Three connected particles and two different tensions · Short practice
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Recall
Three connected particles and two different tensions — objective 1
Maths4U Original · Short practice
Three particles A, B, C lie in that front-to-rear order along a horizontal rough track and move right. Their masses are 5, 4, 4 kg. Light inextensible strings join AB and BC. A pull \(78\) N acts right on A. Each particle has sliding friction \(\displaystyle F=\mu R\) with \(\displaystyle \mu =\)\(\displaystyle \frac{3}{10}\). The system starts from rest with both strings taut. Use \(\displaystyle g= \frac{10m}{s^{2}}\). No other horizontal force acts.
Find the common acceleration before any break, 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
Three connected particles and two different tensions — objective 1
Maths4U Original · Short practice
Three particles A, B, C lie in that front-to-rear order along a horizontal rough track and move right. Their masses are 6, 5, 5 kg. Light inextensible strings join AB and BC. A pull \(80\) N acts right on A. Each particle has sliding friction \(\displaystyle F=\mu R\) with \(\displaystyle \mu =\)\(\displaystyle \frac{1}{10}\). The system starts from rest with both strings taut. Use \(\displaystyle g= \frac{10m}{s^{2}}\). No other horizontal force acts.
Find the common acceleration before any break, 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
Three connected particles and two different tensions — objective 2
Maths4U Original · Short practice
Three particles A, B, C lie in that front-to-rear order along a horizontal rough track and move right. Their masses are 6, 5, 5 kg. Light inextensible strings join AB and BC. A pull \(80\) N acts right on A. Each particle has sliding friction \(\displaystyle F=\mu R\) with \(\displaystyle \mu =\)\(\displaystyle \frac{1}{10}\). The system starts from rest with both strings taut. Use \(\displaystyle g= \frac{10m}{s^{2}}\). No other horizontal force acts.
Find the tension in the front string AB 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 connected particles and two different tensions — objective 2
Maths4U Original · Short practice
Three particles A, B, C lie in that front-to-rear order along a horizontal rough track and move right. Their masses are 7, 2, 6 kg. Light inextensible strings join AB and BC. A pull \(45\) N acts right on A. Each particle has sliding friction \(\displaystyle F=\mu R\) with \(\displaystyle \mu =\)\(\displaystyle \frac{1}{5}\). The system starts from rest with both strings taut. Use \(\displaystyle g= \frac{10m}{s^{2}}\). No other horizontal force acts.
Find the tension in the front string AB 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 connected particles and two different tensions — objective 3
Maths4U Original · Short practice
Three particles A, B, C lie in that front-to-rear order along a horizontal rough track and move right. Their masses are 7, 2, 6 kg. Light inextensible strings join AB and BC. A pull \(45\) N acts right on A. Each particle has sliding friction \(\displaystyle F=\mu R\) with \(\displaystyle \mu =\)\(\displaystyle \frac{1}{5}\). The system starts from rest with both strings taut. Use \(\displaystyle g= \frac{10m}{s^{2}}\). No other horizontal force acts.
Find the tension in the rear string BC 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 connected particles and two different tensions — objective 3
Maths4U Original · Short practice
Three particles A, B, C lie in that front-to-rear order along a horizontal rough track and move right. Their masses are 3, 3, 7 kg. Light inextensible strings join AB and BC. A pull \(65\) N acts right on A. Each particle has sliding friction \(\displaystyle F=\mu R\) with \(\displaystyle \mu =\)\(\displaystyle \frac{3}{10}\). The system starts from rest with both strings taut. Use \(\displaystyle g= \frac{10m}{s^{2}}\). No other horizontal force acts.
Find the tension in the rear string BC 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
Three connected particles and two different tensions — objective 4
Maths4U Original · Short practice
Three particles A, B, C lie in that front-to-rear order along a horizontal rough track and move right. Their masses are 3, 3, 7 kg. Light inextensible strings join AB and BC. A pull \(65\) N acts right on A. Each particle has sliding friction \(\displaystyle F=\mu R\) with \(\displaystyle \mu =\)\(\displaystyle \frac{3}{10}\). The system starts from rest with both strings taut. Use \(\displaystyle g= \frac{10m}{s^{2}}\). No other horizontal force acts.
Immediately after AB breaks, find the signed acceleration of B and C, positive right, 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
Three connected particles and two different tensions — objective 4
Maths4U Original · Short practice
Three particles A, B, C lie in that front-to-rear order along a horizontal rough track and move right. Their masses are 4, 4, 2 kg. Light inextensible strings join AB and BC. A pull \(40\) N acts right on A. Each particle has sliding friction \(\displaystyle F=\mu R\) with \(\displaystyle \mu =\)\(\displaystyle \frac{1}{10}\). The system starts from rest with both strings taut. Use \(\displaystyle g= \frac{10m}{s^{2}}\). No other horizontal force acts.
Immediately after AB breaks, find the signed acceleration of B and C, positive right, 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.