A spider monkey (mass 4 kg) is frolicking through the jungle at a speed of 3.2 m/s. All of a sudden, a jaguar appears and tries to eat the monkey. The monkey begins to run frantically—now he has a speed of 13 m/s. How much work does the monkey do to increase its speed? Show your calculations.
Answer (1)
To find out how much work the monkey does to increase its speed, we will use the concept of kinetic energy. The work done by the monkey is equal to the change in its kinetic energy.
The formula for kinetic energy K E is given by:
K E = 2 1 m v 2
where:
m is the mass of the object (in kilograms), and
v is the velocity of the object (in meters per second).
First, calculate the initial kinetic energy when the monkey's speed is 3.2 m/s:
K E ini t ia l = 2 1 × 44 × ( 3.2 ) 2 K E ini t ia l = 2 1 × 44 × 10.24 K E ini t ia l = 224.64 Joules
Next, calculate the final kinetic energy when the monkey's speed is 13 m/s:
K E f ina l = 2 1 × 44 × ( 13 ) 2 K E f ina l = 2 1 × 44 × 169 K E f ina l = 3718 Joules
The work done W is the change in kinetic energy:
W = K E f ina l − K E ini t ia l W = 3718 − 224.64 W = 3493.36 Joules
Therefore, the monkey does 3493.36 Joules of work to increase its speed.
