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devlian [24]
3 years ago
6

A student standing on a stationary skateboard tosses a textbook with a mass of mb = 1.5 kg to a friend standing in front of him.

The student and the skateboard have a combined mass of mc = 105 kg and the book leaves his hand at a velocity of vb = 2.97 m/s at an angle of 26° with respect to the horizontal.
(a)Write an expression for the magnitude of the velocity of the student,vs, after throwing the book(b)Calculate the magnitude of the velocity of the student,vs, in meters per second?(c)What is the magnitude of the momentum,pe, which was transferred from the skateboard to the the Earth during the time the book isbeing thrown (in kilogram meters per second)?
Physics
1 answer:
RSB [31]3 years ago
5 0

Answer:

a) v_s=\frac{m_bv_bcos\theta}{m_c}

b)  v_s=0.0385 m/s

c) P_e= 1.952 kg.m/s

Explanation:

Given:

Mass of the skateboard, m_b = 1.5 kg

Combined mass, m_c = 105 kg

velocity of the book, v_b = 2.97 m/s

angle, θ = 26°

thus,

horizontal component of the velocity = vcosθ

vertical component of velocity = vsinθ

a) Applying the concept of conservation of momentum

m_bv_bcos\theta=m_cv_s

where,

v_s is the velocity of the the student

thus,

v_s=\frac{m_bv_bcos\theta}{m_c}      ............(1)

b) on substituting the values, in the equation we get the magnitude

v_s=\frac{1.5\times2.97cos26^o}{105}

or

v_s=0.0385 m/s

c) Now, the momentum (P) transferred is given as:

P = mass × velocity

on substituting the values, we get

P_e= mass × velocity

or

P_e= m_b\times v_b\times \sin\theta

on substituting the values, we get

P_e= 1.5\times 2.97\times \sin26^o

or

P_e= 1.952 kg.m/s

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<h2>Answer:</h2>

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Energy = <em>3.54 x 10³³ J</em>

Average power = <em>1.02 x 10²⁸ W</em>

<h2>Explanation:</h2>

(a) Torque (τ) is the rotational effect of a given force.  

It is given by

τ = I x α          -------------(i)

Where;

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α = angular acceleration of the object.

In this case, the object is the Earth. Therefore,

I = 9.71 x 10³⁷ kg m²

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<em>1 day = 24 hours and 1 hour = 3600seconds</em>

<em>1 day = 24 x 3600 seconds = 86400seconds</em>

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<em>=> ω = 7.29 × 10⁻⁵ rad/s</em>

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t = 4 days = 4 x 24 x 3600 seconds = 345600 seconds

=> α = ω / t

=> α = 7.29 × 10⁻⁵ / 345600

=> α = (7.29 × 10⁻⁵) / (3.456 x 10⁵)

=> α = (7.29 × 10⁻⁵⁻⁵) / (3.456)

=> α = (7.29 × 10⁻¹⁰) / (3.456)

=> α = 2.11 × 10⁻¹⁰ rad/s²

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τ = 9.71 x 10³⁷ x 2.11 × 10⁻¹⁰

τ = 9.71 x 10²⁷ x 2.11

τ = 20.5 x 10²⁷ Nm

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(ii) The energy (rotational energy) E is given by;

E = \frac{1}{2} x I x ω

E = \frac{1}{2} x 9.71 x 10³⁷ x 7.29 × 10⁻⁵

E = 35.4 x 10³² J

E = 3.54 x 10³³ J

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P = E / t

P = 3.54 x 10³³ / 345600

P = 1.02 x 10²⁸ W

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