Question\begin{tabular}{|l|l|l|} \hline Pulley Setup & Weight of Load & Tension in Rope \\ \hline Pulley A & 10 N & 10 N \\ \hline Pulley B & 10 N & 5 N \\ \hline \end{tabular}
Based on the data and the diagram, why is the tension in the rope lower in pulley B? Prove your explanation using force-acceleration equaticns for the loads in both pulley systems. $\square$ B I $\underline{\cup}$ $x^{2} \quad x_{2} \Omega$ 2

Studdy Solution

STEP 1

1. Pulley A and Pulley B are ideal pulleys with no friction.
2. The weight of the load is the force due to gravity acting on it.
3. The tension in the rope is the force transmitted through the rope.
4. The system is in equilibrium, meaning the net force acting on each load is zero.

STEP 2

1. Analyze the forces in Pulley A.
2. Analyze the forces in Pulley B.
3. Compare the tension in both pulley systems using force equations.

STEP 3

For Pulley A, the weight of the load is balanced by the tension in the rope. Since the system is in equilibrium:
$T_A = W_A = 10 \, \text{N}$
where $T_A$ is the tension in Pulley A, and $W_A$ is the weight of the load.

STEP 4

For Pulley B, the tension in the rope is less than the weight of the load. This suggests a mechanical advantage due to the pulley setup. The force balance equation is:
$2T_B = W_B$
where $T_B$ is the tension in Pulley B, and $W_B = 10 \, \text{N}$ .

STEP 5

Solve for $T_B$ :
$2T_B = 10 \, \text{N}$
$T_B = \frac{10 \, \text{N}}{2} = 5 \, \text{N}$

STEP 6

Compare the tension in both pulley systems:
- In Pulley A, the tension equals the weight of the load because there is no mechanical advantage. - In Pulley B, the tension is half the weight of the load due to the mechanical advantage provided by the pulley configuration.
The tension in the rope is lower in Pulley B because the pulley system provides a mechanical advantage, effectively distributing the load across two segments of the rope, thereby reducing the tension required to balance the load.

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Studdy Solution

STEP 1

1. Pulley A and Pulley B are ideal pulleys with no friction.
2. The weight of the load is the force due to gravity acting on it.
3. The tension in the rope is the force transmitted through the rope.
4. The system is in equilibrium, meaning the net force acting on each load is zero.

STEP 2

1. Analyze the forces in Pulley A.
2. Analyze the forces in Pulley B.
3. Compare the tension in both pulley systems using force equations.

STEP 3

For Pulley A, the weight of the load is balanced by the tension in the rope. Since the system is in equilibrium:
$T_A = W_A = 10 \, \text{N}$
where $T_A$ is the tension in Pulley A, and $W_A$ is the weight of the load.

STEP 4

For Pulley B, the tension in the rope is less than the weight of the load. This suggests a mechanical advantage due to the pulley setup. The force balance equation is:
$2T_B = W_B$
where $T_B$ is the tension in Pulley B, and $W_B = 10 \, \text{N}$ .

STEP 5

Solve for $T_B$ :
$2T_B = 10 \, \text{N}$
$T_B = \frac{10 \, \text{N}}{2} = 5 \, \text{N}$

STEP 6

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Studdy Solution

STEP 1

1. Pulley A and Pulley B are ideal pulleys with no friction.2. The weight of the load is the force due to gravity acting on it.3. The tension in the rope is the force transmitted through the rope.4. The system is in equilibrium, meaning the net force acting on each load is zero.

STEP 2

1. Analyze the forces in Pulley A.2. Analyze the forces in Pulley B.3. Compare the tension in both pulley systems using force equations.

STEP 3

For Pulley A, the weight of the load is balanced by the tension in the rope. Since the system is in equilibrium:TA=WA=10 N T_A = W_A = 10 \, \text{N} TA​=WA​=10Nwhere TA T_A TA​ is the tension in Pulley A, and WA W_A WA​ is the weight of the load.

STEP 4

For Pulley B, the tension in the rope is less than the weight of the load. This suggests a mechanical advantage due to the pulley setup. The force balance equation is:2TB=WB 2T_B = W_B 2TB​=WB​where TB T_B TB​ is the tension in Pulley B, and WB=10 N W_B = 10 \, \text{N} WB​=10N.

STEP 5

Solve for TB T_B TB​:2TB=10 N 2T_B = 10 \, \text{N} 2TB​=10NTB=10 N2=5 N T_B = \frac{10 \, \text{N}}{2} = 5 \, \text{N} TB​=210N​=5N

STEP 6

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1. Pulley A and Pulley B are ideal pulleys with no friction.
2. The weight of the load is the force due to gravity acting on it.
3. The tension in the rope is the force transmitted through the rope.
4. The system is in equilibrium, meaning the net force acting on each load is zero.

1. Analyze the forces in Pulley A.
2. Analyze the forces in Pulley B.
3. Compare the tension in both pulley systems using force equations.

For Pulley A, the weight of the load is balanced by the tension in the rope. Since the system is in equilibrium:
$T_A = W_A = 10 \, \text{N}$
where $T_A$ is the tension in Pulley A, and $W_A$ is the weight of the load.

For Pulley B, the tension in the rope is less than the weight of the load. This suggests a mechanical advantage due to the pulley setup. The force balance equation is:
$2T_B = W_B$
where $T_B$ is the tension in Pulley B, and $W_B = 10 \, \text{N}$ .

Solve for $T_B$ :
$2T_B = 10 \, \text{N}$
$T_B = \frac{10 \, \text{N}}{2} = 5 \, \text{N}$