Question

use concepts from this unit to solve all problems. i.e. you should use equations/concepts in relation to work and energy to solve problems related to speed/velocity.

1. a 85 kg couch is pushed with a force of 150 n right for 5.0 m over a 7.0 s period. if the couch is initially moving at a speed of 1.3 m/s, what will be the final velocity of the couch? 3 marks - a
2. an object is dropped from a cliff of unknown height. assume the process of energy transformation is only 67% efficient:

a. what is the height of the cliff if the object is falling at a speed of 18 m/s just before hitting the ground? 3 marks - a
b. how high would the cliff be instead, if the object is falling at 18 m/s, but the efficiency is 100%? 3 marks - a

1. runner b finishes a 50 m race in less time than runner a. explain why runner a may still be the more powerful runner using correct terminologies and formulae where applicable. 3 marks - c

Explanation:

Step1: Calculate work done

Work \(W = F\times d\), where \(F = 150\space N\) and \(d=5.0\space m\). So \(W=150\times5 = 750\space J\)

Step2: Use work - energy theorem

The work - energy theorem states that \(W=\Delta K=\frac{1}{2}m(v_f^{2}-v_i^{2})\)
We know \(m = 85\space kg\), \(v_i = 1.3\space m/s\) and \(W = 750\space J\)
Substitute the values into the formula: \(750=\frac{1}{2}\times85\times(v_f^{2}-(1.3)^{2})\)
First, simplify the right - hand side: \(750 = 42.5\times(v_f^{2}- 1.69)\)
Then, \(\frac{750}{42.5}=v_f^{2}-1.69\)
\(17.65 = v_f^{2}-1.69\)
\(v_f^{2}=17.65 + 1.69=19.34\)
\(v_f=\sqrt{19.34}\approx 4.4\space m/s\)

Answer:

The final velocity of the couch is approximately \(4.4\space m/s\)