An 1100 kg car accelerates from rest to 90 km/h over a distance of 25 m. A) How much work is done? B) What is the average force applied through this distance?
Ghj
To find the answers to these questions, we need to use the formulas for work and force.
A) The work done can be calculated using the formula:
Work = Force * Distance * Cos(θ)
where θ is the angle between the direction of force and the displacement.
In this case, the car is accelerating in a straight line, so the angle between the force and displacement is 0 degrees. Therefore, Cos(θ) = 1.
The distance is given as 25 m, and we need to find the force.
B) The average force can be calculated using the formula:
Average Force = Change in Momentum / Time
The change in momentum can be calculated using the formula:
Change in Momentum = Mass * (Final Velocity - Initial Velocity)
Given that the car starts from rest, the initial velocity is 0 and the final velocity is 90 km/h, which needs to be converted to m/s.
Now, let's solve each question step by step:
A) Work Done:
Work = Force * Distance * Cos(θ)
In this case, θ = 0, so Cos(θ) = 1.
Work = Force * Distance
B) Average Force:
Change in Momentum = Mass * (Final Velocity - Initial Velocity)
To convert km/h to m/s, we need to divide by 3.6 (1 km/h = 1000 m / 3600 s = 1/3.6 m/s).
Change in Momentum = Mass * (Final Velocity - Initial Velocity)
Average Force = Change in Momentum / Time
Now, let's plug in the values:
Mass = 1100 kg
Distance = 25 m
Initial Velocity = 0 m/s
Final Velocity = (90 km/h) / (3.6 m/s) = 25 m/s
Now, let's calculate the answers:
A) Work Done:
Work = Force * Distance
= Force * 25 m
B) Average Force:
Change in Momentum = Mass * (Final Velocity - Initial Velocity)
= 1100 kg * (25 m/s - 0 m/s)
Average Force = (Change in Momentum) / Time
By solving these equations, we can find the answers to the questions.
force = work done / distance
Hey, let us see what you have done yourself.