A student eats a dinner containing 8.0 X 10^6 Joules of energy. He wishes to do an equivalent amount of work in a nearby gym by lifting 60 Kg object. How many times must he raise the object to expand this much energy? Assume that he raises it a distance of 2.0 metres each time?
work = force * distance = (60g * 2)n = 8*10^6
Solve for n, the number of reps.
60*2 =8*10*6
To determine how many times the student must raise the 60 kg object to expend 8.0 x 10^6 Joules of energy, we need to calculate the amount of work done with each lift and then divide the total energy by the work done per lift.
The work done (W) can be calculated using the formula:
W = m * g * d
Where:
W is the work done,
m is the mass (in kg) of the object being lifted,
g is the acceleration due to gravity (approximately 9.8 m/s^2),
d is the distance (in meters) the object is lifted.
Given that the mass of the object (m) is 60 kg and the distance lifted (d) is 2.0 meters, let's calculate the work done per lift:
W = 60 kg * 9.8 m/s^2 * 2.0 m
W = 1176 Joules
Now, we can determine the number of lifts required by dividing the total energy expended (8.0 x 10^6 Joules) by the work done per lift:
Number of lifts = Total energy / Work done per lift
Number of lifts = (8.0 x 10^6 Joules) / (1176 Joules)
To simplify the division, we need to convert 8.0 x 10^6 Joules to scientific notation:
8.0 x 10^6 Joules = 8.0 x 10^6 Joules
Now, let's divide:
Number of lifts = 8.0 x 10^6 Joules / 1176 Joules
To perform the division, we need to express both numbers with the same exponent:
Number of lifts = (8.0 x 10^6) / (1176 x 10^0)
Dividing the numbers:
Number of lifts ≈ 6802
Therefore, the student needs to raise the 60 kg object approximately 6802 times to expend 8.0 x 10^6 Joules of energy.