Grade 11 Physical Sciences · Mechanics

Solve problems with connected bodies

Use F_net = ma for each of two or more joined objects to find their acceleration or the tension in the string (two blocks pulled by a rope).

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Grade 11 Newton Laws: Connected objectsKevinmathscience

Newton's Laws Exam Practice Question Gr 11 and 12 Physics: Two body systemMiss Martins Maths and Science

Calculating Contact Forces Between Two Blocks Using Free Body DiagramsThe Organic Chemistry Tutor

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Question 2.4 · May/June 2023 · Paper 1 · National (DBE) · 5 marks

Block A of mass m is connected to block B of mass

7, 5

kg by a light inextensible rope passing over a frictionless pulley. Block B is initially held at a height of

1, 5

m above the ground, while block A is initially stationary on the ground, as shown in the diagram below.

When block B is released, it moves vertically downwards and strikes the ground with a velocity of

3, 41

m·s

^{- 1}

.

Ignore the effects of friction. Diagram for this question

2.4 Calculate the value of m by applying Newton's Second Law to EACH BLOCK while they are in motion.(5)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: solve problems with connected bodies

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3. Question 2.3.2 · November 2024 · Paper 1 · National (DBE) · 5 marks
In an experiment, a crate of mass $8, 5$ kg, lying stationary on a rough horizontal table, is connected to a mass hanger by means of a light inextensible string passing over a frictionless pulley, as shown in the diagram below. Mass pieces are added to the mass hanger and the acceleration of the crate is measured. The experiment is repeated several times by adding different masses to increase the hanging mass each time.

Ignore the effects of air friction.

The results obtained were used to draw the sketch graph below.
2.3 Calculate the:
2.3.2 Magnitude of the acceleration represented by Y on the graph if the coefficient of kinetic friction between the crate and the table is $0, 40$ (5)
Show the memo (5 ticks)Memo
1. ✓
  Newton's second law for the crate (any one)For the crate: $F_{n e t} = ma$
  $T - f_{k} = ma$
  (OR $f_{k} - T = ma$ )
  $T - μ_{k} m g = ma$
  1 mark · Solve problems with connected bodies
2. ✓
  Friction term for the crate $T - 0, 4 (8, 5) (9, 8) = 8, 5 a$ ...... Eqn (1)
  
  (The tick is for $T - 0, 4 (8, 5) (9, 8)$ .)
  1 mark · Solve problems with connected bodies
3. ✓
  Forces on the hanging massFor the hanging mass: $F_{n e t} = ma$
  $m g - T = ma$
  $7, 4 (9, 8) - T = 7, 4 a$ ...... Eqn (2)
  
  (The tick is for $7, 4 (9, 8) - T$ .)
  1 mark · Solve problems with connected bodies
4. ✓
  $ma$ side of the equations (any one) $= 8, 5 a$ in Eqn (1) OR $= 7, 4 a$ in Eqn (2)
  1 mark · Solve problems with connected bodies
5. ✓
  AnswerAdding Eqn (1) and Eqn (2): $72, 52 - 33, 32 = 15, 9 a$
  $Y = a = 2, 47$ (m·s $^{- 2}$ )
  1 mark · Solve problems with connected bodies
4. Question 2.3.2 · November 2023 · Paper 1 · National (DBE) · 3 marks
Two blocks, $A$ , of mass $4$ kg, and $B$ , of mass $9$ kg, are connected by a light inextensible string. The blocks are held at rest on a plane which is inclined at an angle of $35°$ with the horizontal.

A constant force, $F$ , acting parallel to the plane, is applied to block $B$ , as shown in the diagram below. The blocks now accelerate up the plane at $2$ m·s $^{- 2}$ .
2.3 Calculate the magnitude of:
2.3.2 Force $F$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Substitution of the forcesFor block B, up the incline as positive:
  $F_{n e t} = ma$
  $F - T - f_{k} - m g sin θ = ma$
  $F - 36, 36 - 13, 23 - 9 (9, 8) sin 35°$
  1 mark · Solve problems with connected bodies
2. ✓
  Substitution of ma $= (9) (2)$
  1 mark · Solve problems with connected bodies
3. ✓
  Answer with unit $F = 118, 18$ N
  1 mark · Solve problems with connected bodies
5. Question 2.3.2 · November 2022 · Paper 1 · National (DBE) · 3 marks
Crate P of mass $1, 25$ kg is connected to another crate, Q, of mass $2$ kg by a light inextensible string. The two crates are placed on a rough horizontal surface. A constant force F of magnitude $7, 5$ N, acting at angle $θ$ to the horizontal, is applied on crate Q, as shown in the diagram below.

The crates accelerate at $0, 1$ m·s $^{- 2}$ to the right.

Crate P experiences a constant frictional force of $1, 8$ N and crate Q experiences a constant frictional force of $2, 2$ N.
2.3 Calculate the magnitude of:
2.3.2 Angle $θ$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Substitution of forces on QFor Q, right as positive:
  $F_{n e t} = ma$
  $F cos θ - T - f = ma$
  $7, 5 cos θ - 1, 93 - 2, 2$
  1 mark · Solve problems with connected bodies
2. ✓
  Substitution of ma $= (2) (0, 1)$
  1 mark · Solve problems with connected bodies
3. ✓
  Answer $7, 5 cos θ = 0, 2 + 1, 93 + 2, 2 = 4, 33$
  $θ = 54, 74°$
  1 mark · Solve problems with connected bodies
6. Question 3.2.3 · November 2025 · Paper 1 · Provincial · 3 marks
Truck $A$ , of mass $4500$ kg travels at a CONSTANT VELOCITY while towing bakkie $B$ , of mass $1250$ kg. The engine of truck $A$ produces a force of $11270$ N. The road surface exerts a frictional force of $8820$ N on truck $A$ .
3.2 Calculate the:
3.2.3 Magnitude tension in the tow rope(3)
Show the memo (3 ticks)Memo
1. ✓
  Fnet expression for the truckTruck A:
  $F_{n e t} = F - f_{k} - T$
  1 mark · Solve problems with connected bodies
2. ✓
  Substitution $0 = 11270 + (- 8820) - T$
  1 mark · Solve problems with connected bodies
3. ✓
  Answer with unit $T = 2450$ N
  1 mark · Solve problems with connected bodies

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