An adult with a child is cycling along a straight level path. The child is in a trailer, which is connected to the bike by a tow bar. The combined mass of the bike and the adult is 85 kg. The combined mass of the child and trailer is 28 kg. The forward force on the bike and trailer is 125 N. A frictional force of 45 N acts on the bike. A frictional force of 15 N acts on the trailer. (a) Show that the acceleration of the bike and trailer is 0.58 m/s². (b) Determine the magnitude of the tension in the tow bar. (c) As the speed of the bike and trailer increases, the friction forces on both the bike and the trailer increase. State whether the tension in the tow bar increases, decreases, or stays the same. Justify your answer.

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An adult with a child is cycling along a straight level path - Scottish Highers Physics - Question 2 - 2023

Question 2

An adult with a child is cycling along a straight level path. The child is in a trailer, which is connected to the bike by a tow bar. The combined mass of the bike ... show full transcript

Worked Solution & Example Answer:An adult with a child is cycling along a straight level path - Scottish Highers Physics - Question 2 - 2023

Step 1

Show that the acceleration of the bike and trailer is 0.58 m/s².

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Answer

To find the acceleration, we first need to analyze the forces acting on the system. The net force acting on the bike and trailer can be calculated using:

$F_{net} = F_{forward} - F_{friction}$

The total friction acting on the bike and trailer is:

$F_{friction, total} = 45 ext{ N (bike)} + 15 ext{ N (trailer)} = 60 ext{ N}$

The total forward force acting on the system is given as 125 N. Thus, the net force can be calculated as:

$F_{net} = 125 ext{ N} - 60 ext{ N} = 65 ext{ N}$

The total mass of the bike and trailer is:

$M_{total} = 28 ext{ kg} + 85 ext{ kg} = 113 ext{ kg}$

Using Newton's second law, we can find the acceleration:

ightarrow a = \frac{F}{m} = \frac{65 ext{ N}}{113 ext{ kg}} \approx 0.58 ext{ m/s}²$$ This confirms that the acceleration of the bike and trailer is indeed 0.58 m/s².

Step 2

Determine the magnitude of the tension in the tow bar.

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Answer

To determine the tension in the tow bar, we can again apply Newton's second law. The equation for the forces acting on the child and trailer can be expressed as:

$F_{net} = T - F_{friction}$

The net force acting on the trailer (combined mass of child and trailer is 28 kg) is given by:

$F_{net} = ma = 28 ext{ kg} imes 0.58 ext{ m/s}² = 16.24 ext{ N}$

Substituting the known values:

$16.24 ext{ N} = T - 15 ext{ N}$

Now, solving for T:

$T = 16.24 ext{ N} + 15 ext{ N} = 31.24 ext{ N}$

Hence, the magnitude of the tension in the tow bar is approximately 31.24 N.

Step 3

State whether the tension in the tow bar increases, decreases, or stays the same.

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Answer

The tension in the tow bar increases. As the speed of the bike and trailer increases, the friction forces also increase. However, the net unbalanced force acting on the system remains constant, therefore leading to an increase in tension to counterbalance the growing frictional forces acting on the system. This results in the necessity for the tension to increase in order to maintain the same net force required for the given acceleration.

An adult with a child is cycling along a straight level path - Scottish Highers Physics - Question 2 - 2023

Worked Solution & Example Answer:An adult with a child is cycling along a straight level path - Scottish Highers Physics - Question 2 - 2023

Show that the acceleration of the bike and trailer is 0.58 m/s².

Determine the magnitude of the tension in the tow bar.

State whether the tension in the tow bar increases, decreases, or stays the same.

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