). The right string makes acute angle β above the rightward horizontal, with \(\displaystyle \sin\beta=\frac{5}{13},\ \cos\beta=\frac{12}{13}\). Let \(\displaystyle T_{1}\) be the left-string tension and \(\displaystyle T_{2}\) the right-string tension. No other forces except weight act. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

Find the sum of the upward tension components 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.