Maths4U Original · Short practice

A 3 kg particle is projected up a fixed rough plane at \(\displaystyle \frac{10m}{s}\). The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{8}{17},\quad\cos\alpha=\frac{15}{17}\). The coefficient is \(\displaystyle \frac{3}{10}\), with static limit \(\displaystyle F\le \mu R\) and sliding friction \(\displaystyle F=\mu R\). Use \(\displaystyle g= \frac{10m}{s^{2}}\). The plane is long enough for the complete motion to the first stop and subsequent return.

Find the positive deceleration magnitude while the particle moves up the plane, 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.

Maths4U Original · Short practice

A 4 kg particle is projected up a fixed rough plane at \(\displaystyle \frac{11m}{s}\). The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{3}{5},\quad\cos\alpha=\frac{4}{5}\). The coefficient is \(\displaystyle \frac{1}{10}\), with static limit \(\displaystyle F\le \mu R\) and sliding friction \(\displaystyle F=\mu R\). Use \(\displaystyle g= \frac{10m}{s^{2}}\). The plane is long enough for the complete motion to the first stop and subsequent return.

Find the positive deceleration magnitude while the particle moves up the plane, 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.

Maths4U Original · Short practice

A 4 kg particle is projected up a fixed rough plane at \(\displaystyle \frac{11m}{s}\). The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{3}{5},\quad\cos\alpha=\frac{4}{5}\). The coefficient is \(\displaystyle \frac{1}{10}\), with static limit \(\displaystyle F\le \mu R\) and sliding friction \(\displaystyle F=\mu R\). Use \(\displaystyle g= \frac{10m}{s^{2}}\). The plane is long enough for the complete motion to the first stop and subsequent return.

Find the distance travelled up the plane 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.

Maths4U Original · Short practice

A 5 kg particle is projected up a fixed rough plane at \(\displaystyle \frac{12m}{s}\). The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{5}{13},\quad\cos\alpha=\frac{12}{13}\). The coefficient is \(\displaystyle \frac{1}{5}\), with static limit \(\displaystyle F\le \mu R\) and sliding friction \(\displaystyle F=\mu R\). Use \(\displaystyle g= \frac{10m}{s^{2}}\). The plane is long enough for the complete motion to the first stop and subsequent return.

Find the distance travelled up the plane 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.

Maths4U Original · Short practice

A 5 kg particle is projected up a fixed rough plane at \(\displaystyle \frac{12m}{s}\). The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{5}{13},\quad\cos\alpha=\frac{12}{13}\). The coefficient is \(\displaystyle \frac{1}{5}\), with static limit \(\displaystyle F\le \mu R\) and sliding friction \(\displaystyle F=\mu R\). Use \(\displaystyle g= \frac{10m}{s^{2}}\). The plane is long enough for the complete motion to the first stop and subsequent return.

Find the sliding friction magnitude in either moving stage, 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 projected up a fixed rough plane at \(\displaystyle \frac{13m}{s}\). The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{8}{17},\quad\cos\alpha=\frac{15}{17}\). The coefficient is \(\displaystyle \frac{3}{10}\), with static limit \(\displaystyle F\le \mu R\) and sliding friction \(\displaystyle F=\mu R\). Use \(\displaystyle g= \frac{10m}{s^{2}}\). The plane is long enough for the complete motion to the first stop and subsequent return.

Find the sliding friction magnitude in either moving stage, 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 projected up a fixed rough plane at \(\displaystyle \frac{13m}{s}\). The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{8}{17},\quad\cos\alpha=\frac{15}{17}\). The coefficient is \(\displaystyle \frac{3}{10}\), with static limit \(\displaystyle F\le \mu R\) and sliding friction \(\displaystyle F=\mu R\). Use \(\displaystyle g= \frac{10m}{s^{2}}\). The plane is long enough for the complete motion to the first stop and subsequent return.

Find the acceleration down the plane after it starts sliding back, 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.

Maths4U Original · Short practice

A 7 kg particle is projected up a fixed rough plane at \(\displaystyle \frac{14m}{s}\). The acute angle α satisfies \(\displaystyle \sin\alpha=\frac{3}{5},\quad\cos\alpha=\frac{4}{5}\). The coefficient is \(\displaystyle \frac{1}{10}\), with static limit \(\displaystyle F\le \mu R\) and sliding friction \(\displaystyle F=\mu R\). Use \(\displaystyle g= \frac{10m}{s^{2}}\). The plane is long enough for the complete motion to the first stop and subsequent return.

Find the acceleration down the plane after it starts sliding back, 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.