Hint
Choose and retain a positive direction; distinguish signed quantities from magnitudes. Resolve the weight down the plane and divide by mass.
Worked solution
(a)
Resolve the weight down the plane and divide by mass.
Ma=Mg sin α gives \(\displaystyle a=\)\(\displaystyle \frac{50}{13}\) \(\displaystyle \frac{m}{s^{2}}\).
Answer: \(\displaystyle \frac{50}{13}\) \(\displaystyle \frac{m}{s^{2}}\)
(b)
Use the constant downslope acceleration and the positive speed root.
Using \(\displaystyle v^{2}\)=2as gives \(4.80\) m/s.
Answer: \(4.80\) m/s
(c)
Use zero acceleration perpendicular to the fixed plane.
Normal balance gives \(\displaystyle R=Mg \cos \alpha =\)\(\displaystyle \frac{240}{13}\) N.
Answer: \(\displaystyle \frac{240}{13}\) N
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 2 marks
- 1 mark: Resolve the weight down the plane and divide by mass.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Use Mg sin α for the downslope component, not the full weight.
(b) · 2 marks
- 1 mark: Use the constant downslope acceleration and the positive speed root.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and required final precision is acceptable.
Common error: A smooth surface removes friction, not gravity.
(c) · 2 marks
- 1 mark: Use zero acceleration perpendicular to the fixed plane.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Use Mg sin α for the downslope component, not the full weight.
Total: 6 marks.