Question

Jon does 2000 J of work as he starts riding his bicycle from rest. Jon and the bicycle have a combined mass of 90 kg. a. What is the kinetic energy of Jon and the bike after he does the work? b. What is his velocity after he does the work?

Answer 1

Answer:

Part A: 2000J and Part B: 6.67 m/s

Explanation:

I will refer to Kinetic Energy as KE from this point on.

Part A:

Work and KE both have units of Joules because they are related. Work, which is a force acting through a distance, can be redefined as the change in KE like so: W = ΔKE = KE2 - KE1, where KE2 is the final KE and KE1 is the initial KE.

Jon starts from rest, meaning that he initally does not have any KE. Thus, if he does 2000 J of work starting from rest, KE2 = W + KE1 = 2000 J + 0 J = 2000J.

Part B:

Furthermore, since KE = 0.5mv^2, ΔKE = KE2 - KE1 = 0.5m(v2)^2 - 0.5m(v1)^2.

Thus, W = ΔKE = 0.5m(v2)^2 - 0.5m(v1)^2.

We can rewrite this equation to solve for v2: $v_{2} =\sqrt{\frac{2W}{m}+v_1^{2} }$.

Substituing W = 2000 J, m = 90 kg, and v1 = 0 m/s (since he starts from rest), we get that v2 = 6.67 m/s.

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