Chapter 9: Q. 45 (page 229)

Susan’s $10$ kg baby brother Paul sits on a mat. Susan pulls the mat across the floor using a rope that is angled $30 °$ above the floor. The tension is a constant $30$ N and the coefficient of friction is $0.20$ . Use work and energy to find Paul’s speed after being pulled $3.0$ m.

Short Answer

Expert verified

Paul's speed after being pulled $3$ m is $2.37$ m/s

Step by step solution

Step 1. Given Information

Mass $m = 10$ kg

Tension $= 30$ N

the coefficient of friction $= 0.20$

Step 2. Find the magnitude of friction

We use second Newton's law for direction perpendicular to motion, or $y$ direction

$m a_{y} = 0 = - F_{g r a v i t a t i o n a l} + N + F \sin 30 ° N = m g - F \sin 30 ° N = 10 k g \cdot 9.8 m / s^{2} - 30 N \cdot 0.5 N = 83 N$

Friction is defined as

$F_{f r i c t i o n} = N μ F_{f r i c t i o n} = 83 N \cdot 0.2 F_{f r i c t i o n} = 16.6 N$

Step 3. Work done by friction if Paul is pulled 3 m

$W_{f r i c t i o n} = F_{f r i c t i o n} \cdot d W_{f r i c t i o n} = 16.6 N \cdot 3 m W_{f r i c t i o n} = 49.8 J$

Step 4. Work done by rope on Paul

$W_{r o p e} = F \cos 30 ° \cdot d W_{r o p e} = 30 N \cdot \cos 30 ° \cdot 3 m W_{r o p e} = 77.9 J$

Step 5. Total work done on mat and Paul

$W_{r o p e} = W_{r o p e} + W_{f r i c t i o n} W = 77.9 J - 49.8 J W = 28.1 J$

Step 6. Find Paul's speed

From the work-kinetic theorem, we can calculate Paul's speed

$W = ∆ K W = K_{f i n a l} - K_{i n i t i a l} W = \frac{1}{2} m {v^{2}}_{f i n a l} \Rightarrow v_{f i n a l} = \sqrt{\frac{2 W}{m}} v_{f i n a l} = \sqrt{\frac{2 \cdot 28.1 J}{10 k g}} v_{f i n a l} = 2.37 m / s$

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Susan’s $10$ kg baby brother Paul sits on a mat. Susan pulls the mat across the floor using a rope that is angled $30 °$ above the floor. The tension is a constant $30$ N and the coefficient of friction is $0.20$ . Use work and energy to find Paul’s speed after being pulled $3.0$ m.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find the magnitude of friction

Step 3. Work done by friction if Paul is pulled 3 m

Step 4. Work done by rope on Paul

Step 5. Total work done on mat and Paul

Step 6. Find Paul's speed

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Susan’s 10 kg baby brother Paul sits on a mat. Susan pulls the mat across the floor using a rope that is angled 30°above the floor. The tension is a constant 30N and the coefficient of friction is 0.20. Use work and energy to find Paul’s speed after being pulled3.0 m.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find the magnitude of friction

Step 3. Work done by friction if Paul is pulled 3 m

Step 4. Work done by rope on Paul

Step 5. Total work done on mat and Paul

Step 6. Find Paul's speed

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism and Electromagnetic Induction

Astrophysics

Solid State Physics

Translational Dynamics

Atoms and Radioactivity

Conservation of Energy and Momentum

Study anywhere. Anytime. Across all devices.

Susan’s $10$ kg baby brother Paul sits on a mat. Susan pulls the mat across the floor using a rope that is angled $30 °$ above the floor. The tension is a constant $30$ N and the coefficient of friction is $0.20$ . Use work and energy to find Paul’s speed after being pulled $3.0$ m.