Maths4U Original · Short practice

A 8 kg particle is released from rest on a rough fixed plane with \(\displaystyle \sin \alpha = \frac{3}{5}\) and \(\displaystyle \cos \alpha = \frac{4}{5}\). The coefficient of friction is \(\displaystyle \frac{9}{10}\). For the initial release, no additional applied force acts. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

Find the friction required for rest, 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 9 kg particle is released from rest on a rough fixed plane with \(\displaystyle \sin \alpha = \frac{3}{5}\) and \(\displaystyle \cos \alpha = \frac{4}{5}\). The coefficient of friction is \(1\). For the initial release, no additional applied force acts. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

Find the friction required for rest, 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 9 kg particle is released from rest on a rough fixed plane with \(\displaystyle \sin \alpha = \frac{3}{5}\) and \(\displaystyle \cos \alpha = \frac{4}{5}\). The coefficient of friction is \(1\). For the initial release, no additional applied force acts. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

Find the maximum available 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.

Maths4U Original · Short practice

A 10 kg particle is released from rest on a rough fixed plane with \(\displaystyle \sin \alpha = \frac{3}{5}\) and \(\displaystyle \cos \alpha = \frac{4}{5}\). The coefficient of friction is \(\displaystyle \frac{11}{10}\). For the initial release, no additional applied force acts. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

Find the maximum available 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.

Maths4U Original · Short practice

A 10 kg particle is released from rest on a rough fixed plane with \(\displaystyle \sin \alpha = \frac{3}{5}\) and \(\displaystyle \cos \alpha = \frac{4}{5}\). The coefficient of friction is \(\displaystyle \frac{11}{10}\). For the initial release, no additional applied force acts. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

Find the amount by which the friction cap exceeds the required friction, 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 released from rest on a rough fixed plane with \(\displaystyle \sin \alpha = \frac{3}{5}\) and \(\displaystyle \cos \alpha = \frac{4}{5}\). The coefficient of friction is \(\displaystyle \frac{4}{5}\). For the initial release, no additional applied force acts. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

Find the amount by which the friction cap exceeds the required friction, 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 released from rest on a rough fixed plane with \(\displaystyle \sin \alpha = \frac{3}{5}\) and \(\displaystyle \cos \alpha = \frac{4}{5}\). The coefficient of friction is \(\displaystyle \frac{4}{5}\). For the initial release, no additional applied force acts. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

With the same coefficient, find the greatest acute plane angle permitting rest without another force, 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 4 kg particle is released from rest on a rough fixed plane with \(\displaystyle \sin \alpha = \frac{3}{5}\) and \(\displaystyle \cos \alpha = \frac{4}{5}\). The coefficient of friction is \(\displaystyle \frac{9}{10}\). For the initial release, no additional applied force acts. Use \(\displaystyle g= \frac{10m}{s^{2}}\).

With the same coefficient, find the greatest acute plane angle permitting rest without another force, 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.