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Recall
Energy on a smooth curved track — objective 1
Maths4U Original · Short practice
A bead of mass 7 kg is constrained to a smooth fixed guide in a vertical plane. At A its speed is \(\displaystyle \frac{6m}{s}\). It descends a vertical height \(\displaystyle \frac{133}{20}\) m to B, then the guide rises far enough for it to reach its first stop. Gravity is the only force doing work, and the bead remains on the guide. Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find its speed at B in m/s.
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
Energy on a smooth curved track — objective 1
Maths4U Original · Short practice
A bead of mass 8 kg is constrained to a smooth fixed guide in a vertical plane. At A its speed is \(\displaystyle \frac{7m}{s}\). It descends a vertical height \(\displaystyle \frac{147}{20}\) m to B, then the guide rises far enough for it to reach its first stop. Gravity is the only force doing work, and the bead remains on the guide. Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find its speed at B in m/s.
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
Energy on a smooth curved track — objective 2
Maths4U Original · Short practice
A bead of mass 8 kg is constrained to a smooth fixed guide in a vertical plane. At A its speed is \(\displaystyle \frac{7m}{s}\). It descends a vertical height \(\displaystyle \frac{147}{20}\) m to B, then the guide rises far enough for it to reach its first stop. Gravity is the only force doing work, and the bead remains on the guide. Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find its kinetic-energy increase from A to B in J.
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
Energy on a smooth curved track — objective 2
Maths4U Original · Short practice
A bead of mass 9 kg is constrained to a smooth fixed guide in a vertical plane. At A its speed is \(\displaystyle \frac{2m}{s}\). It descends a vertical height \(\displaystyle \frac{221}{20}\) m to B, then the guide rises far enough for it to reach its first stop. Gravity is the only force doing work, and the bead remains on the guide. Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find its kinetic-energy increase from A to B in J.
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
Energy on a smooth curved track — objective 3
Maths4U Original · Short practice
A bead of mass 9 kg is constrained to a smooth fixed guide in a vertical plane. At A its speed is \(\displaystyle \frac{2m}{s}\). It descends a vertical height \(\displaystyle \frac{221}{20}\) m to B, then the guide rises far enough for it to reach its first stop. Gravity is the only force doing work, and the bead remains on the guide. Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find how far above A it can rise before its first stop, in m.
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
Energy on a smooth curved track — objective 3
Maths4U Original · Short practice
A bead of mass 3 kg is constrained to a smooth fixed guide in a vertical plane. At A its speed is \(\displaystyle \frac{3m}{s}\). It descends a vertical height \(\displaystyle \frac{247}{20}\) m to B, then the guide rises far enough for it to reach its first stop. Gravity is the only force doing work, and the bead remains on the guide. Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find how far above A it can rise before its first stop, in m.
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
Energy on a smooth curved track — objective 4
Maths4U Original · Short practice
A bead of mass 3 kg is constrained to a smooth fixed guide in a vertical plane. At A its speed is \(\displaystyle \frac{3m}{s}\). It descends a vertical height \(\displaystyle \frac{247}{20}\) m to B, then the guide rises far enough for it to reach its first stop. Gravity is the only force doing work, and the bead remains on the guide. Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find the greatest vertical height above B in m.
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
Energy on a smooth curved track — objective 4
Maths4U Original · Short practice
A bead of mass 4 kg is constrained to a smooth fixed guide in a vertical plane. At A its speed is \(\displaystyle \frac{4m}{s}\). It descends a vertical height \(\displaystyle \frac{273}{20}\) m to B, then the guide rises far enough for it to reach its first stop. Gravity is the only force doing work, and the bead remains on the guide. Use \(\displaystyle g= \frac{10m}{s^{2}}\).
Find the greatest vertical height above B in m.
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.