how much work is required to lift a 98-N block of ice if
A) it is lifted a vertical distance of 5-m.?
B) you push the same block of ice up a 7-m long ramp using in acompare to the work required in b.?
C) How does the work required in A compare to the work required in B.?
D) Find the potential engery of both blocks of ice if they both end up at a height of 5-m.?
a. 490 j
To answer these questions, we can use the formula for work:
Work = Force * Distance * cos(θ)
where:
- Work is the amount of work done or energy transferred
- Force is the force applied
- Distance is the displacement
- θ is the angle between the applied force and the direction of displacement
Let's break down each question and calculate the work required:
A) To lift the 98-N block of ice vertically by 5 m, we can use the formula:
Work = Force * Distance * cos(θ)
In this case, θ = 0° because the force and displacement are in the same direction (vertical). The equation simplifies to:
Work = Force * Distance
So, Work = 98 N * 5 m = 490 J (Joules)
B) If we push the same block of ice up a 7-m long ramp, we need to consider that the force applied is acting at an angle. Assuming the angle of the ramp is 30°, we can now calculate the work using the formula:
Work = Force * Distance * cos(θ)
Work = 98 N * 7 m * cos(30°)
Work = 98 N * 7 m * (√3/2) ≈ 423.99 J (rounded to two decimal places)
C) To compare the work required in A and B, we can simply compare the values we calculated. The work done in A is 490 J, and the work done in B is approximately 423.99 J. Therefore, the work required in A is greater than the work required in B.
D) The potential energy of an object can be calculated using the formula:
Potential Energy = Mass * Gravity * Height
Since the mass of the ice block is not given, we can use the formula Mass = Force / Gravity:
Mass = 98 N / 9.8 m/s^2 = 10 kg
For both blocks of ice at a height of 5 m, the potential energy can be calculated:
Potential Energy = Mass * Gravity * Height
Potential Energy = 10 kg * 9.8 m/s^2 * 5 m = 490 J
Therefore, the potential energy of both blocks of ice at a height of 5 m is 490 Joules.