Question

You and your bicycle have combined mass 80.0 kg. When you reach the base of a bridge, you are travelling along the road at 7.50 m/s. At the top of the bridge, you have climbed a vertical distance of 5.20 m and have slowed to 3.00 m/s. Ignore work done by friction and any inefficiency in the bike or your legs.
Part A
What is the total work done on you and your bicycle when you go from the base to the top of the bridge?

Part B
How much work have you done with the force you apply to the pedals?

Answer 1

We have that K.E and work done is

• $K.E=-1890J$
• $W=2186J$

From the Question we are told that

mass= 80.0 kg

Velocity= 7.50 m/s.

vertical distance of 5.20 m

Slowed to 3.00 m/s.

Generally the equation for Kinetic energy   is mathematically given as

$K.E=\frac{mv^2}{2}-\frac{mv^2}{2}\\\\K.E=\frac{80*3^2}{2}-\frac{80*7.5^2}{2}$

$K.E=-1890J$

B)

$P.E=mgh\\\\P.E=80*9.8*5.2\\\\P.E=4076$

Therefore

$W=4076-1890J$

$W=2186J$

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