A rough incline coupled to a hanging particle · 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
A rough incline coupled to a hanging particle — objective 1
Maths4U Original · Short practice
A 2 kg particle is on a rough fixed plane. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{3}{5},\quad\cos\alpha=\frac{4}{5}\). It is connected to a hanging 4 kg particle by a light inextensible string over a smooth fixed pulley. The string is parallel to the plane at the contacting particle. The hanging particle descends and the plane particle slides up with \(\displaystyle F=\mu R\), where \(\displaystyle \mu =\)\(\displaystyle \frac{1}{10}\). The string stays taut and no boundary is reached. Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find the common acceleration magnitude in \(\displaystyle \frac{m}{s^{2}}\).
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
A rough incline coupled to a hanging particle — objective 1
Maths4U Original · Short practice
A 3 kg particle is on a rough fixed plane. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{5}{13},\quad\cos\alpha=\frac{12}{13}\). It is connected to a hanging 6 kg particle by a light inextensible string over a smooth fixed pulley. The string is parallel to the plane at the contacting particle. The hanging particle descends and the plane particle slides up with \(\displaystyle F=\mu R\), where \(\displaystyle \mu =\)\(\displaystyle \frac{1}{5}\). The string stays taut and no boundary is reached. Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find the common acceleration magnitude in \(\displaystyle \frac{m}{s^{2}}\).
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
A rough incline coupled to a hanging particle — objective 2
Maths4U Original · Short practice
A 3 kg particle is on a rough fixed plane. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{5}{13},\quad\cos\alpha=\frac{12}{13}\). It is connected to a hanging 6 kg particle by a light inextensible string over a smooth fixed pulley. The string is parallel to the plane at the contacting particle. The hanging particle descends and the plane particle slides up with \(\displaystyle F=\mu R\), where \(\displaystyle \mu =\)\(\displaystyle \frac{1}{5}\). The string stays taut and no boundary is reached. Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find the 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
A rough incline coupled to a hanging particle — objective 2
Maths4U Original · Short practice
A 4 kg particle is on a rough fixed plane. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{8}{17},\quad\cos\alpha=\frac{15}{17}\). It is connected to a hanging 8 kg particle by a light inextensible string over a smooth fixed pulley. The string is parallel to the plane at the contacting particle. The hanging particle descends and the plane particle slides up with \(\displaystyle F=\mu R\), where \(\displaystyle \mu =\)\(\displaystyle \frac{3}{10}\). The string stays taut and no boundary is reached. Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find the 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.
Apply
A rough incline coupled to a hanging particle — objective 3
Maths4U Original · Short practice
A 4 kg particle is on a rough fixed plane. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{8}{17},\quad\cos\alpha=\frac{15}{17}\). It is connected to a hanging 8 kg particle by a light inextensible string over a smooth fixed pulley. The string is parallel to the plane at the contacting particle. The hanging particle descends and the plane particle slides up with \(\displaystyle F=\mu R\), where \(\displaystyle \mu =\)\(\displaystyle \frac{3}{10}\). The string stays taut and no boundary is reached. Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find the normal reaction on the plane particle 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
A rough incline coupled to a hanging particle — objective 3
Maths4U Original · Short practice
A 5 kg particle is on a rough fixed plane. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{3}{5},\quad\cos\alpha=\frac{4}{5}\). It is connected to a hanging 10 kg particle by a light inextensible string over a smooth fixed pulley. The string is parallel to the plane at the contacting particle. The hanging particle descends and the plane particle slides up with \(\displaystyle F=\mu R\), where \(\displaystyle \mu =\)\(\displaystyle \frac{1}{10}\). The string stays taut and no boundary is reached. Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find the normal reaction on the plane particle 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.
Check understanding
A rough incline coupled to a hanging particle — objective 4
Maths4U Original · Short practice
A 5 kg particle is on a rough fixed plane. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{3}{5},\quad\cos\alpha=\frac{4}{5}\). It is connected to a hanging 10 kg particle by a light inextensible string over a smooth fixed pulley. The string is parallel to the plane at the contacting particle. The hanging particle descends and the plane particle slides up with \(\displaystyle F=\mu R\), where \(\displaystyle \mu =\)\(\displaystyle \frac{1}{10}\). The string stays taut and no boundary is reached. Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find the sliding friction 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.
Fresh review variant
A rough incline coupled to a hanging particle — objective 4
Maths4U Original · Short practice
A 6 kg particle is on a rough fixed plane. The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{5}{13},\quad\cos\alpha=\frac{12}{13}\). It is connected to a hanging 8 kg particle by a light inextensible string over a smooth fixed pulley. The string is parallel to the plane at the contacting particle. The hanging particle descends and the plane particle slides up with \(\displaystyle F=\mu R\), where \(\displaystyle \mu =\)\(\displaystyle \frac{1}{5}\). The string stays taut and no boundary is reached. Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find the sliding friction 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.