A girl pushes a load of mass 20kg to a distance of 10 metres in 5 seconds calculate (1) the work done (2) the energy used (3) the girl's power (a=g=10m/s square)
I assume no friction, so the thing is accelerating
F = m a
F = 20 a
a = F/20
distance = (1/2) a t^2
10 = .5 * a * 25
a = 20/25 = 4/5 = .8 m/s^2
so F = 20 a = 160 Newtons
(1) work = 160 * 10 = 1600 Joules
(2) that work is the enegy used
(3) power = energy/time = 1600/5 = 320 Watts
To calculate the work done, energy used, and the girl's power in pushing the load, we can use the following formulas:
(1) Work Done = Force x Distance
(2) Energy Used = Work Done
(3) Power = Work Done / Time
First, we need to find the force applied by the girl to push the load. The force can be calculated using Newton's second law:
Force = mass x acceleration
Given:
Mass (m) = 20 kg
Acceleration (a) = g = 10 m/s^2
Using Newton's second law, we can find the force:
Force = 20 kg x 10 m/s^2 = 200 N
Now, let's calculate each value step by step:
(1) Work Done = Force x Distance
Work Done = 200 N x 10 m = 2000 J (Joules)
(2) Energy Used = Work Done
Energy Used = 2000 J
(3) Power = Work Done / Time
Time = 5 s
Power = 2000 J / 5 s
Power = 400 W (Watts)
Therefore, the answers to the calculations are:
(1) The work done is 2000 J (joules).
(2) The energy used is also 2000 J (joules).
(3) The girl's power is 400 W (watts).
To calculate the work done, energy used, and the girl's power, we need to use the relevant formulas:
1. Work Done (W) = Force (F) × Displacement (d) × Cosine of the angle (θ) between the applied force and the direction of displacement.
2. Energy Used = Work Done
3. Power (P) = Work Done / Time (t)
Given:
Mass (m) = 20 kg
Distance (d) = 10 m
Time (t) = 5 s
Acceleration due to gravity (g) = 10 m/s²
Let's calculate each value step by step:
1. Work Done (W):
To find the work done, we need to calculate the force applied first.
Force (F) can be calculated using Newton's second law of motion:
Force (F) = Mass (m) × Acceleration (a)
Acceleration can be calculated using the formula:
Acceleration (a) = Force (F) / Mass (m)
Substituting the given values:
a = g = 10 m/s²
F = m × a = 20 kg × 10 m/s² = 200 N
Now, we can find the work done using the formula:
Work Done (W) = F × d × Cos(θ)
As no angle is given, we'll assume the angle to be 0 degrees (θ = 0).
Cos(0°) = 1
Substituting the values:
W = 200 N × 10 m × 1 = 2000 J (Joules)
Therefore, the work done is 2000 Joules (J).
2. Energy Used:
The energy used in this case is equivalent to the work done.
So, Energy Used = Work Done = 2000 J
Therefore, the energy used is 2000 Joules (J).
3. Power (P):
Power is defined as the rate at which work is done.
Using the formula:
Power (P) = Work Done (W) / Time (t)
Substituting the values:
P = 2000 J / 5 s = 400 W (Watts)
Therefore, the girl's power is 400 Watts (W).