1.
A particle has constant acceleration 3 m s⁻². It starts at 4 m s⁻¹. Find its velocity after 5 s.
[2 marks]
- v = u + at
- Final answer: 19 m s⁻¹
JD SCIENCE
Mechanics
Indicative marking points. Award marks for equivalent scientific or mathematical wording. Do not issue this sheet with the student worksheet.
2.
It travels with u = 16 m s⁻¹, a = −2 m s⁻² for 4 s. Find the displacement.
[3 marks]
- s = ut + ½at²
- Final answer: 48 m
3.
A car accelerates from rest to 20 m s⁻¹ in 8 s. Find the acceleration and the distance travelled.
[3 marks]
- Final answer: a = 2.5 m s⁻²; s = 80 m
4.
A ball is thrown vertically upwards at 14 m s⁻¹. Take g = 9.8 m s⁻². Find the time to the top and the greatest height.
[4 marks]
- v=0 at top
- Final answer: t = 14/9.8 = 1.43 s; h = 10 m
5.
State the difference between distance and displacement, and between speed and velocity.
[3 marks]
- Displacement is a vector
- Velocity is a vector / has direction
6.
A particle moves with v = 3t² − 4. Find the acceleration at t = 2 and the displacement from t = 0 to 2 if s(0)=0.
[4 marks]
- a=dv/dt=6t; s=∫v dt = t³ − 4t
- Final answer: a = 12; s = 0
7.
Two forces 5 N and 12 N act at right angles. Find the magnitude of the resultant.
[2 marks]
- Pythagoras
- Final answer: 13 N
8.
Resolve a 20 N force at 30° to the horizontal into horizontal and vertical components.
[3 marks]
- 20 cos30, 20 sin30
- Final answer: 10√3 N horizontal, 10 N vertical
9.
A 3 kg particle is on a smooth horizontal surface. A 6 N force acts. Find the acceleration.
[2 marks]
- F=ma
- Final answer: 2 m s⁻²
10.
The same 3 kg particle is on a rough surface, μ = 0.2, g = 10. A horizontal 9 N force acts. Find the acceleration.
[4 marks]
- R=30 N
- Final answer: Friction = 6 N; a = 1 m s⁻²
11.
State the modelling assumptions for a particle and for a smooth surface.
[2 marks]
- Particle: mass concentrated at a point, no size/air resistance unless stated
- Smooth: no friction
12.
A 4 kg block is on a plane inclined at 30°. The plane is smooth. Find the acceleration down the plane. g = 10.
[3 marks]
- g sin30
- Final answer: 5 m s⁻²
13.
If that plane is rough with μ = 1/√3, show that the block is in limiting equilibrium or find the acceleration.
[4 marks]
- Compare mg sinθ with μ mg cosθ
- Final answer: F = μR = (1/√3)(4g cos30) = 4g/2 = 2g; component down = 2g, so limiting equilibrium if g=10: check numbers
14.
Connected particles: A (2 kg) on a table, B (3 kg) hanging, string smooth, pulley light. Find the acceleration. g=10.
[4 marks]
- 3g − T = 3a, T = 2a
- Final answer: a = 6 m s⁻²; T = 12 N
15.
Why is the tension the same throughout a light inextensible string that passes over a smooth pulley?
[2 marks]
- Light: no mass so net force on a string element is zero
- Smooth pulley: no friction
16.
A projectile is launched at 20 m s⁻¹ at 30° to the horizontal. g = 10. Find the time of flight on level ground and the range.
[5 marks]
- uy=10, T=2uy/g
- Final answer: T = 2 s; R = 20√3 m
17.
For that projectile, find the greatest height.
[3 marks]
- uy²/2g
- Final answer: 5 m
18.
Find the speed of that projectile after 1 s.
[3 marks]
- vx constant
- Final answer: √( (10√3)² + 0² ) = 10√3 m s⁻¹ at the top? At 1 s, vy=0, vx=10√3
19.
Write the suvat equations and state when they may be used.
[3 marks]
- Constant acceleration only
- v=u+at, s=ut+½at², v²=u²+2as, s=(u+v)t/2
20.
Momentum: a 2 kg trolley at 3 m s⁻¹ collides and sticks to a 1 kg trolley at rest. Find the common speed.
[3 marks]
- Conservation of momentum
- Final answer: 2 m s⁻¹
21.
The collision lasts 0.1 s. Find the impulse on the 1 kg trolley and the mean force.
[3 marks]
- I = Δmv
- Final answer: Impulse 2 N s; mean force 20 N
22.
State the difference between elastic and inelastic collisions in terms of kinetic energy.
[2 marks]
- Elastic: KE conserved
- Inelastic: KE not conserved
23.
A 50 N force does work moving a box 4 m along its line of action. Find the work done. If the force is at 60° to the displacement, find the work done.
[3 marks]
- W = Fd cosθ
- Final answer: 200 J ; 100 J
24.
A 2 kg mass falls 5 m. Find the loss in GPE and the speed if all becomes KE. g=10.
[3 marks]
- mgh = ½mv²
- Final answer: 100 J; v=10 m s⁻¹
25.
Power: a car travels at a constant 15 m s⁻¹ against a 400 N resistance. Find the driving force and the power.
[3 marks]
- P=Fv
- Final answer: F=400 N; P=6000 W
26.
A moment: a uniform 4 m beam of weight 20 N is supported at each end. A 10 N weight sits 1 m from A. Find the reactions at A and B.
[4 marks]
- Equilibrium
- Final answer: Take moments about A: 4B = 20×2 + 10×1; B=12.5 N, A=17.5 N
27.
State the two conditions for equilibrium of a rigid body.
[2 marks]
- Net force zero
- Net moment zero
28.
A particle has position r = (3t² − 2)i + (4t)j m. Find the velocity and speed at t = 1.
[3 marks]
- Final answer: v = 6i + 4j; speed = √52 = 2√13 m s⁻¹
29.
A OCR mechanics question usually tells you to take g = 9.8 or 10. Why must you state the value you use?
[2 marks]
- The numerical answer depends on g
- Method marks may still be awarded if g is shown
30.
A lift of mass 800 kg accelerates upwards at 0.5 m s⁻². Find the tension in the cable. g=10.
[3 marks]
- N2L
- Final answer: T − 8000 = 400; T = 8400 N
31.
A graph of v against t is a straight line from (0, 0) to (10, 15). Find the distance travelled and the acceleration.
[3 marks]
- Area under graph; gradient
- Final answer: s = 75 m; a = 1.5 m s⁻²
32.
Explain the difference between mass and weight, including units.
[2 marks]
- Mass in kg is scalar amount of matter
- Weight is mg, a force in N